Finding Moonshine

Maths in the City

2011-06-17T21:40:00.002+01:00

I have started an exciting new project called Maths in the City.
Maths in the City aims to highlight the fundamental role that maths plays in society by viewing the urban environment in a mathematical way. Conventionally, the urban environment is used to explore local history, architecture and culture - but it can also provide us with adventures in mathematics.
Maths in the City is an EPSRC funded public engagement project led by myself. The project is produced and managed by the Technology–Assisted Lifelong Learning (TALL) unit of the University of Oxford Department for Continuing Education.
We’d like to hear your mathematical stories of the city no matter who you are — young, old, students, teachers, researchers, member of the public, journalists... Anyone is welcome to shine a mathematical spotlight on their city!
We are also happy for you to either create a Site individually or in a group. If you and your friends or your family have an idea you’d like to work on together, or if you’re a teacher and would like your class to produce a Site, then we’d love to hear from you.
Go to www.mathsinthecity.com to check out examples of sites and to add your own.
To launch the site we ran a competition to find examples of maths in the cities around the world. Five winners were chosen that came to Oxford to celebrate. As part of their prize I constructed some special symmetrical objects which I named after the winners.

The Edward Mak Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 1] Corresponds to an elliptic curve of conductor 365504323038715. Maths in the City site: Burj Khalifa, Dubai, United Arab Emirates.

The Samantha Keung Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 2] Corresponds to an elliptic curve of conductor 365537511174131. Maths in the City site: Most stable shape – triangle.

The Nick Simmonds Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 3] Corresponds to an elliptic curve of conductor 365570706018123. Maths in the City site: Route Planning – the perfect walking tour.

The Liz Meenan Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 4] Corresponds to an elliptic curve of conductor 365603907571075. Maths in the City site: The mathematics of tiling.

The María Ángeles Gilsanz Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 5] Corresponds to an elliptic curve of conductor 365637115833371. Maths in the City site: Wallpaper groups, Segovia.

Competition entries were so strong that we decided that five other entries deserved to be recognised as highly commended. These are:

Hong Kong Space Museum (East Wing) by Cassandra Lee
The Gateway Arch – A Trigonometric delight by Ronan Mehigan
The Golden Ratio in Manchester by Sam Watson and Nicky Watmore
The Wobbling Bridge by Thomas Woolley
Topology on the Metro by Christian Perfect

Objects for the Future on the BBC World Tonight

2011-01-02T16:54:00.003Z

Over the Christmas period the BBC World Tonight programme did a series of features where people proposed an object for the future. Listen here if you want to hear my proposal: a conscious-ometer.

4D Godless Christmas festivities

2010-12-23T16:36:00.008Z

9 Lessons and Carols for Godless People is a show celebrating science at this festive time of year. In its third year, this was my first time performing alongside people like Simon Singh, Robin Ince, Dobby from Peep Show and Chris Addison from In The Thick of It and many other amazing performers.

My spot looked at some of the fun maths in the festivities at this time of year. Take the Jewish festival of Chanucka for example. Already a holiday I love because you have to work modulo 19 to work out when it takes place. Celebrated over 8 days, one of the rituals involves lighting candles on each day. On the first day you light 2 candles, second day 3 candles...until on the last day you light 9 candles. The question every nerdy Jewish kid gets asked: how many candles do you need to celebrate Chanucka?

You could just add up the numbers from 2 to 9 but there is a cleverer way to do this calculation. Look at the triangle of candles you are trying to count:

C C
C C C
C C C C
C C C C C
C C C C C C
C C C C C C C
C C C C C C C C
C C C C C C C C C

If I take another copy of the triangle and invert it then I can put the two triangles together to make an 11 x 8 rectangle which has 88 candles in. So one triangle has 44 candles in it.

Not to be outdone, Christmas has its own mathematical problem. While Chanucka involves 2D triangles, the Christmas problem goes one dimension up and uses 3D pyramids. The problem relates to the famous Christmas song: The Twelve Days of Christmas.

On the first day of Christmas, my true love gave to me...A Partridge in a Pear Tree.
On the second day of Christmas, my true love gave to me...2 Turtle Doves And a Partridge in a Pear Tree.
On the third day of Christmas, my true love gave to me...3 French Hens, 2 Turtle Doves And a Partridge in a Pear Tree.
...and so on, until the last verse:
On the twelfth day of Christmas, my true love gave to me...
12 Drummers Drumming
11 Pipers Piping
10 Lords-a-Leaping
9 Ladies Dancing
8 Maids-a-Milking
7 Swans-a-Swimming
6 Geese-a-Laying
5 Gold Rings
4 Colly Birds
3 French Hens
2 Turtle Doves
And a Partridge in a Pear Tree.

So the maths problem: How many presents did I get from my true love over the twelve days of Christmas? Calculating the number of presents on each day is the same sort of problem as counting the candles at Chanucka. For example on the 12th day I get 12+11+10+...+3+2+1 presents. But how many do I get over the whole of Christmas?

This time you need to stack all the triangles in layers so that you build up a pyramid. On the top is the first Partridge in the Pear Tree. On the second layer: a Partridge and two turtle doves. Here is a picture of 4 layers of the pyramid which I made for the performance.

My arts and crafts skills were pushed to the limits. It took me ages making those little boxes so I gave up after 4 layers. That's why I chose maths...you don't have to get your hands dirty with all that UHU glue.

But how can I calculate quickly the number of boxes I would have had to have made to do all twelve layers. Well it turns out that if you take 6 of these pyramids you can rearrange them all to make a rectangular box with dimensions 12x13x14. So the total number of boxes in one pyramid is 12x13x14/6=364. So one present for every day of the year except Christmas!

If Chanucka is a two dimensional festival (triangles), Christmas is a three dimensional festival (pyrmaids) then I thought I should invent a 4D festival to celebrate at the 9 Lessons and Carols for Godless People.
Here is the formula for Chanucka: \sum_{i=2}^{9} i
The formula for Christmas is a double summation: \sum_{j=1}^{12} \sum_{i=1}^{j} i
So the formula for a 4D Godless festivity is a triple summation: \sum_{k=1}^{N} \sum_{j=1}^{k} \sum_{i=1}^{j} i
where N is the number of days in our 4D Godless festival.
I've been getting people to help me via my twitter account (@MarcusduSautoy) to build up this 4D celebration of science. It is also based on a song...

On the first day of Godless Christmas my geek friend sent to me...a boson in the LHC.
On the second day of Godless Christmas my geek friend sent to me... 2 twin primes and a boson in the LHC ... (but to make it a 4D puzzle we have to repeat the previous day so you also get another)... and a boson in the LHC.
On the third day of Godless Christmas my geek friend sent to me... 3 laws of motion, 2 twin primes and a boson in the LHC ... (and to get it 4D we repeat all the presents from the previous day so)...2 twin primes and a boson in the LHC ... and a boson in the LHC.

So here are the suggestions via twitter for each additional present.

4 pairing bases
5 Platonic Solids
6 Quarks a spinning
7 base units Measuring
8 bits a byte-ing
9 Heegner numbers prime generating
10 Rorschach Inkblots diagnosing
11 dimensions a-stringing
12 astronauts moon-walking
13 Neptune moons an-orbiting

There has also been some debate about how many days the 4D Godless festival should have:
42 was suggested during one show - a good geeky number.
Infinite was suggested in another show - A very long festival ... especially towards the end.
Someone suggested via twitter 28 since it is a perfect number. Quite like that one.
I've gone for 13 at the moment as that proves I'm not superstitious.

But how many presents would we get from our geeky friend? Well that requires building shapes in 4 dimensions. Something that is beyond my arts and crafts skills.

The Beauty of Diagrams

2010-11-17T09:58:00.001Z

BBC 4 (6 x 30 mins)

Transmitting weekly on BBC 4 at 20.30 and 22.00 from Thur 18th November 2010, BBC HD at 23.35

Why do complex scientific theories and equations often only make sense when portrayed in pictures? How have scientific diagrams, drawings, sketches and graphs revolutionised our understanding of science?

One of the most pervasive myths about science is that it doesn’t require art. Science, we’re told, is about the logic of numbers, hard cold facts and the recording of experiences purposefully stripped of emotion. Nothing could be further from the truth.

In this new six part series I will illustrate and explore that far from being a reluctant visual medium, science is actually at the forefront of the design and creation of a number of iconic visual diagrams. From Newton’s Prism to Da Vinci’s Vitruvian Man to Watson and Crick’s extraordinary diagram of the Double Helix diagrams have successfully shaped and defined our understanding of complex scientific theories and over time have become accepted in society as astonishing illustrations in their own right. In this new series I will navigate viewers through the numerous diagrams, graphs, sketches and designs that have revolutionised our understanding of the world around us.

Twitter Fibs

2010-07-11T10:22:00.002+01:00

I'm speaking at the Ledbury Poetry Festival today about the connections between maths and poetry.
Among other things, I am going to be talking about Fibs: a peom with 1,1,2,3,5,8,13 syllables per line. The numbers follow the famous Fibonacci sequence first discovered, not by Fibonacci in fact, but by Indian poets counting the number of rhythms possible with long and short beats.
They were recently championed by Gregory Pincus who created this Fib to describe the form:
One , Small, Precise, Poetic, Spiraling mixture: Math plus poetry yields the Fib.

I set a challenge on my twitter @marcusdusautoy for people to send me Fibs and I would choose the best to present during my talk. The one I chose is the following by @benbush
Tweet/Tweet/Marcus/Here's my fib/(An unwise ad lib?)/Wait: fib? On Twitter? I'm confused/How many of my 140 have I used?

Here are a selection of the other great twitter fibs I got sent. Thanks everyone for all your efforts. Really enjoyed reading them.

From @angelt42
Shell/Snow/Spiral/Sunflower/Natural music/Beautiful living and growing/Mathematics labels the natural growth of life

From @declankh
one/ two/ yahoo/ lets make three/ now five is harder/ 8 is slightly contrived i think/ bugger, 13 doesnt scan very elegantly

From @bongerman
Broad/ Bean./ You're green./ And starchy./ I caress your skin;/ Helps keep my finger on the pulse/And - randomly - engenders dreams of Fibonacci.

From @Col_in_UK
Let, Me, Twitter, Youmyday, Firstofallbreakfast, Thenlunch,dinner&suppertoo, Finallyit'stimeforbed,justonemoretorestmyhead.

From @CtCw_BIGTOE
Black/ then/ White are/ all I see/ in my infancy/ Red & Yellow then came to be/ reaching out to me lets me see there is much in me

From @pjbryant
In
Time
When you
Remember
Things will seem quite clear
Home - the place where you can return
Is the place where you can relax and ease all your fear

From @daniellekurant (and thanks for the plug for my new book)
I/ love/ numbers/ just as a/ fish out of water/ loves to be cast into the sea/ what sweet freedom is found in these Number Mysteries

From @floppymonkey a mini Fib
Yes We Have some Bananas!

From @mrgrasshead the first Fib to be written by a potplant
I/ Love/ Water/ But also/ Pure Mathematics./ Hydrodynamics is my thing!

From @dudegalea who tweeted after sending me half a dozen fibs: ""What A Rotten Thing to do! Saturday morning Wasted writing silly poems!
Shall/ I/ Compare/ Math poems/ To Shakespeare's sonnets?/ Thou art more geeky, and formal!

From @JaneLMcGrath
Maths/ And/ Poems/ Do not mix/ They say but you lure/ The logical mind to capture/ English and confine it into constricted beauty

From @Kateviola (who worried about how many syllables Ledbury has)
O, Hi, Marcus, du Sautoy, Ledbury Festival, Innovative Fibonaccist, Combining words & numbers in true Renaissance style.

From @christianp (who wanted the first line as "Er, Dork, Author" but felt that was a bit disrespectful then noticed he'd missed the number 3. But I like the message so included it here:
hey! you! marcus! we have got to talk / your convoluted verse structure / tends to prose as the length of the poem increases

Symmetry4Charity

2010-04-09T13:06:00.030+01:00

I am trying to help Common Hope get a permanent presence on the UK Global Giving website which will allow UK donors to the charity to benefit from Gift Aid where tax is added to the donation.

Common Hope need to raise £1000 from 50 unique donors by the end of April. Common Hope is an educational charity supporting and empowering children and their families in Guatemala.

To help them reach their goal I have set up a Symmetry4Charity project to name symmetrical objects after people who donate to the site.

In exchange for a minimum donation of £10 to the charity, I will create and name a symmetrical object for you. Donations can be made at my fund-raising site. A clue to why this is my charity of choice can be found in Chapter 12: July of Finding Moonshine.

If you would like to give the group of symmetries as a birthday present or to celebrate an anniversary then email me details of the significant date and I will weave the date into the construction of the symmetry group. Please email me to alert me to the fact that you have left a donation. dusautoy@maths.ox.ac.uk

Stop Press Thanks to all those who donated, Common Hope achieved their target on 24th April and now have a permanent place on the UK Global Giving Website.

Here is a list of the groups created so far that have helped change the lives of children in Guatemala.

The Tom Critchlow Group Set [C[1], C[2], C[3], C[4]]=[31,0,8,1983] Corresponds to an elliptic curve of conductor 3489405992393.

The Aoife McLysaght Group Set [C[1], C[2], C[3], C[4]]=[1976,0,2004,2006] Corresponds to an elliptic curve of conductor 60613926650500572088192.

The Carol Jones Group Set [C[1], C[2], C[3], C[4]]=[0,0,0,2610] Corresponds to an elliptic curve of conductor 48441600.

The Raffaele Malanga Group Set [C[1], C[2], C[3], C[4]]=[2087 0 2089 2099] Corresponds to an elliptic curve of conductor 10860662998996528897934.

The Antonio Cangiano Group Set [C[1], C[2], C[3], C[4]]=[2111 0 2113 2129] Corresponds to an elliptic curve of conductor 188766474306629521300694.

The Adam Tonks Group Set [C[1], C[2], C[3], C[4]]=[2131 0 2137 2141] Corresponds to an elliptic curve of conductor 201253543919366765652458.

The Tim Goldberg Group Set [C[1], C[2], C[3], C[4]]=[14 0 1 2010] Corresponds to an elliptic curve of conductor 368874666643. Named by Michael O'Connor for Tim's birthday.

The Dawn Denyer Group Set [C[1], C[2], C[3], C[4]]=[28 0 1 1974] Corresponds to an elliptic curve of conductor 1926277419109.

The Allen Edwards Group Set [C[1], C[2], C[3], C[4]]=[2143 0 2153 2161] Corresponds to an elliptic curve of conductor 16190845034753857655278.

The Christopher Rath Group Set [C[1], C[2], C[3], C[4]]=[2179 0 2203 2207] Corresponds to an elliptic curve of conductor 119528325153563319394762.

The Jennifer Mallery Group Set [C[1], C[2], C[3], C[4]]=[23 0 1 4] Corresponds to an elliptic curve of conductor 1883254.

The Mr Grasshead Group Set [C[1], C[2], C[3], C[4]]=[15 0 7 2002] Corresponds to an elliptic curve of conductor 1740062254. Named by Pat Galea to celebrate Mr Grasshead's repotting.

The Joyce Hynds Group Set [C[1], C[2], C[3], C[4]]=[6 0 8 1943] Corresponds to an elliptic curve of conductor 120494204588. Named by Matt Jensen in memory of his mother-in-law.

The Harris Philpott Wong Lau Mak Leung Oswald Group Set [C[1], C[2], C[3], C[4]]=[15 0 6 2010] Corresponds to an elliptic curve of conductor 14226022458. Named by Chris Oswald for his Upper Sixth Further Maths class at Campbell College, Belfast.

The Keith Marshall Group Set [C[1], C[2], C[3], C[4]]=[2213 2221 0 2237] Corresponds to an elliptic curve of conductor 53847539164253317.

The Joyce Brown Group Set [C[1], C[2], C[3], C[4]]=[440 415 5040 1958] Corresponds to an elliptic curve of conductor 112390621233323209184. Interesting choice of numbers: "440 (I play the cello and that is standard pitch), 415 (I play the viol and that's Baroque pitch), and 5040 (From my bellringing - 7!, the full extent of all the permutations of 7 bells, and the minimum required for a peal) (I do a masterclass talk on the maths of bellringing); 1958 (Year I was born)."

The Haggis Group Set [C[1], C[2], C[3], C[4]]=[242 4 228 43112608] Corresponds to an elliptic curve of conductor 6500621248808920956132. Named by Julia Collins for Haggis, the mathematical sheep. Check out Haggis's blog at http://haggisthesheep.wordpress.com/

The Judith Cantrell Group Set [C[1], C[2], C[3], C[4]]=[2239 0 2243 2251] Corresponds to an elliptic curve of conductor 71088728997276867992782.

The Frances Allsop Group Set [C[1], C[2], C[3], C[4]]=[24, 0, 9, 1939] Corresponds to an elliptic curve of conductor 839108955077. Named by Richard Allsop.

The Gwyn Bellamy Group Set [C[1], C[2], C[3], C[4]]=[0 0 0 1983] Corresponds to an elliptic curve of conductor 125833248.

The Dave Phillips Group Set [C[1], C[2], C[3], C[4]]=[30 0 5 1945] Corresponds to an elliptic curve of conductor 554774344225. Named by Lucy and Rosana for Dave's birthday.

The Beatrice and Henry McBain Group Set [C[1], C[2], C[3], C[4]]=[20, 3, 31, 7] Corresponds to an elliptic curve of conductor 451166557. Named by James McBain.

