## Plus Blog

November 12, 2008
Wednesday, November 12, 2008

### Mathematical moments — Yutaka Taniyama

Born on the 12th of November 1927 in Kisai, Japan
Died on the 17th of November 1958 in Tokyo, Japan

Taniyama's name is associated with one of the most famous problems in mathematics: Fermat's last theorem. The theorem says that for any whole number n strictly greater than 2, there are no three non-zero whole numbers x, y and z such that xn + yn = zn. Almost 400 years ago Fermat scribbled in the margin of a book that he had a proof for this assertion, which didn't fit in the margin. It wasn't until the 1990s that the theorem was finally proved by Andrew Wiles — and the proof definitely couldn't have been written in any margin!

Andrew Wiles didn't actually prove Fermat's last theorem, but a conjecture which now carries Taniyama's name. In 1955 Taniyama, who was working in algebraic number theory, posed a problem concerning so-called elliptic curves — these are curves defined by points in the plane whose co-ordinates satisfy a particular type of equation. Goro Shimura and André Weil mused over the question and formulated a conjecture: that every elliptic curve should come with a modular form, a mathematical object that is symmetrical in an infinite number of ways. This is now known as the Taniyama-Shimura-Weil conjecture.

The link to Fermat's last theorem was made around 30 years later, when the mathematician Ken Ribet realised that if Fermat's last theorem were false, then this would mean that a particular elliptic curve comes without a modular form. In other words, if Fermat's last theorem were false, then the Taniyama-Shimura-Weil conjecture would be false also. Reformulating this yet again, if the Taniyama-Shimura-Weil conjecture is true, then so is Fermat's last theorem. What Andrew Wiles proved is that the Taniyama-Shimura-Weil conjecture is indeed true for a class of examples that is sufficient to prove Fermat's last theorem. QED.

In 1958, just days after his 31st birthday and not long before he was meant to get married, Taniyama committed suicide. His explanation was this: "Until yesterday I had no definite intention of killing myself. ... I don't quite understand it myself, but it is not the result of a particular incident, nor of a specific matter."

To find out more about Fermat's last theorem and its proof, read the Plus articles Fermat's last theorem and Andrew Wiles and How maths can make you rich and famous.

posted by Plus @ 4:58 PM

At 10:34 AM,  Kuldeep said...

I don't know Taniyama committed suicide. Interesting article.

November 12, 2008
Wednesday, November 12, 2008

Why are some people generous and others selfish? There's no doubt that both strategies pay off under certain circumstances, but research (as well as everyday experience) shows that we are not mere opportunists — some people simply are nicer than others. This raises a question which intrigues evolutionary psychologists: is there a selective force that works in favour of a wide range of personalities, preventing us from all evolving the same optimal character trait? A possible answer has recently been published by mathematicians from the universities of Bristol and Exeter.

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posted by Plus @ 11:44 AM

At 8:12 PM,  Anonymous said...

Can the people who did this research be trusted? How can we be sure they are not motivated by selfish reasons?

At 5:46 PM,  Anonymous said...

this seems to be simply a re hash of robert axelrod's theory of co operation??
i dont see anything new

November 7, 2008
Friday, November 07, 2008

There are three new singing stars on the block, but you're unlikely to hear them on Radio 1. The musical talents of HD49933, HD181420 and HD181906, three nearby stars which are hotter and larger than our Sun, were discovered by a group of scientists, led by Eric Michel, using data from the CoRoT space-based telescope. Michel and his colleagues accurately measured accoustic vibrations in these stars that not only make for eerie listening, but also could reveal important information about how all stars evolve.

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posted by Plus @ 4:25 PM

November 4, 2008
Tuesday, November 04, 2008

### Student poster competition

Are you a university maths student and want to share your passion with younger generations? Then why not take part in the second Further Maths Network - Rolls-Royce poster competition? Undergaduate and PGCE maths students from the UK are invited to submit posters conveying the essence of a mathematical topic they have covered at university. The poster should be aimed at school and college students who are studying AS or A level mathematics. Entries from teams of students are welcome. The closing date is the 31st of March 2009, and two winners will receive a prize of £100 