The Maria Beljajev Group Set [C[1], C[2], C[3], C[4]]=[2267 0 2269 2273] Corresponds to an elliptic curve of conductor 309080878106951538630038.

The bykimbo Group Set [C[1], C[2], C[3], C[4]]=[4 0 3 1824] Corresponds to an elliptic curve of conductor 43484568627. To mark the date the RNLI was founded.

The Thomas Dunham Group Set [C[1], C[2], C[3], C[4]]=[2281 0 2287 2293] Corresponds to an elliptic curve of conductor 64819437055680114154570.

The Peter and Laurie Komorowski Group Set [C[1], C[2], C[3], C[4]]=[7 5 3 2] Corresponds to an elliptic curve of conductor 17299. Named by Isaac Abdullah.

The Neil Davies Group Set [C[1], C[2], C[3], C[4]]=[2297 0 2309 2311] Corresponds to an elliptic curve of conductor 170755749787700804711146.

The James Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2333 0 2339 2341] Corresponds to an elliptic curve of conductor 378769980499583140602578.

The Kiss Chops Hunter Group Set [C[1], C[2], C[3], C[4]]=[13 0 1 1968] Corresponds to an elliptic curve of conductor 381310485302. Named by Neil Brewitt for his girlfriend "The geekiest present ever."

The Nancy Whitney Group Set [C[1], C[2], C[3], C[4]]=[2371 0 2377 2381] Corresponds to an elliptic curve of conductor 424434490670520944020538.

The Niamh and Owain Elsey Group Set [C[1], C[2], C[3], C[4]]=[7, 8, 13, 26] Corresponds to an elliptic curve of conductor 349310. Named by David Elsey for his children

The Hafsa Farhana Group Set [C[1], C[2], C[3], C[4]]=[2383 0 2389 2393] Corresponds to an elliptic curve of conductor 439684906279538095624430.

The Colin Jenkins Group Set [C[1], C[2], C[3], C[4]]=[2399 0 2411 2417] Corresponds to an elliptic curve of conductor 463431595209250290763706.

The Margaret Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2423 0 2437 2441] Corresponds to an elliptic curve of conductor 497218761743202211331006.

The Sean Goddard Group Set [C[1], C[2], C[3], C[4]]=[11 0 7 1997] Corresponds to an elliptic curve of conductor 478893859786. Named by his mother Karen Goddard. Sean's team recently won the UKMT Junior maths challenge in the Cumbria regional finals. Congratulations.

The Nigel Metheringham Group Set [C[1], C[2], C[3], C[4]]=[2447 0 2459 2467] Corresponds to an elliptic curve of conductor 8322830442423051970094.

The Laura Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2473 0 2477 2503] Corresponds to an elliptic curve of conductor 286963521763982408250722.

The Charlotte Campbell Group Set [C[1], C[2], C[3], C[4]]=[2521 0 2531 2539] Corresponds to an elliptic curve of conductor 40930035288396217940662. Named by her mother Christine Campbell to inspire her daughter to become a mathematician.

The Joanne Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2543 0 2549 2551] Corresponds to an elliptic curve of conductor 346036497122670226830634.

The Jenny Pearson Group Set [C[1], C[2], C[3], C[4]]=[2557 0 2579 2591] Corresponds to an elliptic curve of conductor 365494968738038567029426. Named by her husband Andrew.

The James Crick Group Set [C[1], C[2], C[3], C[4]]=[2593 0 2609 2617] Corresponds to an elliptic curve of conductor 800984866525168371236674.

The Pringle Group Set [C[1], C[2], C[3], C[4]]=[2 12 17 25] Corresponds to an elliptic curve of conductor 1024603.

The Patrick Joseph O'Hara Group Set [C[1], C[2], C[3], C[4]]=[23 0 5 1930] Corresponds to an elliptic curve of conductor 120500736670. Named by Shaun for his father's 80th birthday.

The Michaela Schmid Group Set [C[1], C[2], C[3], C[4]]=[2621 0 2633 2647] Corresponds to an elliptic curve of conductor 431360159413383233262178.

The Louise Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2657 0 2659 2663] Corresponds to an elliptic curve of conductor 469183075585812482668954.

The Andrew Burbanks Group Set [C[1], C[2], C[3], C[4]]=[2671 0 2677 2683] Corresponds to an elliptic curve of conductor 122143989488324550049210.

The Graham Elliott Group Set [C[1], C[2], C[3], C[4]]=[2687 0 2689 2693] Corresponds to an elliptic curve of conductor 1015048834019033780426498. Named by Andrew Burbanks for the retirement of his colleague in the maths department at the University of Portsmouth.

The Euclidian Boxes Group Set [C[1], C[2], C[3], C[4]]=[325 0 265 5] Corresponds to an elliptic curve of conductor 1088438966488150. Named by John Edwards after his xbox gamertag and twitter id.

The BCME2010 Group Set [C[1], C[2], C[3], C[4]]=[6 0 4 2010] Corresponds to an elliptic curve of conductor 261881545824. I donated the fee that I was due for the talk I gave to BCME 2010 to Common Hope in order to help them achieve their first place status on the fund-raising challenge.

The Louise Egerton Group Set [C[1], C[2], C[3], C[4]]=[2699 0 2707 2711] Corresponds to an elliptic curve of conductor 525923505004979530688566.

The Richard Bunch Group Set [C[1], C[2], C[3], C[4]]=[2713 0 2719 2729] Corresponds to an elliptic curve of conductor 1091390907796059056481182.

The Nandin G. Rau Group Set [C[1], C[2], C[3], C[4]]=[5 0 5 2010] Corresponds to an elliptic curve of conductor 6586199050. Named by James B. Glattfelder.

The Leon P. Grothe Group Set [C[1], C[2], C[3], C[4]]=[8 0 8 2005] Corresponds to an elliptic curve of conductor 523803243328. Named by James B. Glattfelder.

The Adam Timothy Jackson Group Set [C[1], C[2], C[3], C[4]]=[2731 0 2741 2749] Corresponds to an elliptic curve of conductor 1145536771536211777040122. Named by Anne Jackson.

The Daniel Hagon Group Set [C[1], C[2], C[3], C[4]]=[2753 0 2767 2777] Corresponds to an elliptic curve of conductor 1215991556499890529439214.

The Mara Lytrokapi Group Set [C[1], C[2], C[3], C[4]]=[2789 0 2791 2797] Corresponds to an elliptic curve of conductor 1318270795656516690423226. Named by Leptourgos Pantelis for his girlfriend

The Polly Sinnett-Jones Group Set [C[1], C[2], C[3], C[4]]=[4 0 2 1981] Corresponds to an elliptic curve of conductor 499555204208. Named by John Shimwell for his daughter's maths teacher.

The John Reynolds Group Set [C[1], C[2], C[3], C[4]]=[2801 0 2803 2819] Corresponds to an elliptic curve of conductor 340825568103087059408246.

The Marcus Tomlinson Group Set [C[1], C[2], C[3], C[4]]=[24 0 2 2002] Corresponds to an elliptic curve of conductor 414748597288. Marcus came and interviewed me as part of the NCTEM Special Leaders Award for STEM.

The Senhenn Lewis Group Set [C[1], C[2], C[3], C[4]]=[424, 1109, 787, 1110] Corresponds to an elliptic curve of conductor 10656159592614961931. Created in memory of Alexander Lewis's grandfather.

The Simon Baines-Norton Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 12, 1971] Corresponds to an elliptic curve of conductor 13734429036. From Jacquelyn Arnold for her partner's birthday.

The Joseph Daly Group Set [C[1], C[2], C[3], C[4]]=[2833 0 2837 2843] Corresponds to an elliptic curve of conductor 368225749767160780343246. From his Mum to help distract him from a very painful fractured arm.

The Susan Wonnacott Group Set [C[1], C[2], C[3], C[4]]=[15 0 12 2010] Corresponds to an elliptic curve of conductor 61438942062. To remember my visit to Bath to receive an honorary DSc.

The Laura Evison Group Set [C[1], C[2], C[3], C[4]]=[2851, 0, 2857, 2861] Corresponds to an elliptic curve of conductor 1540697762342693708321498.

The Reverend Jay Ridley's Retirement Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 1, 2011] Corresponds to an elliptic curve of conductor 2792409422309. Named by Mark Ridley for his Dad's retirement.

The Andy Green Group Set [C[1], C[2], C[3], C[4]]=[763, 0, 035, 0] Corresponds to an elliptic curve of conductor 157093058. Named by Marcus Tomlinson to mark Andy Green's land speed record of 763.035 mph.

The Leonard Marson Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 4, 1981] Corresponds to an elliptic curve of conductor 501755813227. Named by Susan Mulligan in memory of her father "who loved maths and taught me to be curious".

The Jessica Williams Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 9, 1995] Corresponds to an elliptic curve of conductor
504655734. From a maths loving family to their daughter for scoring 100% on her GCSE maths and wishing her luck as she embarks on A level maths.

The Johan Nordin Group Set [C[1], C[2], C[3], C[4]]=[2879, 0, 2887, 2897] Corresponds to an elliptic curve of conductor 1655404146508213187596826. A symmetrical object in hyperspace to adorn your new apartment from Torbjörn Jansson.

The Ebtisam Hatem Group Set [C[1], C[2], C[3], C[4]]=[2903, 0, 2909, 2917] Corresponds to an elliptic curve of conductor 1750705875861273269012114. From Torbjörn Jansson to celebrate solving "Ett litet problem".

The Claire Corner Group Set [C[1], C[2], C[3], C[4]]=[28, 0, 5, 2000] Corresponds to an elliptic curve of conductor
7504706935. From Marcus Tomlinson for Mrs Claire Corner as a thank you for being such a wonderfully kind and inspiring teacher.

The Charlotte Macro Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 8, 1984] Corresponds to an elliptic curve of conductor
3096766. From Marcus Tomlinson for Miss Charlotte Macro for all her really kind help with maths and chess.

The Louise Springer Group Set [C[1], C[2], C[3], C[4]]=[6, 0, 7, 1990] Corresponds to an elliptic curve of conductor
515190151459. From Djamschid Safi to celebrate Louise Springer's birthday.

The Lamis Group Set [C[1], C[2], C[3], C[4]]=[2927, 0, 2939, 2953] Corresponds to an elliptic curve of conductor
1865831301990171792354578. A gift from Torbjörn Jansson to Lamis, the Norwegian National Council of Teachers of Mathematics.

The Arthur Group Set [C[1], C[2], C[3], C[4]]=[16, 0, 7, 2011] Corresponds to an elliptic curve of conductor
284936059387. Bought live on air on BBC Radio 4's Loose Ends by Arthur Smith, Unoffical Mayor of Balham.

The Sonja Bartholomew Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 8, 1973] Corresponds to an elliptic curve of conductor
265534721713. From Alex Woodcraft for his girlfriend who is a maths teacher and maths geek.

The Paul Rispin Group Set [C[1], C[2], C[3], C[4]]=[23, 0, 4, 1970] Corresponds to an elliptic curve of conductor
306336944158. From Colleen Usher for her other half.

The Bromley High School Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 1883, 2011] Corresponds to an elliptic curve of conductor
339962077636651. A gift from maths teacher Jo Munday to the school.

The Mitchell Woodman Group Set [C[1], C[2], C[3], C[4]]=[2957, 0, 2963, 2969] Corresponds to an elliptic curve of conductor
1990173394038556429897022. A prize from Mel Curran for excellence in mathematics.

The Supermole Group Set [C[1], C[2], C[3], C[4]]=[24, 0, 7, 1981] Corresponds to an elliptic curve of conductor
121416506771. Named by Joe Malone for his brother's birthday.

The Nik Sargent Group Set [C[1], C[2], C[3], C[4]]=[2971, 0, 2999, 3001] Corresponds to an elliptic curve of conductor
2084720622014853093541714.

The Helen Kent Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 10, 1976] Corresponds to an elliptic curve of conductor
66239468098. Named by Dan Kent for his wife.

The Adrian Brasnett Group Set [C[1], C[2], C[3], C[4]]=[73, 0, 42, 2011] Corresponds to an elliptic curve of conductor
287692484729511. Named by Chris Brasnett for his Dad.

The StevenBradleyofLangleyPark Group Set [C[1], C[2], C[3], C[4]]=[1, 0, 8, 1970] Corresponds to an elliptic curve of conductor
246142199510. Named by Jen for her brother's birthday.

The J.C.P. Miller Group Set [C[1], C[2], C[3], C[4]]=[3011, 0, 3019, 3023] Corresponds to an elliptic curve of conductor
1130088249101822428698802. Named by Alison Smith and her family to remember their father's love of maths.

The Paul Parker Group Set [C[1], C[2], C[3], C[4]]=[27, 0, 7, 1975] Corresponds to an elliptic curve of conductor
852701983546. Named by Benjamin Pring.

The Vincent Murphy Group Set [C[1], C[2], C[3], C[4]]=[15, 23, 8, 1969] Corresponds to an elliptic curve of conductor
120668102111. Named by Michaela Murphy for her autodidactic husband on his 42nd birthday.

The Rodney Jagelman Group Set [C[1], C[2], C[3], C[4]]=[15, 0, 8, 1951] Corresponds to an elliptic curve of conductor
315422032951. Named by Rupert Jagelman for his father's 60th birthday.

The Penelope Garwood Group Set [C[1], C[2], C[3], C[4]]=[6, 0, 9, 2001] Corresponds to an elliptic curve of conductor
176123656377. Named by Adrian and Helen Garwood for their daughter's birthday.

The Eleanor Garwood Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 1, 2003] Corresponds to an elliptic curve of conductor
128784499418. Named by Adrian and Helen Garwood for their daughter's birthday.

The Michelle Doggett Group Set [C[1], C[2], C[3], C[4]]=[4, 0, 10, 2011] Corresponds to an elliptic curve of conductor
133766205052. Named by Spencer Doggett for his wife's birthday.

The Alasdair Hunter Group Set [C[1], C[2], C[3], C[4]]=[3037, 0, 3041, 3049] Corresponds to an elliptic curve of conductor
2397079763494449095534242. Named by Su Knight for her boyfriend.

The Peter Baxendall Group Set [C[1], C[2], C[3], C[4]]=[3061, 0, 3067, 3079] Corresponds to an elliptic curve of conductor
1269675294767721689908126. Named by Su Knight for her tutor at the OU.

The Charles Rule Group Set [C[1], C[2], C[3], C[4]]=[3083, 0, 3089, 3109] Corresponds to an elliptic curve of conductor
2676620509058079475578242. Named by Abie Cohen.

The Magda Nilges Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 1, 1927] Corresponds to an elliptic curve of conductor
203604256438. Named by Guido Stemme to celebrate his mother-in-law's 85th birthday.

The Secret You: Horizon BBC2

2009-10-19T12:05:00.004+01:00

Horizon: THE SECRET YOU

BBC2 Tuesday 20 October 2009 9pm

With the help of a hammer wielding scientist, Jennifer Aniston and a general anaesthetic Prof Marcus de Sautoy leaves the certainty of numbers behind and goes in search of answers to one of science’s greatest mysteries: how do we know who we are? It’s a simple question, but one science finds difficult to answer. The feelings and thoughts that make us ‘us’ and make us self aware are easy to experience. But the brain processes that give rise to them are difficult to explain and understanding them is one of the great challenges faced by scientists.

To find out what progress they are making Marcus becomes a human guinea-pig in a series of mind probing experiments. He begins by asking when our self awareness emerges and witnesses a cunning test that convincingly reveals a child’s sense of self before they are even capable of talking about what they are feeling. The experiment begs a question: are we alone in the world in being aware of ourselves? He meets Professor Gordon Gallup, a pioneer of animal psychology to find out.

But to find out how we become self aware, Marcus needs to delve into the inner machinations of the human brain. He starts of by witnessing a brain dissection, but not before he has the sobering experience of holding a human brain in his hands.

Seeing the dissected brain, he wonders when our consciousness disappears and whether answering this question might explain who he is. So Marcus volunteers for a cutting edge medical experiment that will rob him of his sense of self. At the University of Cambridge Wolfson Brain Imaging Centre he undergoes anaesthesia while having his brain scanned. He begins to home in on the areas of the brain that make him who he is.

Marcus’ work as a lab-rat continues in Sweden’s Karolinska Institute. Thanks to an ingenious set of spectacles, Marcus is subjected to a disorientating out of body experience, which serves to illustrate how a sense of self is a trick of the mind.

Marcus’s journey continues to America where he meets Professor Christof Koch of the California Institute of Technolgy. Christof is looking for evidence of consciousness in one of the smallest units of the brain: the individual neuron. He has made some surprising discoveries, helped by celebrities Jennifer Anniston and Halle Berry.

By the time Marcus reaches the University of Wisconsin he is getting closer to an answer to his question. He takes part in an un-nerving experiment featuring transcranial magnetic stimulation – the rapid discharge of electric shocks to a specific region of the brain. Measuring how these shocks travel through the brain’s labyrinthine connections when volunteers are awake and asleep has allowed scientists to demonstrate how the interconnectivity of the brain gives rise to consciousness.

The last experiment Marcus takes part in is perhaps the most perturbing. Keen to find out how taking a choice might reveal the secrets of his inner self, Marcus wants to discover the provenance of his decisions. He takes part in a simple experiment overseen by Professor John-Dylan Haynes at the Bernstein Centre for Computational Neuroscience in Berlin. Marcus is shocked to learn that by studying his unconscious brain Professor Haynes is able to accurately predict Marcus’ decisions and that it is his unconscious brain that presides over his conscious mind.

Marcus concludes the film with a fuller understanding of the state of brain science, but also a sense of how much remains to be revealed. To help the process on its way he commits to one final experiment – one that will take place after his death – and bequeaths his brain to science.

Bonus feature: Hole in the hand

Also check out an article on BBC News Online

The Times Cheltenham Literature Festival

2009-10-12T07:28:00.002+01:00

I will be appearing at the Times Cheltenham Literature Festival on Friday 16 October 2009 at 10:00 am at the Town Hall talking about Finding Moonshine.
Book online.

Simetria

2009-10-11T19:47:00.003+01:00

The Spanish edition of Finding Moonshine was published this week by Acantilado.
I was in Spain this week promoting the book. I gave a talk in Madrid at the prestigious Residencia de Estudiantes, home to Dali, Lorca and Bunuel. Other people who have lectured there include Albert Einstein, Paul Valéry, Marie Curie, Igor Stravinsky, John M. Keynes, Alexander Calder, Walter Gropius, Henri Bergson and Le Corbusier.
I also gave a talk in Barcelona at the CosmaCaixa museum. It is a fantastic science museum and I thoroughly recommend it to anyone visiting Barcelona.

Here are some reviews that have appeared in Spain:

El Pais: La Alhambra es un microcosmos de simetrías
Agencia EFE: El científico Marcus Du Sautoy dice que "la simetría es un lenguaje fundamental"

Simonyi Lecture

2009-09-08T09:39:00.003+01:00

JOIN TIMOTHY GOWERS

For this years

CHARLES SIMONYI LECTURE

at OXFORD PLAYHOUSE

Friday 2 October at 5pm

Rouse Ball Professor of Mathematics at Cambridge University and Fellow of Trinity College, Timothy Gowers, gives this year's Charles Simonyi Lecture, the annual lecture for the public understanding of science at Oxford Playhouse on Friday 2 October.

Gowers will talk about his recent involvement in an experimental attempt to solve a serious mathematical research problem publicly and collaboratively on the internet. He will discuss the problem itself, the difficulties involved, the surprising outcome, and what this suggests for the future of mathematics.

The Simonyi Lectures are a series of annual lectures in Oxford, set up in 1999 by Richard Dawkins, in order to promote the public understanding of science. Now in it’s eleventh year, Marcus du Sautoy follows Richard Dawkins as the new Charles Simonyi Professor.

Tickets for The Charles Simonyi Lecture at Oxford Playhouse are available from the Box Office on 01865 305305 or Oxford Playhouse Website

TED

2009-07-24T08:43:00.007+01:00

The subject of TEDGlobal 2009 held in Oxford this week was the Substance of Things Unseen. My talk, given in the section Curious and Curiouser on Wednesday, attempted to illustrate how mathematics is a powerful language to allow us to get access to things unseen. In particular, symmetry is superficially about something visual, something seen. We say a face is symmetrical because we can see that the left side is a mirror of the right side. But how can we "see" that two walls in the Alhambra for example have the same group of symmetries although they visually look very different. The power of mathematics is to be able to "see" an abstract entity underlying the object. It's like the concept of number. Do you ever "see" the number 5? No. You see visual representations of the number 5. This is the power of the language of symmetry that the French revolutionary Evariste Galois developed at the beginning of the 19th century. It allows us to articulate why two objects have the same symmetries although they visually look very diffferent.
It also has the power to prove when we have seen examples of all the symmetries possible. In the Alhambra for example, mathematicians proved that there are only 17 different groups of symmetries possible on a two dimensional wall. There are many more than 17 different wall designs across the palace but they are all examples of one of these 17 symmetry groups. For example, these two walls look very different. But the language of symmetry allows us to explain why the underlying symmetries are exactly the same:

This allows us to explore the symmetries of things seen. But the real power of mathematics is to create symmetries of things unseen. My work concerns creating symmetrical objects that exist beyond our three dimensional visual world. Only with the power of mathematical language can we "see" in 4, 5 even infinite dimensional space.
To celebrate TEDGlobal 2009 I constructed a new symmetrical object that cannot be seen but using mathematical language can be explored and played with. It was won in a competition I ran during my 18 minute talk by another of the TED speakers astronomer Andrea Ghez.

TED blog entry about my talk

Twitter Snapshot: Marcus du Sautoy on symmetry

Groups for Charity If you want your own "unseen" symmetrical object, then a donation through my FirstGiving page to the charity CommonHope will get your name on a new mathematical shape.

The Complete Sexy Maths

2009-07-04T08:49:00.008+01:00

This week saw the last column in the Sexy Maths series in The Times for the time being. The newspaper is downsizing for the summer. It may reappear in a new reincarnation in the autumn. Here is an archive of links to all the columns that appeared during the year, some including the beautiful illustrations of Joe McLaren who will be illustrating my new book The Num8er My5teries.

1 Jul 2009 Oh, it’s such a perfect day. We have discovered 47 perfect numbers — the largest has nearly 26 million digits.

24 June 2009 How to avoid a grudge match. Never mind Arsenal against Spurs. How about NP versus P?

17 June 2009 Arithmetic eases swine flu. Figuring out the rate of contagion can make you feel better

10 June 2009 When it pays to play the odds. Mathematicians, and the laws of probability, can tell you whether to have a flutter, or keep hold of your money.

27 May 2009 A new bicycle reinvents the wheel, with a pentagon and triangle. Guan’s bicycle isn’t the first to exploit these shapes — they have been used by urban planners as manholes.

20 May 2009 A game of 12 pentagons. Why a football match is actually geometry in motion.

13 May 2009 in search of the poetry of Muslim symmetry. Galois’s group theory allowed mathematicians to articulate the theory of symmetry.

6 May 2009 Formula won ... the key to boosting faster travel. How mathematicians can get you to the Grand Prix finishing line — and through an airport — more quickly.

29 April 2009 The lemming theory. There is no mass suicide pact keeping the numbers of lemmings down.

22 April 2009 What's unique about the number 1,729?

15 April 2009 The Fibonacci sequence's prime rate.

8 April 2009 Drawing parallels in geometry. This year's Abel Prize honours some of the most revolutionary contributions to geometry since those of Euclid.

25 March 2009 Go fourth... into another dimension.

18 March 2009 Twists and turns that make a rollercoaster ride.

11 March 2009 A number-munching celebration.

4 March 2009 Ditch the GPS, just follow the colour code.

25 February 2009 Tails of a curious submariner. A US Marine with a lot of time on his hands has noticed that a strange thing happens when you keep tossing a coin.

18 February 2009 How to be a flipping genius. It's possible for me to toss a coin and you, who are somewhere else entirely, to know if I have called honestly.

11 February 2009 Why Palladio's proportions are pleasing on the eye and the ears.

4 February 2009 Why do snowflakes have six arms? Are your children out of school? Keep their grey matter going with a question that baffled generations of scientists.

28 January 2009 It's true, young Muggles. Maths can be magic.

21 January 2009 Rubik's Cube returns.

14 January 2009 Solving wobbly restaurant tables. Wedging beer mats or bits of paper under that annoying table leg is no more. Try the mathematical solution instead.

7 January 2009 Survival of the mathematician.

31 December 2008 How to be a perfect timekeeper.

17 December 2008 Warm up with a few festive candles.

10 December 2008 The symmetry of sneezing. Viruses blight many people's lives in winter but the molecular structure of many are things of mathematical beauty.

26 November 2008 Skills of a chess grandmaster.

19 November 2008To infinity - and beyond

12 November 2008 Get the upper hand at poker.

5 November 2008 Why democracy is an ass.

29 October 2008 Get your teeth into this.

22 October 2008 Why the taxman has your number.

15 October 2008 Sexy maths: a calculating approach to love. Mathematics can help you to maximise your chances of landing the best flat – or the best partner.

8 October 2008 Happy (birthday) coincidences. Why Premier League footballers are likely to have dates of birth in common, and how to win more money on the lottery.

1 October 2008 Primes of passion.

Finding Moonshine in Paperback

2009-05-14T19:26:00.003+01:00

Finding Moonshine appears in paperback today with a fun cover: the back is a mirror image of the front. It also includes a PS section with a portrait of the author by Roger Tagholm; top ten favourite pieces of music; a symmetry tour round the world; plus the article "Einstein Plato ...and you?" written for the Telegraph about the project to use symmetry to raise money for Common Hope, a charity in Guatemala.

Click here to buy the paperback from Amazon

To Infinity and beyond

2009-05-13T12:14:00.004+01:00

I've been attempting some Tweetorials on Infinity. For those who would like more than can be expressed in 140 characters (a tough medium to talk about the infinite) here is an account of why there are different infinities.

To infinity and Beyond...

The very concept of number illustrates the power of the human mind to abstract mathematical identity from physically very different settings. In fact we seem genetically programmed to be able to detect when things are numerically identical or not. The decision to fight or fly in the face of the enemy depends on an assessment of whether the number in your pack is bigger or smaller than the number in the opposition. Those that can count, survive.

This ability of animals to detect numerical identity has been identified in many species. Monkeys, cats and dogs count their young to check they are all there; coots can identify when the number of eggs in their nest has increased indicating someone has added a parasite egg; babies as young as 5 months can tell when dolls are taken away from a pile. Even dogs seem to be able to tell that something fishy is going on when experimenters try to trick them into thinking that 1+1=3. But it is humans who have given names to these numerical identities.

Some tribes have only produced names for the first few numbers, lumping together anything too large under the heading “lots”. But even without names for numbers, such tribes are able to compare wealth. The tribe who has numbers “one, two, three, lots” can still say when one member of the tribe has more “lots” than another. If chickens are a mark of wealth then by pairing chickens up we can tell whether one person’s “lots” is bigger than another’s.

This idea of comparison lead to mathematicians in the nineteenth century realising that even in our more sophisticated mathematical tribe we could actually compare infinities and say when two infinite sets are identical in size or not. Prior to the nineteenth century this idea of different sizes of infinity had never been considered. In fact when the German mathematician Georg Cantor proposed the idea in the 1870s, it was considered as almost heretical or at best the thoughts of a madman.

Using the idea of pairing objects, Cantor was able to propose a way of declaring when two infinite sets were numerically identical or not. For example one might be tempted to declare that there are half as many even numbers as compared to all numbers. However Cantor showed there is a way to line up both sets of numbers so that each number has its pair. For example 1 gets paired with 2, 2 with 4, 3 with 6, and n with 2n. So these two sets have the same size. The tribal member with even numbered chickens is as wealthy as the tribesman with chickens numbered with all whole numbers. These infinite sets are identical in size.

You have to be slightly more ingenious to see how to compare all whole numbers against all fractions and prove that both sets are identical in size. At first sight this looks impossible. Between each pair of whole numbers there are infinitely many fractions. But there is a way to match the whole numbers perfectly with all fractions so that no fractions are left unmatched. The procedure starts by producing a systematic way to make a table containing all the fractions. The table has infinitely many rows and columns. The nth colomn consists of a list of all the fractions 1/n,2/n,3/n,…

How then do you pair up the whole numbers with the fractions in this table? The trick is to wend a snake diagonally through the fractions in the table as illustrated below. The number 9 for example gets paired with 2/3, the ninth fraction that one meets as the snake slithers through the table of fractions. Since the snake covers the whole table, every fraction will get paired with some whole number.

This is beginning to look like all infinities are identical in size. Perhaps once a tribal member has infinitely many chickens he won't get beaten by anyone else's collection. Now enter the new big cheese whose chickens are labelled with all the possible decimal expansions there are of numbers. Will the tribal member whose chickens are labelled just with the whole numbers 1,2,3… up to infinity be able to pair his chickens up with this new big cheese? He might start by matching his first chicken with chicken π = 3.1415926…, then the second with e = 2.7182818…

Why can we be sure that however hard he tries to match up chickens we can always guarantee an irrational chicken unaccounted for? Let's take one of his attempts to match his chickens with the irrational chickens belonging to the big cheese.

1 ↔ 3.1415926…
2 ↔ 2.7182818…
3 ↔ 1.4142135…
4 ↔ 1.6180339…
5 ↔ 0.3331779…

…

We are going to build a number with an infinite decimal expansion such that the corresponding irrational chicken has not been paired up with one of the whole numbers. Each decimal place is a number between 0 and 9. In the first decimal place, we choose a number which is different from the first decimal place of the number paired with chicken number 1. In the second decimal place choose a number different from the second decimal place of the number paired with chicken number 2. For example the irrational chicken with number starting 0.28518… is not paired with the first five whole numbers. In this way we can build up a number labelling a chicken which hasn't been paired up with any whole number. If someone claimed it was the chicken paired with say chicken number 101, we could simply say: "check the 101st decimal place, it's different from the 101st decimal of this new number".

There are a few technical points to watch in building this number, for example you don't want to produce the number 0.9999… because this is actually the same as the number 1.000… But the essence of the argument suffices to show that there are more numbers with infinite decimal expansions than there are whole numbers.

The great German mathematician David Hilbert recognized that Cantor was creating a genuinely new mathematics. Hilbert declared Cantor's ideas on infinities to be "the most astonishing product of mathematical thought, one of the most beautiful realisations of human activity in the domain of the purely intelligible…no one shall expel us from the paradise which Cantor has created for us".

Cantor’s illumination of the different mathematical identities hiding inside the idea of infinity lead to a question that would reveal how subtle numbers are. Cantor wanted to know whether there are sets of numbers which are bigger in size than whole numbers but small enough that they can't be paired with all infinite decimal expansions. In other words can there be a tribal member with numbered chickens that is richer than the man with chickens labelled with whole numbers but poorer than the big cheese with chickens labelled with every possible infinite decimal expansion.

The answer to this problem, which finally arrived in the 1960s, rocked the mathematical community to its foundations. Paul Cohen, a logician at Stanford, discovered that both answers were possible. Cohen proved that one couldn't prove from the axioms we currently use for mathematics whether or not there was a set of numbers whose size was strictly between the number of whole numbers and all real numbers. Indeed he produced two different models which satisfied the axioms that we are using for mathematics and in one model the answer to Cantor's question was "yes" and in the second model the answer was "no".

Before Cantor, all infinities had been lumped together under one heading. But Cantor was able to distinguish different sizes of infinities. This feature of mathematics to distinguish different mathematical identities is very much a product of nineteenth century movement in mathematics towards looking for abstract mathematical structures underlying physical reality.

Twitter

2009-05-09T17:53:00.004+01:00

Join me on Twitter if you would like to check out my micro blogging. Tweets on everything from Infinity to Nicholas Cage in Knowing, from Sexy Maths to the trials and tribulations of Arsenal football club.

Follow Marcus du Sautoy.

Alan and Marcus Go Forth and Multiply

2009-04-01T21:09:00.001+01:00

"Ever since he was at school, actor and comedian Alan Davies has hated maths. And like many people, he is not much good at it either. But Alan has always had a sneaking suspicion that he was missing out.
So, with the help of top mathematician Professor Marcus du Sautoy, Alan is going to embark on a maths odyssey. Together they visit the fourth dimension, cross the universe and explore the concept of infinity. Along the way, Alan does battle with some of the toughest maths questions of our age.
But did his abilities peak 25 years ago when he got his grade C O-Level? Or will Alan be able to master the most complex maths concept there is?"

In this BBC Horizon that I made with Alan Davies we started out taking as our model the Oz Clarke/James May programmes but instead of wine we did maths. I got to play the posh Oz Clarke character: "what a wonderful bouquet this equation has" while Alan could play the urbane James May of maths. But actually the thing soon evolved into a completely different journey. It waas a mathematical road-trip. From Weymouth to Brighton, from Teddington to...well, actually it was more a road-trip of the mind. From primes to probability, quantum chaos to hyperspace.

Alan is a clever guy. The village idiot role he plays on QI is just good acting. The director of our Horizon kept on saying: "Alan. Could you pretend you didn't understand the Riemann Hypothesis so quickly". Amazing what a national icon Alan is. Everywhere we went, people would flock to get his autograph. He was mugged by old grannies in Weymouth saying how much they loved Jonathan Creek to teenagers on Brighton Pier who knew him as the Dad in Angus, Thongs and Perfect Snogging. I kept thinking as I stood on my own on the sidelines: "but don't they know I've got a Theorem named after me."

The programme was broadcast on BBC2 at 9pm on the 31st of March 2009. It got 2.3 million viewers. Reviews were mixed but then reviewers love knocking Horizon. One really nice review was in the Sunday Times.

You can see some clips of the programme on the BBC website.

The maths of the beautiful game "During his journey to understand the often vilified science of maths, comedian and Arsenal fan Alan Davies hears that footballers are "mathematical geniuses" and learns how maths can help fans of the game."

Why maths lacks common sense "Comedian Alan Davies - who has hated maths since school - has embarked on a maths odyssey with the help of mathematician Marcus du Sautoy.
In a game of probability, he was challenged to put common sense aside in order to see the power of logical thinking." Here is an explanation of the infamous Monty Hall Game Show.

From Ecstasy to Infinity

2009-03-13T07:28:00.003Z

I've spent the two month making a radio programme about the art and science of the baroque for BBC Radio 3 that is due to be aired this Sunday on the Sunday Feature.

The Baroque was always a style I'd associated with vulgarity and excess. But in this programme I’ve discovered how much control and structure underpins the spectacle of the baroque. The dramatic and sensational effects of the greatest baroque architects like Borromini and Bernini are founded on sound mathematical principles. Painters like Caravaggio and Rubens are battling with the same problems as Newton and Leibniz in their attempt to capture bodies in motion. And the extravagant sounds of Monteverdi and Bach would not be possible without the mathematical development of new ideas of temperament. It is my world of mathematics and science which allows the artist and musician to play with your emotions. Join me on my journey to the conversion of the delights of the baroque.

15 Mar 2009, 21:30 on BBC Radio 3

A Disappearing Number

2009-02-08T21:19:00.004Z

I was the mathematical advisor on Complicite's play A Disappearing Number. PLUS magazine have just released a podcast including interviews with me about my collaboration.

You can see clips from the show at Complicite's website

I also helped devise workshops in connection with the play for maths and drama teachers. More details can be found in the Education section of Complicite's website

Too hard...?

2009-02-07T09:58:00.003Z

Somebody just sent me this quote from Terry Prachett's Thief of Time. Susan is a teacher talking to her Head teacher:

"What precisely was it that you wanted madam?" she said. "It's just that I have left the class doing algebra and they get restless when the've finished".
"Algebra?" said madam Frout............"But that's far too difficult for seven-year-olds!"
"Yes but I didn't tell them that, and so far they havn't found out" said Susan....................

Story of Maths on BBC World

2009-01-08T10:41:00.006Z

Our journey round the world to uncover the story of Maths is appropriately going to be shown on BBC World throughout January. The programmes originally broadcast on BBC4 in October and were available on BBC iPlayer but those outside the UK were unable to catch the series. Now is your chance.

SHOWING TIMES for Programme One: The Language of the Universe.
Showing Saturday 10th January at 0810 GMT.
Repeated: Saturday at 1810 GMT and Sunday 11th at 0210 and 1410 GMT.

If that isn't possible then the series is also available on DVD from the Open University although I'm afraid it is a little pricey which is a shame.

Exciting news: the BBC has chosen The Story of Maths as one of its entries for the Royal Television Awards in Science and History.

BBC World website

Behind the maths block

2008-12-26T09:27:00.005Z

Many people emailed me after hearing Desert Island Discs to ask about what books did my teacher, Mr Bailson, recommend to me behind the back of the maths block when I was 12.

The book which had the biggest impact was

The Language of Mathematics. Frank Land. John Murray (Publishers) Ltd 1960.

You can read a description of the effect of this book on me in Chapter 1 of Finding Moonshine.

The other book which had a big impact probably at a slightly later stage was

A Mathematician’s Apology. G.H. Hardy. Cambridge University Press 1940.

This book made me realise that maths was as much a creative art as a useful science. I was very lucky to have the chance recently to work on Complicite's recent play A Disappearing Number based on the book.

The other thing my teacher recommended was reading Martin Gardner's regular column in Scientific American full of great recreational maths and puzzles. You can get many of these collected together into books.

We were also lucky to do something called the School Mathematics Project or SMP at my comprehensive school. The course taught us about group theory and topology and other exciting topics that count as real maths. I was fortunate to have a teacher who understood the ideas.

I was also lucky to go as a 13 year old to the Royal Institution Christmas Lectures in 1978 when they were first done on maths by Christopher Zeeman.

I was very honoured to be asked to give them my self in 2006. Called The Num8er My5teries they are aimed at 11-16 year olds. You can get a free DVD of the lectures from the Royal Institution and there is an accompanying website full of games

Christmas Lectures 2006

Also I am currently writing a book based on the lectures to be published in 2009 which I am hoping will make perfect material to recommend behind the back of the maths block. It will be called The Num8er My5teries.

Other books in addition to my own that do a great job at inspiring budding mathematicians:
Any book by Rob Eastaway, Ian Stewart, Robin Wilson or Keith Devlin.
The Number Devil by Hans Magnus Enzensberger.
1089 and All That by David Acheson.

Also look out for my regular column Sexy Maths in The Times on a Wednesday.

The Royal Institution run Mathematics Masterclasses for children which are worth checking out. Here is the link for the Masterclasses in London.

Desert Island Discs

2008-12-11T06:34:00.003Z

You can hear me on BBC Radio 4's Desert Island Discs at 9 am on Friday 12th December.

My choices:

1.Frühling-Spring
Performer Lucia Popp with the London Philharmonic Orchestra conducted by Klaus Tennstedt
Composer Strauss
CD Title Strauss: Four Last Songs
Track 1
Label EMI
Rec No CD7470132

2.Fanfare for St Edmondsbury
Performer The Philip Jones Brass Ensemble
Composer Britten
CD Title British Music for Brass:The Philip Jones Brass Ensemble
Track 6
Label LONDON
Rec No 4303692

3 The Prelude to Wagner’s Parsifal
Performer The Berlin Philharmonic conducted by Herbert Von Karajan
Composer Wagner
CD Title Wagner: Parsifal
Track 1
Label DEUTSCHE GRAMMOPHON
Rec No 4133472

4.I Know a Bank from Britten’s A Midsummer Night’s Dream
Performer James Bowman with The Trinity Boy’s Choir & the City of London Sinfonia conducted by Richard Hickox
Composer Britten
CD Title Britten: A Midsummer Night’s Dream
Track Cd1 trk 6
Label VIRGIN CLASSICS
Rec No
VCD7593052

5.Joy of the Blood of the Stars from Messiaen’s Turangalila Symphonie
Performer The City of Birmingham Symphony Orchestra conducted by Sir Simon Rattle
Composer Messiaen
CD Title Messiaen:Turangalila-Symphonie
Track 5
Label EMI
Rec No 5865252

6 Look My Castle Gleams and Brightens
Performer Eve Marton & Samuel Ramey with the Hungarian State Orchestra conducted by Adam Fischer
Composer Béla Bartók
CD Title Béla Bartók: Bluebeard’s Castle
Track 6
Label CBS
Rec No CD44523

7.The second movement of Shostakovich’s String Quartet No.8
Performer The Brodsky Quartet
Composer Shostakovich
CD Title Shostakovich: Brodsky Quartet
Track 5
Label TELDEC
Rec No 2449192

8 The Many Rend the Skies with Loud Applause from the Alexander’s Feast
Performer The Bach Choir of Stockholm and Concentus Musicus of Vienna conducted by Nikolaus Harnoncourt
Composer Handel
CD Title Handel: Alexander’s Feast
Track cd2 trk 2
Label TELDEC
Rec No ZA835671

Record: Wagner’s Parsifal
Book: (instead of the Bible – Mahabharata).
The Glass Bead Game by Hermann Hesse
Luxury: My own trumpet

DVD of Story of Maths now available

2008-12-03T21:16:00.004Z

The DVD of The Story of Maths can now be purchased for £63.24 from the Open University.

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity’s greatest cultural achievements.

This DVD contains
Programme One: The Language of the Universe
Programme Two: The Genius of the East
Programme Three: The Frontiers of Space
Programme Four: To Infinity and Beyond

To purchase visit The Open University Website

Einstein, Plato...and you?

2008-11-08T10:25:00.012Z

To coincide with an article I wrote about my project to name groups for charity, the Daily Telegraph made a donation so that 10 of its readers could have a symmetrical object named after them. Here are the lucky winners:

The Mario Saltao Group Set [C[1], C[2], C[3], C[4]]=[5,0,8,1937] Corresponds to an elliptic curve of conductor 477231270919. Won by Filomena Saltao.

The Julie T Baxter Group Set [C[1], C[2], C[3], C[4]]=[0,0,0,1956] Corresponds to an elliptic curve of conductor 7651872. Won by Keith Baxter.

The David W Beaumont Group Set [C[1], C[2], C[3], C[4]]=[5,10,19,38] Corresponds to an elliptic curve of conductor 34390.

The Shana Vijayan Group Set [C[1], C[2], C[3], C[4]]=[20,0,6,1977] Corresponds to an elliptic curve of conductor 4552076208.

The Philothei-Hope Group Set [C[1], C[2], C[3], C[4]]=[0,0,0,2006] Corresponds to an elliptic curve of conductor 257538304. 'In memory of pure love, never forgotten'. Won by Bob Fish.

The MacArthur Group Set [C[1], C[2], C[3], C[4]]=[28,0,3,1940] Corresponds to an elliptic curve of conductor 1915435348277. Won by Malcolm MacArthur.

The Sarah Mary Alice and Lucy Group, sometimes known as the SMAL Group. Set [C[1], C[2], C[3], C[4]]=[20,0,6,1946] Corresponds to an elliptic curve of conductor 63583921192. Won by Philip Charles Gager. His a PhD from Warwick under Roger Carter in group theory should help him explain the group to his daughters who he chose to name the group after.

The Richber Group Set [C[1], C[2], C[3], C[4]]=[25,6,4,9] Corresponds to an elliptic curve of conductor 1044055. Won by Beryl Abraham. "I have been going round and round in circles
trying to decide the name of the symmetrical object. I have finally landed upon "The Richber Group" from my husband's
name and mine."

If you would like to see the original article then click here: Einstein, Plato...and you?

Richter - Painting by Numbers

2008-10-03T19:08:00.005+01:00

Tomorrow I am giving a talk at the Serpentine Gallery about the new Gerhard Richter exhibition 4900 Colours. I must say that this exhibition has started to obsess me somewhat. The pictures consist of 96 25x25 colour girds. In this exhibition, he puts 4 together to make 49 10x10 colour grids in what he calls Version II. Richter produces the 25x25 colour paintings by randomly picking from a selection of 25 colours. I'll be considering questions tomorrow like: how many possible paintings are there? If they were laid out end to end how far would all the possibilities stretch? What is the chance that you get two colours together? three colours together? How many other versions are possible? (Richter details 11 possible variations.) In how many paintings will a colour be missing?

The exhibition is related to Richter's design for the stain glass windows at Koln cathedral except there he mirrors the random choice making something rather like a Rorschach ink-blot.

The intriguing thing is that when you look at these paintings you are searching out structure. It almost begs a mathematical viewpoint to appreciate them.

Serpentine Website

The Story of Maths

2008-10-02T09:53:00.004+01:00

My new series THE STORY OF MATHS starts on Monday 6th October on BBC4 at 9pm. There are 4 episodes which chart the history of mathematics from Ancient Egypt to modern day.

To find out more visit THE STORY OF MATHS

Sexy Maths

2008-10-01T09:43:00.000+01:00

I've started writing a new column in The Times newspaper every Wednesday that will appear in T2 under the slightly embarrassing name of Sexy Maths. The first piece is about the new record big prime that was found a few weeks ago.

Primes of Passion

England Writers Football Team

2008-09-29T10:17:00.000+01:00

Having published my second book Finding Moonshine I officially qualify to play for the England Writers Football Team. My publisher Fourth Estate has sponsored our kit and we had a match on Saturday against the Spanish Writers Football Team in Madrid. After 90 minutes we were winning 5:2. The Spanish though had booked the pitch for two hours so we battled on another 15 minutes and still managed to be ahead at 6:4. The rest of the weekend was spent talking Foucault and Velazquez at the Prado washed down with some excellent Rioja.

Details of the team can be found at the Writers Team Website

Name a Symmetry for Charity

2008-07-02T09:25:00.150+01:00

Common Hope is an educational charity supporting and empowering children and their families in Guatemala. commonhope.org In exchange for a minimum donation of $10 to the charity, I will create and name a symmetrical object for you. Donations can be made at my fund-raising site firstgiving.com. A clue to why this is my charity of choice can be found in Chapter 12: July of Finding Moonshine.

If you would like to give the group of symmetries as a birthday present or to celebrate an anniversary then leave the significant date in the comments column and I will weave the date into the construction of the symmetry group. Please email me to alert me to the fact that you have left a donation. dusautoy@maths.ox.ac.uk

Here is a list of the groups created so far that have helped change the lives of children in Guatemala.

The Anna Ruth Group Set [C[1], C[2], C[3], C[4]]=[2,0,6,1976] Corresponds to an elliptic curve of conductor 124558021948. A birthday present from her mother who sparked off the whole idea of symmetry for charity when she approached me at the Hay Literary Festival looking for an intriguing birthday present.

The Poppygon Set [C[1], C[2], C[3], C[4]]=[20,0,4,2001] Corresponds to an elliptic curve of conductor 122350161344. From Jasper James to his daughter, Poppy.

The Hollygon Set [C[1], C[2], C[3], C[4]]=[4,0,5,2003] Corresponds to an elliptic curve of conductor 520997230219. From Jasper James to his daughter, Holly.

The Vanilla Beer Group Set [C[1], C[2], C[3], C[4]]=[0,4, 0, 7] Corresponds to an elliptic curve of conductor 672. A birthday present for the 4th of July from Tony Mann.

The Josef Williamson Group Set [C[1], C[2], C[3], C[4]]=[29,0,9,1992] Corresponds to an elliptic curve of conductor 854967496638. A present from his father, a maths teacher who appreciates the beauty of such objects of the mind.

The Robert Williamson Group Set [C[1], C[2], C[3], C[4]]=[25,0,3,1994] Corresponds to an elliptic curve of conductor 34683474002. A present from his father.

The Laurie Ingram Group Set [C[1], C[2], C[3], C[4]]=[41,0,43,47] Corresponds to an elliptic curve of conductor 120505925398. A present from Peter O'Sullivan.

The Campbell Peter Group Set [C[1], C[2], C[3], C[4]]=[53,0,59,61] Corresponds to an elliptic curve of conductor 1545669582458. A present from Peter O'Sullivan.

The Sophie Group Set [C[1], C[2], C[3], C[4]]=[67,0,71,73] Corresponds to an elliptic curve of conductor 7160027904610. A present from Peter O'Sullivan.

The Roger Highfield Group Set [C[1], C[2], C[3], C[4]]=[11,0,7,1958] Corresponds to an elliptic curve of conductor 112691547970. A present from Simon Singh for Roger's 50th birthday.

The Ingrid Group Set [C[1], C[2], C[3], C[4]]=[8,0,18,2008] Corresponds to an elliptic curve of conductor 46454762148. For Ingrid: Happy 10th Anniversary from Bill Goldbloom Bloch.

The Toby William Harold Wallis Group Set [C[1], C[2], C[3], C[4]]=[6,0,1,1949] Corresponds to an elliptic curve of conductor 471074250923. A present from his son Jake.

The Roko Group Set [C[1], C[2], C[3], C[4]]=[10,0,7,1984] Corresponds to an elliptic curve of conductor 485801692003. A birthday present to Roko from Bex Walton and to celebrate completing Part III in maths at the Other Place.

The Bach Group Set [C[1], C[2], C[3], C[4]]=[0,0,0,14] Corresponds to the elliptic curve y^2=x^3+14x of conductor 12544. Betsy Devine decided there should definitely be a symmetrical shape in hyperspace named after the great J.S Bach. He already has the south polar part of Mercury poleward of latitude 65° S named after him: The Bach Qaudrant. I decided that since Bach had an obsession with the number 14 that Bach would have approved of the elliptic curve that is woven into his group. Good choice Betsy!

The David & Kevi Group Set [C[1], C[2], C[3], C[4]]=[12,0,7,2008]. Corresponds to an elliptic curve of conductor 464001236731. From David's uncle Peter.

The Leonard Wee Group Set [C[1], C[2], C[3], C[4]]=[79,0,83,89]. Corresponds to an elliptic curve of conductor 23199545316482. From Sara Hackett in Western Australia: "Just in case you don't get the drill bit named after you."

The Godfrey Allen Group Set [C[1], C[2], C[3], C[4]]=[30,0,4,1936]. Corresponds to an elliptic curve of conductor 42433127756. In memory of Stephanie Wiffen's father.

The Nuria Group Set [C[1], C[2], C[3], C[4]]=[97,0,101,103]. Corresponds to an elliptic curve of conductor 9090419634730. From David Clarke to Nuria "who has plenty of her curves of her own... ;) "

The Aisling Isla Group Set [C[1], C[2], C[3], C[4]]=[14,0,6,2007] Corresponds to an elliptic curve of conductor 21615739008. A present from Peter O'Sullivan to celebrate her first birthday.

The Debs Group Set [C[1], C[2], C[3], C[4]]=[107,0,109,113] Corresponds to an elliptic curve of conductor 175533191226758. A present from an admirer: "Can't buy me love. But, hey, what about symmetric immortality."

The Scholamancuniensis Set [C[1], C[2], C[3], C[4]]=[0,0,0,1515] Corresponds to an elliptic curve of conductor 73447200. A symmetrical shape to inspire the students at Manchester Grammar School.

The Frank Roberts Group Set [C[1], C[2], C[3], C[4]]=[10,0,11,1973] Corresponds to an elliptic curve of conductor 492267567835. For Frank Roberts, a climate physicist who finds beauty in numbers, from his wife.

The Alessandro Butteri Group Set [C[1], C[2], C[3], C[4]]=[8,0,15,1891] Corresponds to an elliptic curve of conductor 459201849243. From Alessandro Butteri's grandson.

The Olivia Andrea Group Set [C[1], C[2], C[3], C[4]]=[9,0,18,1932] Corresponds to an elliptic curve of conductor 10303285662. From Olivia Andrea's son.

The Martin Andrea Group Set [C[1], C[2], C[3], C[4]]=[7,0,13,1956] Corresponds to an elliptic curve of conductor 251620927522. A present to his mathematical brother from Alex.

The Alex Andrea Group Set [C[1], C[2], C[3], C[4]]=[5,0,22,1953] Corresponds to an elliptic curve of conductor 515219441905. For Alex Andrea, who was hoping for "an elegant picture" of the symmetrical object but will have to make do with his brother explaining the elegance of things beyond our three dimensional world.

The Åmand Group Set [C[1], C[2], C[3], C[4]]=[-1,-1,-1,5] Corresponds to an elliptic curve of conductor 10693. A present from Åmand's boyfriend Johan Falk who won the chance to name a group during my talk at ESOF 2008 in Barcelona. The coefficients mirror those in the Falk group thus providing an eternal mathematical bond between the names of Åmand and Falk.

The Laura Group Set [C[1], C[2], C[3], C[4]]=[20, 0, 11, 2004] Corresponds to an elliptic curve of conductor 110307398677. From Laura's grandmother, Brenda Maddox. An object in hyperspace to inspire Laura in her dream to become an astronaut when she grows up.

The Sinead O'Connor Group Set [C[1], C[2], C[3], C[4]]=[0, 31, 0, 7] Corresponds to an elliptic curve of conductor 104496. From Pete Wilkins to his "beautiful, mathematical wife" to celebrate their anniversary.

The Rowan Robertson Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 11, 2004] Corresponds to an elliptic curve of conductor 10988969958. To stimulate his already burgeoning mathematical talents.

The Mun Yau Group Set [C[1], C[2], C[3], C[4]]=[0,11, 0, 9] Corresponds to an elliptic curve of conductor 2040. From Elizabeth Lewis to celebrate the birthday of her daughter-in-law who is a maths graduate from York University.

The Sean 7 Birthday Group Set [C[1], C[2], C[3], C[4]]=[16,8, 0, 2001] Corresponds to an elliptic curve of conductor 90285120. For Sean White's seventh birthday from his grandparents. Sean has been a dedicated "groupie" of Finding Moonshine, having come already to two of my lectures and asking a very pertinent question about sporadic groups. Hope the Sean 7 Birthday Group spurs him on to great things.

The Miri Group Set [C[1], C[2], C[3], C[4]]=[0,18, 0, 8] Corresponds to an elliptic curve of conductor 4672. A present from Christoph Nowak for Miri's birthday.

The Grace K. Group Set [C[1], C[2], C[3], C[4]]=[127,0, 131, 137] Corresponds to an elliptic curve of conductor 601251522940274. A present from Lisa Black for Grace's 12th birthday.

The Samuel Kirkland Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 11, 2003] Corresponds to an elliptic curve of conductor 103015407215. The Marcus Kirkland Group Set [C[1], C[2], C[3], C[4]]=[11, 10, 0, 2003] Corresponds to an elliptic curve of conductor 107617184. Twin groups for twins of Laura Lamont who spends her days latexing maths so probably understands what this is all about by now.

The Ryan Heaffey Group Set [C[1], C[2], C[3], C[4]]=[23, 0, 1, 1993] Corresponds to an elliptic curve of conductor 608925100798. A prize for Ryan who won a competition at the London Mathematics Summer School for showing strong promise at Mathematics and Mathematics Communication.

The Margaret Chambers Group Set [C[1], C[2], C[3], C[4]]=[139, 0, 149, 151] Corresponds to an elliptic curve of conductor 591420329470598. From Margaret's son Andrew.

The George Goodwin Group Set [C[1], C[2], C[3], C[4]]=[0, 30, 0, 10] Corresponds to an elliptic curve of conductor 137600. From Su Knight to her prospective father-in-law for his birthday.

The Robin Deeley Group Set [C[1], C[2], C[3], C[4]]=[31, 0, 1, 1980] Corresponds to an elliptic curve of conductor 396092524418. From Reyna Jenkyns to her math PhD student boyfriend who she met in the math department at the University of Waterloo.

The Christian Korninger Group Set [C[1], C[2], C[3], C[4]]=[157, 0, 163, 167] Corresponds to an elliptic curve of conductor 1313459491946782. From Leahanne Hobson.

The Martin Golumbic Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 9, 1948] Corresponds to an elliptic curve of conductor 2924045005085. Mathematician and Algorithmic Graph Theorist.

The Samuel Eilenberg Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 9, 1913] Corresponds to an elliptic curve of conductor 2835555384565. From Martin Golumbic for his thesis advisor, Samuel Eilenberg, Mathematician and Algebraic Topologist.

The Armstrong Group Set [C[1], C[2], C[3], C[4]]=[12, 0, 11, 0] Corresponds to an elliptic curve of conductor 15741. "For the best maths teacher a Queenie could wish for... Happy Birthday Mr Armstrong." From Jenny and Naomi.

The Scott Thomas Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 12, 1968] Corresponds to an elliptic curve of conductor 1243262310. For my brother Scott Thomas who is 40 on 11th December this year and is obsessed with symmetry to almost OCD levels, the fool. From Marc Thomas.

The Sharoné Bentoné Group Set [C[1], C[2], C[3], C[4]]=[18, 0, 3, 1969] Corresponds to an elliptic curve of conductor 90679839931. From Tim: "Happy 40th Birthday".

The Abigail Pepperell Group Set [C[1], C[2], C[3], C[4]]=[173, 0, 179, 181] Corresponds to an elliptic curve of conductor 5074383987971138. From Geoff Savage. "My girlfriend is an English teacher who nearly became a science teacher and retains a strong fondness for the subject (she is still devoted to watching the Christmas lectures every year and passionately supports your belief in exposing children to complex ideas)."

The Stephen Ives Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 6, 2009] Corresponds to an elliptic curve of conductor 8062834141. From Karen "to celebrate our 25th anniversary".

The Bentley Group Set [C[1], C[2], C[3], C[4]]=[40, 13, 4, 4] Corresponds to an elliptic curve of conductor 19135372. From Tony Mann: "A group to commemorate the wonderful goal scored by David Bentley last week from 40 yards in the 13th minute in the 4:4 draw between Spurs and Arsenal." This group certainly tested my commitment to the charity. As Tony knows, I am a big Arsenal fan. I was at the match and it was painful seeing Bentley's goal go in (Bentley is an ex-Arsenal who moved to Spurs and got booed all night). We thought we'd done enough at 4:2 with one minute of normal time to go. I've never heard the Emirates go so quiet after Spurs scored two last gasp goals to draw 4:4. Thank God for beating Man U. today. Tony, you are a cruel man!

The Matt Emanuele Group Set [C[1], C[2], C[3], C[4]]=[191, 0, 193, 197] Corresponds to an elliptic curve of conductor 9758279989066946. A Christmas present from Cliff Cunningham.

The Bas Kokshoorn Group Set [C[1], C[2], C[3], C[4]]=[199, 0, 211, 223] Corresponds to an elliptic curve of conductor 7412124287628142. A present from Ionica Smeets. "Bas Kokshoorn is a biologist and he named a snail after me, so this seemed the least I could do for him!"

The Dean David Group Set [C[1], C[2], C[3], C[4]]=[16, 0, 9, 1957] Corresponds to an elliptic curve of conductor 264377808699.

The Amy Baudains Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 12, 2001] Corresponds to an elliptic curve of conductor 7418587161. From her Dad Ian. "As a very mediocre maths graduate, I may have some problems explaining to her precisely what it is, but I think it’s a great idea and something very special."

The Georgina Clark-Mazo Group Set [C[1], C[2], C[3], C[4]]=[227, 0, 229, 233] Corresponds to an elliptic curve of conductor 32425730045771918. A Christmas present from Georgina's husband Jeffrey.

The David Wheable Group Set [C[1], C[2], C[3], C[4]]=[28, 0, 2, 1989] Corresponds to an elliptic curve of conductor 1975062918032. From David's father John "My son David is in his second year reading Maths at Leeds. Hopefully he'll be able to explain it to me soon."

The Chloe Richmond Balfour Group Set [C[1], C[2], C[3], C[4]]=[13, 0, 4, 2004] Corresponds to an elliptic curve of conductor 26100675818. From Jason "for the date I met my wife."

The Wells-Mulligan Group Set [C[1], C[2], C[3], C[4]]=[239, 0, 241, 251] Corresponds to an elliptic curve of conductor 99724178588722. From Susan and Oliver Mulligan "a Christmas present for our daughter and son-in-law."

The Jessica Samuel Group Set [C[1], C[2], C[3], C[4]]=[257, 0, 263, 269] Corresponds to an elliptic curve of conductor 79905342249760922. From Julian to his daughter "who did not belive that such things can be done. "

The Julian Ransom Group Set [C[1], C[2], C[3], C[4]]=[2, 0, 12, 1964] Corresponds to an elliptic curve of conductor 7714154704. A symmetrical object to immortalize Mr Perfect, from a secret admirer.

The Lucy Corena Parkes Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 9, 1975] Corresponds to an elliptic curve of conductor 2992995730853. A Christmas present from Lucy's husband Laurence.

The Kitty Bittersplit Group Set [C[1], C[2], C[3], C[4]]=[1, 1, 4, 4] Corresponds to an elliptic curve of conductor 1462. From Francis Potts.

The Ethan Duffell Group Set [C[1], C[2], C[3], C[4]]=[14, 0, 12, 1979] Corresponds to an elliptic curve of conductor 99412586764. A birthday present from Karen Reid.

The Justine Hartley Group Set [C[1], C[2], C[3], C[4]]=[8, 0, 8, -8] Corresponds to an elliptic curve of conductor 8288. "A symmetry group after the beautiful symmetry in my life Justine Hartley, my wife." The date encoded in the group is their wedding anniversary 8/8/1992 which Tom remembers as 8/8/-8. A true mathematician!

The Repussiahtnamas Group Set [C[1], C[2], C[3], C[4]]=[22, 21, 2, 6] Corresponds to an elliptic curve of conductor 17356628. "Sweet idea, dude! A group named for my girlie, Sammy." From Cam Ewens.

The Pip Group Set [C[1], C[2], C[3], C[4]]=[271, 0, 277, 281] Corresponds to an elliptic curve of conductor 114571909805857838. From Geoff Wright to his symmetrical palindromic brother Pip. "I intend to print T-shirts for the whole family to wear at XMAS containing the object, rotated on the front and inverted on the back, so a nice symmetry will be appreciated :-) " Might be a challenge printing an object in hyperspace on a t-shirt but at least you can print the equation at the top of the post which generates the object.

The Jonathan Camfield Group Set [C[1], C[2], C[3], C[4]]=[283, 0, 293, 307] Corresponds to an elliptic curve of conductor 10274520264457426. From Derek Camfield to his eldest son who studied maths at Cambridge and whose birthday is coming up soon. "Being from maths background myself (maths, economics and statistics at Birmingham), I am
particularly pleased that in your new position you may help to raise the status of maths to become
a cool subject to study."

The Tim Moore Group Set [C[1], C[2], C[3], C[4]]=[311, 0, 313, 317] Corresponds to an elliptic curve of conductor 290443732551869066. From Derek Camfield to Tim for his 17th birthday. "He’s studying maths at A-level and, with his family,
is also a Dr Who fan. He and his parents really appreciated the present of a
symmetrical object in hyperspace – it seems very Dr Who-ish."

The Ashley Carter Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 1, 1972] Corresponds to an elliptic curve of conductor 218828042458. From Morgan Parker for Ashley's birthday.

The Phung Luu Group Set [C[1], C[2], C[3], C[4]]=[331, 0, 337, 347] Corresponds to an elliptic curve of conductor 29207729268459674. From David Plevin.

The David Pickup Group Set [C[1], C[2], C[3], C[4]]=[349, 0, 353, 359] Corresponds to an elliptic curve of conductor 329878042828105666. "For our son david who is studying maths/phys at warwick university."

The Crackhouseceilidhband Group Set [C[1], C[2], C[3], C[4]]=[367, 0, 373, 379] Corresponds to an elliptic curve of conductor 118268480847339994. Named by Iain Brassington.

The Kim Lasscock Group Set [C[1], C[2], C[3], C[4]]=[383, 0, 389, 397] Corresponds to an elliptic curve of conductor 1279154466551486474. From Kim's daughter Sara. "Merry Christmas Gap "

The David Hurn Group Set [C[1], C[2], C[3], C[4]]=[0, 27, 0, 12] Corresponds to an elliptic curve of conductor 32688. From David's son Mark for his birthday.

The Jessica Goodman Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 31415926] Corresponds to an elliptic curve of conductor 63165466011998464. From Simon and Emily who were keen to cook pi into the symmetry.

The Noodle Group Set [C[1], C[2], C[3], C[4]]=[401, 0, 409, 419] Corresponds to an elliptic curve of conductor 446373494996309666. From a Pieceofstring to his wife Noodle.

The b4thebigbang Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 13700000000] Corresponds to an elliptic curve of conductor 1201216. Named by Peter Cohen who wanted a symmetrical object that relates to the shape of empty space.

The Ricci & Spinne Group Set [C[1], C[2], C[3], C[4]]=[27, 0, 5, 2009] Corresponds to an elliptic curve of conductor 1716726955870. For Mr. & Mrs. Ricci & Spinne Downard's 20th Wedding Anniversary on 27 May 2009.

The Wimmett Group Set [C[1], C[2], C[3], C[4]]=[258, 301, 344, 384] Corresponds to an elliptic curve of conductor 88535365183360. From Stewart Robertson for his perfectly symetrical wife this Christmas. The group has encoded in it some character degrees of SU_3(7). "My maths is very rusty, but about 30 years ago I tinkered briefly with Lie Groups and Lie Algebras, looking at the symmetries of elementary particles, so anything related to SU(3) would be particularly appreciated! Thanks for the great books & TV, and what you're doing to fight poverty!"

The Tessa Keytes Markham Group Set [C[1], C[2], C[3], C[4]]=[8, 0, 11, 1998] Corresponds to an elliptic curve of conductor 527582450987. From Adam and Vicky Markham to their daughter who at 10 is a mathematician in the making. "This brilliant idea of yours – which I read about in New Scientist – may help continue to grow her interest in both maths and philanthropy. If you can get her group up on your blog by Christmas that would be great – who doesn’t want their very own elliptic curve under the tree!"

The Calum MacLeod Group Set [C[1], C[2], C[3], C[4]]=[421, 0, 431, 433] Corresponds to an elliptic curve of conductor 2479605410685210214. From Kenny to his Dad who has just retired from teaching Maths after 40-odd years. "He's never lost his sense of enthusiasm and curiosity about the subject, which I think is remarkable after teaching countless hundreds of reluctant students."

The Miners Hochheimer Kirkman Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 2003] Corresponds to an elliptic curve of conductor 128384288. Named by James Miners whose generous donation took funds raised for Common Hope to the first prime after 2000.

The Alexander James Heggie Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 12, 1943] Corresponds to an elliptic curve of conductor 37896380. From Vanessa to celebrate her father's 65th birthday.

The Yakov Group Set [C[1], C[2], C[3], C[4]]=[439, 0, 443, 449] Corresponds to an elliptic curve of conductor 296138264886917662. From Su Chiang to her husband.

The Evangeline Group Set [C[1], C[2], C[3], C[4]]=[457, 0, 461, 463] Corresponds to an elliptic curve of conductor 2136360038099416790. From Su Chiang to her cousin.

The Peter Christopher Carroll Group Set [C[1], C[2], C[3], C[4]]=[57, 0, 40, 58] Corresponds to an elliptic curve of conductor 716712588058. Named by Aoife Fitzpatrick for her wonderful husband. "Thank you for the opportunity to donate, and for the opportunity to pass on such an interesting, philosphically challenging, beautiful
and, actually, quite moving gift."

The Wandja Group Set [C[1], C[2], C[3], C[4]]=[467, 0, 479, 487] Corresponds to an elliptic curve of conductor 2601578536477673458. Named by Carol Poole. Merry Christmas.

The Catrin Lewis Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 4.1x10^586] Corresponds to an elliptic curve of conductor 10758400. Named by Andrew Langworthy for his gorgeous girlfriend for Christmas. One can only speculate at the significance of such a large number in their relationship.

The Judith Rolfe Group Set [C[1], C[2], C[3], C[4]]=[12, 0, 9, 1958] Corresponds to an elliptic curve of conductor 436967312507. Named by Rob Rolfe for his wife.

The Alan Williamson Group Set [C[1], C[2], C[3], C[4]]=[25, 0, 7, 1949] Corresponds to an elliptic curve of conductor 1077636797162. A present from Secret Santa who says that you of all people with your PhD in group theory should understand what this group is all about.

The Jenny Danczak Group Set [C[1], C[2], C[3], C[4]]=[491, 0, 499, 503] Corresponds to an elliptic curve of conductor 3595593229000931302. Named by Julian Dickens.

The Felix Danczak Group Set [C[1], C[2], C[3], C[4]]=[509, 0, 521, 523] Corresponds to an elliptic curve of conductor 2336359840205816966. Named by Julian Dickens.

The Fran Danczak Group Set [C[1], C[2], C[3], C[4]]=[541, 0, 547, 557] Corresponds to an elliptic curve of conductor 14170826984968211114. Named by Julian Dickens.

The Leo Danczak Group Set [C[1], C[2], C[3], C[4]]=[563, 0, 569, 571] Corresponds to an elliptic curve of conductor 1152595426554951278. Named by Julian Dickens.

The Dan Salter Group Set [C[1], C[2], C[3], C[4]]=[919, 0, 929, 937] Corresponds to an elliptic curve of conductor 571829388597171645214. Named by Cherry Lewis. "A great idea for Xmas presents, and a nice change from the Oxfam goats and chickens!"

The Leon Salter Group Set [C[1], C[2], C[3], C[4]]=[941, 0, 947, 953] Corresponds to an elliptic curve of conductor 667269326466624957470. Named by Cherry Lewis.

The Jo Smyth Group Set [C[1], C[2], C[3], C[4]]=[967, 0, 971, 977] Corresponds to an elliptic curve of conductor 803769097553289303194. Named by Cherry Lewis.

The Teresa Gray Group Set [C[1], C[2], C[3], C[4]]=[983, 0, 991, 997] Corresponds to an elliptic curve of conductor 908676036071455805326. Named by Cherry Lewis.

The Chris Smyth Group Set [C[1], C[2], C[3], C[4]]=[1009, 0, 1013, 1019] Corresponds to an elliptic curve of conductor 270413451369674373158. Named by Cherry Lewis for a number theorist in Edinburgh who can explain what's going on to the rest of Cherry's clan.

The Banda Group Set [C[1], C[2], C[3], C[4]]=[577, 0, 587, 593] Corresponds to an elliptic curve of conductor 22338170231254069814. Named by Ruben Flores, a Mexican PhD
candidate in Sociology at the University of Kent interested in contributing to development in Latin America.

The Tia Eustolita Group Set [C[1], C[2], C[3], C[4]]=[599, 0, 601, 607] Corresponds to an elliptic curve of conductor 14111748419094544178. Named by Ruben Flores, a Mexican PhD
candidate in Sociology at the University of Kent interested in contributing to development in Latin America.

The Rory Browne Group Set [C[1], C[2], C[3], C[4]]=[613, 0, 617, 619] Corresponds to an elliptic curve of conductor 8290914111359460658. Named by Tony Mann. Happy Christmas.

The Calum Browne Group Set [C[1], C[2], C[3], C[4]]=[631, 0, 641, 643] Corresponds to an elliptic curve of conductor 2584923289182691174. Named by Tony Mann. Happy Christmas.

The Andreas Mann Group Set [C[1], C[2], C[3], C[4]]=[647, 0, 653, 659] Corresponds to an elliptic curve of conductor 12234186943678509998. Named by Tony Mann. Happy Christmas.

The Niklas Mann Group Set [C[1], C[2], C[3], C[4]]=[661, 0, 673, 677] Corresponds to an elliptic curve of conductor 57663962798415443726. Named by Tony Mann. Happy Christmas.

The Katie Reid Group Set [C[1], C[2], C[3], C[4]]=[683, 0, 691, 701] Corresponds to an elliptic curve of conductor 72201888470849537942. Named by Tony Mann. Happy Christmas.

The Joanna Reid Group Set [C[1], C[2], C[3], C[4]]=[709, 0, 719, 727] Corresponds to an elliptic curve of conductor 46953727861032288482. Named by Tony Mann. Happy Christmas.

The Eilidh Reid Group Set [C[1], C[2], C[3], C[4]]=[733, 0, 739, 743] Corresponds to an elliptic curve of conductor 58248775917005188990. Named by Tony Mann. Happy Christmas.

The Dawn Pfeil Group Set [C[1], C[2], C[3], C[4]]=[751, 0, 757, 761] Corresponds to an elliptic curve of conductor 137980116991018190798. Named by Tony Mann. Happy Christmas.

The Matthew Kippen Group Set [C[1], C[2], C[3], C[4]]=[769, 0, 773, 787] Corresponds to an elliptic curve of conductor 20502405894074885378. From Sarah Langford to her brother.

The Stephen Poyer Group Set [C[1], C[2], C[3], C[4]]=[797, 0, 809, 811] Corresponds to an elliptic curve of conductor 52878209484444161198. From Chris Grollman to Stephen Poyer, "who looks so like me that we are often confused." So a bit of symmetry seems appropriate.

The Noah Slater Group Set [C[1], C[2], C[3], C[4]]=[5, 0, 2, 1983] Corresponds to an elliptic curve of conductor 500365533065. Named by Alison Wilde.

The Nerida Dicko Group Set [C[1], C[2], C[3], C[4]]=[821, 0, 823, 827] Corresponds to an elliptic curve of conductor 31810440742807494622. A Christmas present from Gareth Dickinson "to my fantastic wife!"

The David Woolf Group Set [C[1], C[2], C[3], C[4]]=[829, 0, 839, 853] Corresponds to an elliptic curve of conductor 280877690224362556594. A Christmas present to a man whose first love was Physics and growing crystals/semiconductors but now aspires to be a Time Lord. From his wife Alison and daughter Ellen. "Such a great idea, especially when looking for a present for the "man who has everything" - said man has declared he doesn't want a present this year and suggested, perhaps not entirely seriously, that a goat could go on his behalf to the Third World. I think he'll like this better."

The Kevlin Henney Group Set [C[1], C[2], C[3], C[4]]=[857, 0, 859, 863] Corresponds to an elliptic curve of conductor 171740916276470528254. Some symmetry from Carolyn Morris to her husband "so for once I am giving him order instead of chaos." [If you send me your email I'll send you a certificate]

The Anni Uibu Group Set [C[1], C[2], C[3], C[4]]=[877, 0, 881, 883] Corresponds to an elliptic curve of conductor 50561397167771465030. From Mari Järve to a fellow mathematician.

The Graham Perkins Group Set [C[1], C[2], C[3], C[4]]=[887, 0, 907, 911] Corresponds to an elliptic curve of conductor 227345263670881519582. A Christmas present from Andrew to his brother.

The Madeleine Shepherd Group Set [C[1], C[2], C[3], C[4]]=[1021, 0, 1031, 1033] Corresponds to an elliptic curve of conductor 1183938363633519730414. A Christmas present from Scott Keir with best wishes for 2009.

The Evatt Bourne Group Set [C[1], C[2], C[3], C[4]]=[1039, 0, 1049, 1051] Corresponds to an elliptic curve of conductor 334366632813643462474. Named by Jade Suine for Evatt, "who has become very excited by the things he has been reading about you and your work." For a wonderful 2009.

The Marjorie Marks Group Set [C[1], C[2], C[3], C[4]]=[1061, 0, 1063, 1069] Corresponds to an elliptic curve of conductor 1530717085799808534394. Named by Melissa Young for Marjorie Marks "who is a great College Algebra teacher & is very cool. Thank you for having a place where I can combine my interest in math, community outreach, and learning."

The Kristen Harley Group Set [C[1], C[2], C[3], C[4]]=[4, 0, 4, 1988] Corresponds to an elliptic curve of conductor 15872033048. For Kristen's 21st birthday from her parents. "Kristen is in her fourth year of a Maths/Physics degree at QUT (Queensland University of Technology) here in Brisbane, Australia. Perhaps it was inevitable she'd have a passion for maths, when she was born on 4/4/88."

The Paul Simon David Group Set [C[1], C[2], C[3], C[4]]=[17, 0, 12, 1960] Corresponds to an elliptic curve of conductor 4277374566. Named by Dean David in memory of Paul Simon David.

The Jermaine Defoe Group Set [C[1], C[2], C[3], C[4]]=[7, 0, 1, 15000000] Corresponds to an elliptic curve of conductor 107999805487384972499842. Named by Tony Mann for "the star who will make Spurs the best team in north London." That's TWO Tottenham players Tony has immortalised in hyper-space. Where are all you Gooners? Help me in the fight back against our arch-rivals at White Hart Lane. Surely Fabregas deserves a symmetrical object named after him after all the triangles he threads on the pitch?

The Kai Kuehner Group Set [C[1], C[2], C[3], C[4]]=[27, 0, 1, 2009] Corresponds to an elliptic curve of conductor 1644317287102. Named by Kai's grandparent's for Kai's birthday.

The Ameli Gottstein Group Set [C[1], C[2], C[3], C[4]]=[25, 0, 12, 2008] Corresponds to an elliptic curve of conductor 8129515890. Ameli's prize for winning the Greenwich University Christmas Maths Quiz. She preferred that to an Amazon token - clearly a mathematician in the making.

The Marta Kupis Group Set [C[1], C[2], C[3], C[4]]=[17, 0, 1, 1984] Corresponds to an elliptic curve of conductor 15879470398. For Marta's 25th birthday from Frank Neumann.

The Craig Gallagher Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 1, 2009] Corresponds to an elliptic curve of conductor 266039568082. Named by Darshini Gallagher for her father's birthday, "the loveliest geek in the world!"

The Joel Ineson Group Set [C[1], C[2], C[3], C[4]]=[14, 0, 2, 1968] Corresponds to an elliptic curve of conductor 86842276988. A birthday and Valentine's day present with love as always from Rachel.

The Mark and Susan Oeltjenbruns Group Set [C[1], C[2], C[3], C[4]]=[4, 5, 15, 1996] Corresponds to an elliptic curve of conductor 526617649243 A group is in celebration of Mark and Susan's wedding anniversary and their five wonderful kids.

The Tim Camfield Group Set [C[1], C[2], C[3], C[4]]=[0, 15, 0, 2009] Corresponds to an elliptic curve of conductor 17934056. A group is in celebration of Tim's 15th birthday.

The Harald Bohr Group Set [C[1], C[2], C[3], C[4]]=[22, 0, 4, 1887] Corresponds to an elliptic curve of conductor 103121269204. Named by Simon Singh for Harald Bohr, mathematician and footballer, born on 22 April 1887. Harald's brother, Niels, was ultimately to become more famous as one of the creators of the theory of quantum physics. Harald himself had already carved out some notoriety having been a key player in Denmark's Olympic football team that secured silver at the 1908 Olympics. But his greatest contributions were in studying the zeros of the Riemann zeta function. You can find out more about his discoveries in Chapter 5 of The Music of the Primes.

The Dong-ke Zhang Group Set [C[1], C[2], C[3], C[4]]=[8, 0, 3, 1964] Corresponds to an elliptic curve of conductor 477775260811. A present from David for his father "who first taught me the wonders of mathematics. Happy Birthday."

The Pauline "Popsie" Byron Group Set [C[1], C[2], C[3], C[4]]=[22, 0, 4, 1943] Corresponds to an elliptic curve of conductor 105656241812. A present from Olwyn for her mother for her birthday.

The Doris Whitworth Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 8, 1929] Corresponds to an elliptic curve of conductor 449578789168. From Geoffrey Morley in memory of his first cousin who died on the 31st of March.

The Andrew Plater Group Set [C[1], C[2], C[3], C[4]]=[1087, 0, 1091, 1093] Corresponds to an elliptic curve of conductor 1812931295453793579070. From David Hunt in memory of Dr Andrew Plater, a man who touched the hearts and minds of many.

The Georgina Knight Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 8, 1991] Corresponds to an elliptic curve of conductor 478466261623. From Chris Buckley "for my wonderful girlfriend".

The Jansson Group Set [C[1], C[2], C[3], C[4]]=[1097 0 1103 1109] Corresponds to an elliptic curve of conductor 1946805281289695949842. Named by Torbjörn Jansson for his family.

The Dahlström Group Set [C[1], C[2], C[3], C[4]]=[1117 0 1123 1129] Corresponds to an elliptic curve of conductor 2208554106995230334702. Named by Magnus Dahlström. "I enjoyed your lecture in Gothenburg."

The Ben Moore Group Set [C[1], C[2], C[3], C[4]]=[1131 0 1137 1149] Corresponds to an elliptic curve of conductor 807293329303094999694. Named by Derek Camfield for Ben on his 15 Birthday. "Keep up the good work in science!"

The Anna Shimwell Group Set [C[1], C[2], C[3], C[4]]=[28 0 5 1996] Corresponds to an elliptic curve of conductor 2056908575317. Named by John Shimwell for his daughter on her Birthday.

The Lena Jansson Group Set [C[1], C[2], C[3], C[4]]=[26 0 6 1959] Corresponds to an elliptic curve of conductor 75184952064. Named by Torbjörn Jansson for his sister-in-law to celebrate her 50th birthday.

The Dave Edwards Group Set [C[1], C[2], C[3], C[4]]=[20, 0, 6, 2009] Corresponds to an elliptic curve of conductor 118040761232. Named by Linda Higginbottom: "For my science and book buddy to celebrate his birthday.

The Sophia Group Set [C[1], C[2], C[3], C[4]]=[29, 0, 9, 2009] Corresponds to an elliptic curve of conductor 2601346244402. "For my sunshine Sophia for our anniversary ".

The Lasse Johansson Group Set [C[1], C[2], C[3], C[4]]=[1151, 0, 1153, 1163] Corresponds to an elliptic curve of conductor 678375945011528041802. From Torbjörn, Birgitta, Roland, Ann-Louise.

The Suzanne Stonehouse Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 8, 1965] Corresponds to an elliptic curve of conductor 54911265687. From Alec Stonehouse to his wife for her birthday: "A trailblazing secondary school Maths teacher & Symmetry fan." [August '65...a very good vintage]

The Rolf Nyberg Group Set [C[1], C[2], C[3], C[4]]=[1, 0, 9, 2009] Corresponds to an elliptic curve of conductor 522431328766. From Torbjörn Jansson for his friend and colleague in recognition of his retirement.

The Torbjörn Jansson Group Set [C[1], C[2], C[3], C[4]]=[1171 0 1181 1187] Corresponds to an elliptic curve of conductor 386482449719183404618. For Torbjörn Jansson. Many thanks for all your support with my project.

The Cathy and Greg Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 9, 2009] Corresponds to an elliptic curve of conductor 529117450658. From the Staff and Students of CSI Dublin to mark Cathy and Greg's wedding anniversary.

The Stefan Ottmar Haug Group Set [C[1], C[2], C[3], C[4]]=[4, 0, 9, 2009] Corresponds to an elliptic curve of conductor 531918335323. From Benjamin Volk and Panagiotis Konstantis for Stefan Ottmar Haug's birthday.

The Tordoff Group Set [C[1], C[2], C[3], C[4]]=[1193 0 1201 1213] Corresponds to an elliptic curve of conductor 3526360473742239108358. From Thomas Walton for Rachel who organised our trip to the Emirates achievement.

The Arnau Rios Huguet Group Set [C[1], C[2], C[3], C[4]]=[15, 0, 10, 1980] Corresponds to an elliptic curve of conductor 266464350. From Flor, Maria, Nacho and Yago "for our friend Arnau Rios Huguet to celebrate his 2^2+3^2+4^2 birthday."

The Venexia Group Set [C[1], C[2], C[3], C[4]]=[1217 0 1223 1229] Corresponds to an elliptic curve of conductor 4019178174064472055002. From David Walker for his daughter.

The PALYAB Group Set [C[1], C[2], C[3], C[4]]=[1231 0 1237 1249] Corresponds to an elliptic curve of conductor 4374420264075456706982. Named by Abby Pace.

The TJ Group Set [C[1], C[2], C[3], C[4]]=[22 0 7 1992] Corresponds to an elliptic curve of conductor 435446962861. Named by Tim Ladd for a young man with Leukemia in MI. Check out his website at tjsjourney.com or his mom's youtube channel: *http://www.youtube.com/user/WackaDoodleFreeZone

The Dadhaniya Group Set [C[1], C[2], C[3], C[4]]=[1259 0 1277 1279] Corresponds to an elliptic curve of conductor 2587295415673917568522. Named by Darpan Dadhaniya for his family.

The Mozz Group Set [C[1], C[2], C[3], C[4]]=[16 0 10 2009] Corresponds to an elliptic curve of conductor 296901944560. From Billy Boyle to celebrate Mozz's birthday.

The Jarrod Tanton Group Set [C[1], C[2], C[3], C[4]]=[22 0 12 1987] Corresponds to an elliptic curve of conductor 4087829532. From Zachary Tanton "for my cousin who with his vastly superior mathematical knowledge would be very intrigued."

The John and Jana Hoffman Group Set [C[1], C[2], C[3], C[4]]=[1283 0 1289 1291] Corresponds to an elliptic curve of conductor 724256730128301773266. Named by Irene Hoffman for her beloved parents.

The georgeNgeorge Group Set [C[1], C[2], C[3], C[4]]=[1297 0 1301 1303] Corresponds to an elliptic curve of conductor 623137684751104311490. Named by Klupu.

The Martens Group Set [C[1], C[2], C[3], C[4]]=[1307 0 1319 1321] Corresponds to an elliptic curve of conductor 6655565208577887603842. Named by Joel Martens. "I saw your TED Talks video on youtube and was fascinated. Your idea to raise money by naming mathematical objects is brilliant. I am an undergrad student studying mathematics and physics and i'd love to get some details on the properties, behavior and origins of the object that you end up naming for me. Im going to start by getting your book but i'd really appreciate any additional specifics you could send me. Thanks again for such a brilliant initiative."

The Stephanie Simon Group Set [C[1], C[2], C[3], C[4]]=[1327 0 1361 1367] Corresponds to an elliptic curve of conductor 3833593484133661049542. Named by Jonathan Joyce.

The Neville Neill Group Set [C[1], C[2], C[3], C[4]]=[20 0 7 1978] Corresponds to an elliptic curve of conductor 433344982589. Named by Jackie Neill to mark the day she married Neville.

The Doozer Group Set [C[1], C[2], C[3], C[4]]=[19 0 10 2009] Corresponds to an elliptic curve of conductor 18999485185. Named by Michelle Robert for her financée to mark their engagement.

The Awesome Allsworth Group Set [C[1], C[2], C[3], C[4]]=[21 0 10 2009] Corresponds to an elliptic curve of conductor 264031198435. To celebrate "the epic US install trip" 21st Oct 2009 from Owlstone.

The Elizabeth Davies Group Set [C[1], C[2], C[3], C[4]]=[25 2 12 2009] Corresponds to an elliptic curve of conductor 1218057747373. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Russell Collins Group Set [C[1], C[2], C[3], C[4]]=[25 3 12 2009] Corresponds to an elliptic curve of conductor 1241585245589. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Trevor Addenbrooke Group Set [C[1], C[2], C[3], C[4]]=[25 5 12 2009] Corresponds to an elliptic curve of conductor 1289081106757. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Julie Newton Group Set [C[1], C[2], C[3], C[4]]=[25 7 12 2009] Corresponds to an elliptic curve of conductor 1337164695413. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Patricia O'Rorke Group Set [C[1], C[2], C[3], C[4]]=[25 11 12 2009] Corresponds to an elliptic curve of conductor 1435094612821. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Phil Peel Group Set [C[1], C[2], C[3], C[4]]=[25 13 12 2009] Corresponds to an elliptic curve of conductor 1484940720389. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Lucy Hibbert Group Set [C[1], C[2], C[3], C[4]]=[25 17 12 2009] Corresponds to an elliptic curve of conductor 1586394680293. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Ben Ponniah Group Set [C[1], C[2], C[3], C[4]]=[25 19 12 2009] Corresponds to an elliptic curve of conductor 1638002311445. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Ian Gordon-Brown Group Set [C[1], C[2], C[3], C[4]]=[25 23 12 2009] Corresponds to an elliptic curve of conductor 1742978323189. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Michael Ingham Group Set [C[1], C[2], C[3], C[4]]=[25 29 12 2009] Corresponds to an elliptic curve of conductor 2254251545. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Greg Kerr Group Set [C[1], C[2], C[3], C[4]]=[25 31 12 2009] Corresponds to an elliptic curve of conductor 1959970247861. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Allan Westman Group Set [C[1], C[2], C[3], C[4]]=[25 37 12 2009] Corresponds to an elliptic curve of conductor 2128870621253. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The James Graef Group Set [C[1], C[2], C[3], C[4]]=[1373 0 1381 1399] Corresponds to an elliptic curve of conductor 4720208163786201526262. Named by Edward McCoy.

The Kim Sundermann Group Set [C[1], C[2], C[3], C[4]]=[1 0 11 2009] Corresponds to an elliptic curve of conductor 523208880658.

The Greg Conklin Group Set [C[1], C[2], C[3], C[4]]=[1409 0 1423 1427] Corresponds to an elliptic curve of conductor 176447821050061918346. Named by Brian Quistorff.

The Aparicio Group Set [C[1], C[2], C[3], C[4]]=[1429 0 1433 1439] Corresponds to an elliptic curve of conductor 6152335086016734640366. Named by Jose Aparicio. "I have to say that I really appreciate your efforts, and think this is a most wonderful way to use your craft to raise money to help in the advancement of mathematical education. Cheers!"

The Nick Sweeting Group Set [C[1], C[2], C[3], C[4]]=[1447 0 1451 1453] Corresponds to an elliptic curve of conductor 2678552181868463134670. From Tania+Frank+Corey for Nick's 13th birthday.

The Berheide Group Set [C[1], C[2], C[3], C[4]]=[1459 0 1471 1481] Corresponds to an elliptic curve of conductor 14422328284176205274114.

The Magiel Harmse Group Set [C[1], C[2], C[3], C[4]]=[11 0 7 2009] Corresponds to an elliptic curve of conductor 9954646702. Named by Attie Harmse for her brother's birthday.

The Igal Levine Group Set [C[1], C[2], C[3], C[4]]=[1483 0 1487 1489] Corresponds to an elliptic curve of conductor 2271922558380688700326. "Thank you for this unique opportunity to give a special gift and at the same time contribute to a very good cause."

The Moni Group Set [C[1], C[2], C[3], C[4]]=[1493 0 1499 1511] Corresponds to an elliptic curve of conductor 8412243298709054785774. "I just watched your TED talk and greatly enjoyed it. I especially love your fundraising idea. My first time living, working, and volunteering abroad was in Guatemala, it's a really special place and I'm excited to see that you're helping out there." Thanks for the symmetrical donation of 33.33. It took my fundraising over $4000.

The Niarte Group Set [C[1], C[2], C[3], C[4]]=[12 0 11 2009] Corresponds to an elliptic curve of conductor 481945494923. For Niarte's birthday. "a nerdy idea, with a rather warm hearty background. Bravo. :-)"

The Sethi Group Set [C[1], C[2], C[3], C[4]]=[1523 0 1531 1543] Corresponds to an elliptic curve of conductor 9691174762659229308974. Named by Nikhil Sethi.

The Lassonde Group Set [C[1], C[2], C[3], C[4]]=[7 0 9 2009] Corresponds to an elliptic curve of conductor 533597989426. Named by Nate Derbinsky.

The Charco Group Set [C[1], C[2], C[3], C[4]]=[23 0 11 1982] Corresponds to an elliptic curve of conductor 40133119646. For Charco's birthday.

The Elliot C Wilson Group Set [C[1], C[2], C[3], C[4]]=[12 0 7 1983] Corresponds to an elliptic curve of conductor 148729963977. For Elliot's birthday.

The Lovely Emma Group Set [C[1], C[2], C[3], C[4]]=[22 0 7 1973] Corresponds to an elliptic curve of conductor 432578991749. Named by Andy Low for Emma's birthday.

The Teacher I Is Group Set [C[1], C[2], C[3], C[4]]=[1583 0 1597 1601] Corresponds to an elliptic curve of conductor 25447571350049764792166. Named by Andrew Hirst for his family. "I named the group "Teacher I Is" partly due to my profession but also because it is an anagram containing all of my families initials."

The Nick Buzatu Group Set [C[1], C[2], C[3], C[4]]=[1549 0 1553 1559] Corresponds to an elliptic curve of conductor 10809368363512852108666. Named by Daniel Buzatu.

The Alex Buzatu Group Set [C[1], C[2], C[3], C[4]]=[1567 0 1571 1579] Corresponds to an elliptic curve of conductor 5866683193921799919238. Named by Daniel Buzatu.

The istemfer Group Set [C[1], C[2], C[3], C[4]]=[16 0 11 2009] Corresponds to an elliptic curve of conductor 301317556843. Named by Uygar Polat.

The Gomez Paez Group Set [C[1], C[2], C[3], C[4]]=[8 0 12 1968] Corresponds to an elliptic curve of conductor 2642786148. Named by Tim Sheehy.

The Anna Blume Group Set [C[1], C[2], C[3], C[4]]=[2 11 2009 3924944911] Corresponds to an elliptic curve of conductor 429970662482840185163704716195. Named by Jonathan Joyce to mark the publication of a collection of poetry by Anna Blume published November 2 on the subject of the Berlin Wall: West + Ost = Deutsch (ISBN: 3924944911). "An interesting (a)symmetry if ever I saw one.."

The uygarpolat Group Set [C[1], C[2], C[3], C[4]]=[11 0 16 2009] Corresponds to an elliptic curve of conductor 524730931183. Named by Istem Fer for her boyfriend. "Thank you for your being sensible for the children in Guetamala, I really appreciate that."

The Norman and Wendy Kay Group Set [C[1], C[2], C[3], C[4]]=[1583 0 1597 1601] Corresponds to an elliptic curve of conductor 25447571350049764792166. Named by Jeremy Levine for his wife's amazing parents.

The Verity Robertson Group Set [C[1], C[2], C[3], C[4]]=[6 0 11 2009] Corresponds to an elliptic curve of conductor 41490446231. Named by Calum Robertson for his daughter "so that she doesn't get jealous of her brother Rowan's group!"

The Vince Ion Group Set [C[1], C[2], C[3], C[4]]=[13 0 10 1950] Corresponds to an elliptic curve of conductor 4071505070. Named by Danny Ion for his Dad.

The Thomas Epping Group Set [C[1], C[2], C[3], C[4]]=[1607 0 1609 1613] Corresponds to an elliptic curve of conductor 27848720171084562011258. Named by Saskia Kersten.

The Lowe Group Set [C[1], C[2], C[3], C[4]]=[18 0 11 2009] Corresponds to an elliptic curve of conductor 132567234011. Named by Torbjörn and Birgitta Jansson for their first grandchild.

The Jules DesJacques Group Set [C[1], C[2], C[3], C[4]]=[1619 0 1621 1627] Corresponds to an elliptic curve of conductor 7343047481438450220754. Named by Aline Dutruel "my wee cousin Jules DesJacques, who's mad about mathematics, and will be thrilled with his Christmas present!"

The Charles Tyler Rives Group Set [C[1], C[2], C[3], C[4]]=[1637 0 1657 1663] Corresponds to an elliptic curve of conductor 16216485370370651836142.

The Bri and Jason Bird Group Set [C[1], C[2], C[3], C[4]]=[1667 0 1669 1693] Corresponds to an elliptic curve of conductor 36417295608366083835898.

The Kevin Moon Group Set [C[1], C[2], C[3], C[4]]=[1697 0 1699 1709] Corresponds to an elliptic curve of conductor 40912117957088347054634. Named by Peter and Susanne.

The Nicole Newman Group Set [C[1], C[2], C[3], C[4]]=[7 0 11 2009] Corresponds to an elliptic curve of conductor 539073092638. Named by Jeff Newman.

The Ryan McDonald Group Set [C[1], C[2], C[3], C[4]]=[1721 0 1723 1733] Corresponds to an elliptic curve of conductor 45132406297277785685618.

The Sean McDonald Group Set [C[1], C[2], C[3], C[4]]=[1723 0 1733 1721] Corresponds to an elliptic curve of conductor 45342629941969349921534.

The Kyle McDonald Group Set [C[1], C[2], C[3], C[4]]=[1733 0 1721 1723] Corresponds to an elliptic curve of conductor 11600957669426085848222.

The Young Group Set [C[1], C[2], C[3], C[4]]=[1741 0 1747 1753] Corresponds to an elliptic curve of conductor 49041509901414143107070.

The Gerry Callaghan Group Set [C[1], C[2], C[3], C[4]]=[1759 0 1777 1783] Corresponds to an elliptic curve of conductor 26707285435472064591334. Named by Sarah Callaghan for her Dad.

The Madeleine Leidheiser Group Set [C[1], C[2], C[3], C[4]]=[8 0 7 1985] Corresponds to an elliptic curve of conductor 505340998651. Named by Nils Blass.

The Elke Group Set [C[1], C[2], C[3], C[4]]=[1787 0 1789 1801] Corresponds to an elliptic curve of conductor 58779893562687073577422.

The Emma Group Set [C[1], C[2], C[3], C[4]]=[29 0 10 1968] Corresponds to an elliptic curve of conductor 635598612014. Named by Patrick.

The Kiwiokie Group Set [C[1], C[2], C[3], C[4]]=[1811 0 1823 1831] Corresponds to an elliptic curve of conductor 32547242821662244941586. Named by Shaun.

The Billy Sample Group Set [C[1], C[2], C[3], C[4]]=[12 0 0 2008] Corresponds to an elliptic curve of conductor 13525888.

The Dianne Group Set [C[1], C[2], C[3], C[4]]=[1847 0 1861 1867] Corresponds to an elliptic curve of conductor 9345512474654393927438. Named by Davin.

The Rola Al-Hammoud Group Set [C[1], C[2], C[3], C[4]]=[3 3 3 2009] Corresponds to an elliptic curve of conductor 520643420189.

The Implex Group Set [C[1], C[2], C[3], C[4]]=[1871 0 1873 1877] Corresponds to an elliptic curve of conductor 80692188750802744959026. Named by Meredith.

The Garrod Musto Group Set [C[1], C[2], C[3], C[4]]=[16 0 2 2009] Corresponds to an elliptic curve of conductor 262681892848. Named by Garrod's children for his Christmas present.

The Garry Musto Group Set [C[1], C[2], C[3], C[4]]=[10 10 10 10] Corresponds to an elliptic curve of conductor 298600. Named by Garrod for an inspirational father.

The Bencsics Group Set [C[1], C[2], C[3], C[4]]=[12 0 3 87] Corresponds to an elliptic curve of conductor 50085063.

The LEDERMAN Group Set [C[1], C[2], C[3], C[4]]=[1879 0 1889 1901] Corresponds to an elliptic curve of conductor 84199111164843313025306.

The Tamp Lawrence Group Set [C[1], C[2], C[3], C[4]]=[21 0 7 1977] Corresponds to an elliptic curve of conductor 265680465534.

The James Dickson Group Set [C[1], C[2], C[3], C[4]]=[20 0 2 1965] Corresponds to an elliptic curve of conductor 129862983568. Named by Emma Dickson.

The Gwyneth Vaughan Lamboll Group Set [C[1], C[2], C[3], C[4]]=[1907 0 1913 1931] Corresponds to an elliptic curve of conductor 11657705732456630725882. Named by Lori "in honour of our elegant grandmother".

The Keith Group Set [C[1], C[2], C[3], C[4]]=[29 0 5 1922] Corresponds to an elliptic curve of conductor 287854345474. Named by the Lavery family.

The Gimmie Wiekewak Group Set [C[1], C[2], C[3], C[4]]=[1933 0 1949 1951] Corresponds to an elliptic curve of conductor 51362462217075650615474. Named by Calvin.

The Jonathan Blain Group Set [C[1], C[2], C[3], C[4]]=[25 41 12 2009] Corresponds to an elliptic curve of conductor 2244400844581. Named by his brother Nick.

The WEHRWEIN Group Set [C[1], C[2], C[3], C[4]]=[1973 0 1979 1987] Corresponds to an elliptic curve of conductor 14710465782248172436438.

The Lucy Jarman Group Set [C[1], C[2], C[3], C[4]]=[0 0 0 19489] Corresponds to an elliptic curve of conductor 24308551744.

The James Howe Group Set [C[1], C[2], C[3], C[4]]=[30 0 1 2010] Corresponds to an elliptic curve of conductor 2789915804973. Named by Ameli Gottstein for James's birthday. It's actually the prize for the Greenwich Christmas maths competition, which was won for the second year in a row by Ameli Gottstein, and since she already has a group named after her because she won it last year, she's asked for one for James as her birthday present for him!

The Hutchinson-Harte Group Set [C[1], C[2], C[3], C[4]]=[4 5 14 2131] Corresponds to an elliptic curve of conductor 637765256384.

The Michael Group Set [C[1], C[2], C[3], C[4]]=[9 0 7 1987] Corresponds to an elliptic curve of conductor 62433804878.

The Brothbri Group Set [C[1], C[2], C[3], C[4]]=[1993 0 1997 1999] Corresponds to an elliptic curve of conductor 62824653885895079710166.

The Mabey Group Set [C[1], C[2], C[3], C[4]]=[14 0 2 2010] Corresponds to an elliptic curve of conductor 37325897240. "In honor of my husband for Valentine's Day in our name "Mabey." We met in a calculus class so this is a fitting gift."

The Pillinger-Cork Group Set [C[1], C[2], C[3], C[4]]=[2003 0 2011 2017] Corresponds to an elliptic curve of conductor 130904249021155079862106.

The Martin Group Set [C[1], C[2], C[3], C[4]]=[18,0,3,1957] Corresponds to an elliptic curve of conductor 86570025499. Named by Rosemary Phillips for her husband's birthday. "He is a physicist, not a mathematician!"

The Bruce Eyley Group Set [C[1], C[2], C[3], C[4]]=[5 0 3 1961] Corresponds to an elliptic curve of conductor 485757218386. Named by Siobhan and Zac Eyley for their Dad's birthday. "This is an awesome idea, one that I read about in someone else's paper on a very boring train journey and had to steal half a page so I could donate once I got home."

The Katrin Group Set [C[1], C[2], C[3], C[4]]=[2017 0 2027 2029] Corresponds to an elliptic curve of conductor 137433798921676185125674. Named by Jon Sutton.

The Andrew Rivett Group Set [C[1], C[2], C[3], C[4]]=[16 0 3 2010] Corresponds to an elliptic curve of conductor 89126386905. Named by Charlie Khan for Andrew's birthday.

The Paul Cooper Group Set [C[1], C[2], C[3], C[4]]=[23 0 3 2010] Corresponds to an elliptic curve of conductor 356603622. Named by Rachael Graves for Paul's birthday.

The Grifafterbroydandthewilliwizup Group Set [C[1], C[2], C[3], C[4]]=[60 0 60 24] Corresponds to an elliptic curve of conductor 6062416092. For the team that made the best maths clock.

The Joel Rees Group Set [C[1], C[2], C[3], C[4]]=[2039 0 2053 2063] Corresponds to an elliptic curve of conductor 6791656376802946335170.

The Ada Thireou Group Set [C[1], C[2], C[3], C[4]]=[2 0 4 2010] Corresponds to an elliptic curve of conductor 261380113760. Named by Prodromos E. Atlamazoglou for Ada's birthday.

The Eric Werley Group Set [C[1], C[2], C[3], C[4]]=[2069 0 2081 2083] Corresponds to an elliptic curve of conductor 20563241482931075918578.

These objects live in hyperspace, beyond the 3-dimensional world that we inhabit. So it is impossible to draw pictures or make models of them. Instead, we use the powerful language of mathematics and in particular group theory to explore their properties. The complicated formula at the top of the post describes how the symmetries inside this object can be built by taking combinations of 9 basic symmetries called a₁,a₂,a₃,b₁,b₂,b₃,X,Y,Z. The complicated formula tells you how these symmetries interact with each other. For example if you do symmetry a₁ followed by b₂, the formula tells you that that leaves the object in the same position as if you'd first done symmetry X first then b₂ and then a₁.

A similar thing happens with objects we can see. Take a beer mat. Place it on the table. First rotate it 90 degrees clockwise then reflect or flip the mat in the vertical line running down the middle of the mat. This is the same as if I start by rotating the beer mat 180 degrees then flip in the vertical then do the rotation by 90 degrees clockwise.

Each symmetrical object constructed above is unique because the symmetries interact with each other in their own special way. Often these interactions are controlled by the numbers in the date of birth of the person after whom the symmetrical object is named. They are special because the structures of these objects are connected to the arithmetic of elliptic curves. Trying to understand solutions to elliptic curves is one of the big open problems in mathematics related to one of the Clay Millennium Problems (The Birch-Swinnerton-Dyer Conjecture). The elliptic curve associated with each group of symmetries is got by taking the numbers [C[1], C[2], C[3], C[4]] and putting them into the following equation:

Y²+C[1]XY+C[3]Y=X³+C[2]X²+C[4]X.

If you would like to explore a little bit more of the mathematical significance of these groups then these two papers are where the first groups I constructed are explained. But, be warned, you'll probably need a maths degree to understand the intricacies of these papers.

A nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups, Israel J. of Math 126 (2001), 269-288.
Counting subgroups in nilpotent groups and points on elliptic curves, J. Reine Angew. Math. 549 (2002) 1-21.

New Scientist

2008-06-12T10:11:00.001+01:00

Grand Designs: Symmetry's hidden depths An article in the New Scientist about the award of the Abel Prize 2008 to John Thompson and Jacques Tits for their amazing contribution to the classification of finite simple groups.

There is also a New Scientist competition running alongside the article to name one of the symmetrical objects that I have created. Come up the best suggestion and you could win the group! There is an interesting debate about the name going on at the New Scientist bulletin board.

Samuel Johnson Longlist

2008-04-16T09:05:00.000+01:00

Finding Moonshine makes the longlist for the Samuel Johnson Prize for Non-fiction 2008. Having been a judge myself on this prize a few years ago I know what a feat it is to make it through the hundreds of books that the judges have to read.

The Longlist
The Longlist

The 19th Step

2008-04-11T11:21:00.003+01:00

I have been involved in the last three weeks in creating a performance piece in collaboration with composer Dorothy Ker, Choreographer Carol Brown and Sculptor Kate Allen. Dorothy is the composer that features in Chapter 9 of Finding Moonshine. The piece takes three stories by the Argentine writer Borges as an inspiration. The performers include myself, three dancers and three musicians.

We have a blog which has been an integral part of the creative process and contains videos of parts of the performance and rehearsals. It can be accessed via the19thstep.co.uk.

The performance includes me dancing a proof of the irrationality of the square root of 3. Must be a first in the history of mathematics.

Performance details:

7.30pm 9th April, Michaelis Dance Studio, Roehampton University
Roehampton Lane, London SW14 5PU
Tickets £5.00 / £3.00 advance bookings 020 8392 5016

7.30pm 12th April, Studio Theatre, Laban
Creekside, Deptford, London SE8 3DZ
Tickets £5.00 / £3.00 advance bookings 020 8469 9500
or book online

pg 69 test

2008-03-16T15:46:00.005Z

There is an interesting blog which asks authors to comment on whether page 69 is representative of their book. Here is link to the page 69 test of Finding Moonshine. An interesting result. The page describes part of my visit to the Alhambra and discusses the image at the top this post.

US publication

2008-03-14T06:44:00.003Z

The 11th of March saw the US publication of the book. Finding Moonshine has rather strong connotations in America so my US publishers went for a bold upfront title:

SYMMETRY: A Journey into the Patterns of Nature.

Want a group named after you?

2008-03-07T13:01:00.021Z

People have stars named after them, craters on the moon, even comets...but how about having a symmetrical object in hyperspace named after you.

Part of Finding Moonshine narrates my discovery of some new symmetrical objects that have interesting connections with objects in number theory called elliptic curves. During my presentations there is the chance to win one of these groups and have the group named after you. I have created infinitely many of these groups so they won't run out! (I did think of selling them for a dollar a group, like the guy who sold a million pixels for a dollar a pixel and became a millionaire. With infinitely many groups that could make me very rich.)

Here are the groups that have been named so far. Each group specifies what values [C[1], C[2], C[3], C[4]] should take in the presentation of the groups pictured at the top of this post.

The Vandewalle Group. Won in Belgium on 14 December 2007. Set [C[1], C[2], C[3], C[4]]=[1,1,0,-2] Corresponds to an elliptic curve of conductor 102.

The Mitrokhin Group. Won at Imperial College on 19 February 2008. Set [C[1], C[2], C[3], C[4]]=[1,0,0,-8] Corresponds to an elliptic curve of conductor 114.

The Lane Group. Won at the Royal Society on 21 February 2008. Set [C[1], C[2], C[3], C[4]]=[0,1,0,-20] Corresponds to an elliptic curve of conductor 120.

The Sutton Group. Won at the Bath Literary Festival on 23 February 2008. Set [C[1], C[2], C[3], C[4]]=[1,0,1,2] Corresponds to an elliptic curve of conductor 122.

The Chiodo Group. Won in Cambridge on 26 February 2008. Set [C[1], C[2], C[3], C[4]]=[0,-1,1,1] Corresponds to an elliptic curve of conductor 131.

The Course Group. Won at Wanstead Library in the east end of London on 28 February 2008. Set [C[1], C[2], C[3], C[4]]=[0,1,0,3] Corresponds to an elliptic curve of conductor 132.

The Arnott Group. Won at Brighton Science Festival on 2 March 2008. [C[1], C[2], C[3], C[4]]=[0,1,0,-4] Corresponds to an elliptic curve of conductor 136.

The Jones and Rippington Group. Won at Didcot Girl's School as part of Oxford University's Science Week Roadshow on 12 March 2008. The first group to be named after two winners. But after all, many of the sporadic groups are also have two names associated with them, e.g. The Harada-Norton Group. [C[1], C[2], C[3], C[4]]=[0,-1,1,-1] Corresponds to an elliptic curve of conductor 141.

The Cork Group. Won at the Wadham College Mathematics Reunion on 15 March 2008. [C[1], C[2], C[3], C[4]]=[0,1,0,-12] Corresponds to an elliptic curve of conductor 168.

The Vivi Group Won at the Oxford Literary Festival on 3 April 2008 by a young man who very romantically dedicated the group to his girlfriend sitting next to him. [C[1], C[2], C[3], C[4]]=[0,0,1,6] Corresponds to an elliptic curve of conductor 171.

The Stevens Group Won at the Oxford-North American Reunion in New York on the 5 April 2008. [C[1], C[2], C[3], C[4]]=[0,0,1,-3] Corresponds to an elliptic curve of conductor 189.

The McBride Group Won at the Swindon Literary Festival on 15 May 2008. [C[1], C[2], C[3], C[4]]=[0,-1,1,2] Corresponds to an elliptic curve of conductor 201.

The Harris Group Won at the Hay Literary Festival on 31 May 2008. [C[1], C[2], C[3], C[4]]=[1,1,0,2] Corresponds to an elliptic curve of conductor 206.

The Cousins Group Won at the Oxford Science Centre on 18 June 2008. [C[1], C[2], C[3], C[4]]=[1,0,1,1] Corresponds to an elliptic curve of conductor 214.

The Falk Group Won at ESOF 2008 Barcelona on 20 July 2008. [C[1], C[2], C[3], C[4]]=[1,1,1,-5] Corresponds to an elliptic curve of conductor 235.

The Wallis Group Won at The Oxford UK Summer School in Theoretical Chemistry, 11 September 2008. [C[1], C[2], C[3], C[4]]=[1, 1, 0, 16] Corresponds to an elliptic curve of conductor 222.

The Morris Group Won at M500 The Open University's 34th Revision Weekend at Aston University in Birmingham, 13 September 2008. [C[1], C[2], C[3], C[4]]=[0 1, 0, 2] Corresponds to an elliptic curve of conductor 224.

The Keller Group Won at Manchester Grammar School, 16 October 2008. [C[1], C[2], C[3], C[4]]=[0 -1, 1, 1] Corresponds to an elliptic curve of conductor 131.

The Barge and Wright Group Won at a talk given to the Liverpool Mathematics Society, 16 October 2008. [C[1], C[2], C[3], C[4]]=[0, 1, 0, 3] Corresponds to an elliptic curve of conductor 132.

The Stewart-Price-Hawkins Group Won at a talk given to the Kellogg College Gaudy, 24 January 2009. [C[1], C[2], C[3], C[4]]=[0, -1, 1, -1] Corresponds to an elliptic curve of conductor 141.

The Ozaki Group Won at a talk given at the Royal Academy of Arts, 30 January 2009. [C[1], C[2], C[3], C[4]]=[0, 1, 0, -12] Corresponds to an elliptic curve of conductor 168.

The Banga Group Won at the Geary Lecture given at City University, London, 20 March 2009. [C[1], C[2], C[3], C[4]]=[0, 0, 1, 6] Corresponds to an elliptic curve of conductor 171.

If you would like to explore a little bit more of the mathematical significance of these groups then these two papers are where the first groups I constructed are explained:

A nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups, Israel J. of Math 126 (2001), 269-288.
Counting subgroups in nilpotent groups and points on elliptic curves, J. Reine Angew. Math. 549 (2002) 1-21.

YouTube

2008-03-06T07:20:00.003Z

Here are some of my favourite math moments on YouTube. Enjoy!

The Numberwang code "There are numbers everywhere Charles". Mitchell and Webb's take on The Da Vinci Code. Can't help thinking they might have watched The Music of the Primes DVD.

That's Numberwang The maths game show everyone's talking about...after Mindgames that is.

The Numberwang board game I've just got to get it...especially for those 400 sided dice.

Simple Group of Order 2 Perhaps the theme tune for the new book. You have to be a math geek to get the jokes in this one...but if not, just enjoy the jumpers.

Dedicated Teacher I think this guy watched the Christmas Lectures.

Look Around You...Maths This is one of my favourites.

Life after Poincare Find out what Perelman has been up to...

And a couple of YouTube videos featuring the author.

Infinity of Primes Euclid's proof of the infinity of primes with some help from my football team Recreativo Hackney.

Big Ball Opening sequence to Lecture 2 of the Christmas Lectures. Who said mathematics wasn't fun.

Reviews

2008-02-28T10:16:00.006Z

The book has been reviewed extensively.

Sunday Times Lisa Jardine reviewed the book for the Sunday Times and described it as "mesmerising".

The Guardian Tim Radford thought "Finding Moonshine adds up to a wonderful read. This is a marvellous account of a 4,000-year obsession with symmetry and the secret language of nature."

Daily Telegraph The flip, twirl and shuffle of symmetry. Ed Lake finds it "hard to resist Moonshine's cocktail of anecdote, swashbuckling potted history and haphazard self-revelation."

Sunday Telegraph The beauty of Patterns. "Marcus du Sautoy knows how to tell a story and, even more important, how to make difficult ideas palatable and even entertaining" write Graham Farmelo.

The Economist Mirror Games. "It makes for a fascinating and absorbing read."

Times Higher Education Chosen as Book of the Week. Reviewed by Timothy Gowers, Rouse Ball Professor of Mathematics at the University of Cambridge. "he has pulled off that rare feat of writing in a way that can entertain and inform two different audiences - expert and non-expert - at the same time...What makes the organisation of the book so successful is that it allows du Sautoy to develop one part of his story and then leave you in suspense while he moves on to another. This is of course a well-known literary device, and du Sautoy is very good at using it: he knows just how much information to reveal to keep you interested. The result is a gripping book with a strongly novelistic flavour."

Independent A monster hit for the maths world. Reviewed by Apostolos Doxiadis, author of Uncle Petros and the Goldbach Conjecture. "At the book's core is the mathematical story, which du Sautoy tells with the narrative flair and storyteller's sense of detail, development and suspense also exhibited in his first book, The Music of the Primes. ... it gives an inspiring testimony of what it is like to be a research mathematician."

Sunday Independent Symmetry is an asset prized by nature and man alike. Just ask a mathematician. Reviewed by Simon Ings. "Finding Moonshine is a superlative mathematical entertainment; not pretty to the purist eye, but oh, so effective."

Financial Times The nature of symmetry. "Even if you understand little of the mathematics involved, it’s a fascinating tale " writes Alan Cane.

Nature Multi-dimensional lives. Mark Ronan: "a delightful account".

Talks

2008-02-28T08:29:00.008Z

Finding Moonshine: A Mathematician's Journey Through Symmetry

The following is a partial list of talks that I have given or am about to give based on the book.

6 September 2007 Mantova Festivaletteratura Festivaletteratura

25 September 2007 Venice, CP Snow Anniversary Meeting.

14 December 2007 Leuven University, Kotriijk, Christmas Lecture

19 February 2008, Royal Institution, Imperial College Royal Institution The lecture can be viewed online at the Imperial College website

21 February 2008, Royal Society, Fourth Estate Lecture Series Royal Society This event was filmed and is archived at Video Archive

23 February 2008 Bath Literary Festival.

26 February 2008 University of Cambridge.

28 February 2008 Newham Bookshop event at Wanstead Library 7pm. Newham Bookshop

2 March 2008 Brighton Science Festival 1.30 Brighton Science Festival

12 March 2008 Oxford Science Week Roadshow, Didcot Girls School 6pm Oxford Science Roadshow

15 March 2008 Wadham Mathematics Alumni Meeting, Oxford

3 April 2008 Oxford Literary Festival, 8pm Oxford Literary Festival

5 April 2008 Oxford American Reunion, New York.

31 May 2008 Hay Literary Festival.

5 June 2008 Cheltenham Science Festival.

18 June 2008 Oxford Science Centre. You can see a video of this talk Pulse Project

Il Disordine Perfetto

2007-12-26T09:55:00.000Z

If you can't wait for the English edition then Finding Moonshine has already been published in Italian by Rizzoli. Launched at the Mantova Literary Festival at the beginning of September 2007, IL DISORDINE PERFETTO shot to number 13 (a prime of course) on the non-fiction best seller list.

More about the author

2007-12-21T08:08:00.000Z

Marcus du Sautoy is Professor of Mathematics at the University of Oxford and a Fellow of Wadham College. He is Senior Media Fellow at the EPSRC. He has been named by the Independent on Sunday as one of the UK's leading scientists. In 2001 he won the prestigious Berwick Prize of the London Mathematical Society awarded every two years to reward the best mathematical research made by a mathematician under 40. In 2004 Esquire Magazine chose him as one of the 100 most influential people under 40 in Britain and in 2008 he was included in the prestigious directory Who’s Who. He is author of numerous academic articles and books on mathematics. He has been a visiting Professor at the École Normale Supérieure in Paris, the Max Planck Institute in Bonn, the Hebrew University in Jerusalem and the Australian National University in Canberra.

Marcus du Sautoy is author of the best-selling popular mathematics book "The Music of the Primes" published by Fourth Estate in 2003 and translated into 10 languages. It has won two major prizes in Italy and Germany for the best popular science book of the year. His new book “Finding Moonshine: a mathematician’s journey through symmetry” is also published by Fourth Estate in February 2008.

Marcus du Sautoy writes for the Times, Daily Telegraph, Independent and the Guardian and is frequently asked for comment on BBC radio and television. He has written and presented several series for radio including 5 Shapes for BBC radio 4 in 2004 and Maths and Music for the Essay on BBC radio 3 in 2007. He is also presenter of BBC4’s TV game show Mind Games, for which he has been nominated for the Royal Society of Television’s Best Newcomer to a Network award. In 2005 he presented a one hour documentary for BBC4 and BBC2 based on his book The Music of the Primes. He gave the Royal Institution Christmas Lectures in 2006 entitled THE NUM8ER MY5TERIES, broadcast on Channel Five. He is currently writing and presenting a four part landmark series for the BBC called The Story of Maths which will be broadcast in Autumn 2008. His presentations on mathematics, which include “Why Beckham chose the 23 shirt”, have played to a wide range of audiences: from theatre directors to bankers, from diplomats to prison inmates.

Marcus du Sautoy plays the trumpet and football. Like Beckham he also plays in a prime number shirt, no 17, for Recreativo FC based in the Hackney Marshes. Born in 1965, he lives in London with his wife, three children and cat Freddie Ljungberg.

Welcome

2007-12-21T07:28:00.000Z

"Finding Moonshine: a mathematician's journey through symmetry" is published in the UK by Fourth Estate on the 4th of February 2007. It will also be published in the US by HarperCollins on the 5th of March with the title SYMMETRY.

This new book from the author of 'The Music of the Primes' combines a personal insight into the mind of a working mathematician with the story of one of the biggest adventures in mathematics: the search for symmetry. This is the story of how humankind has come to its understanding of the bizarre world of symmetry -- a subject of fundamental significance to the way we interpret the world around us. Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, from the pyramid to the pentagon. 'Symmetry' indicates a dynamic relationship or connection between objects, and it is all-pervasive: in chemistry and physics the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; symmetry and the breaking of symmetry are central to ideas in art, architecture and music; the mathematics of symmetry is even exploited in industry, for example to find efficient ways to store more music on a CD or to keep your mobile phone conversation from cracking up through interference.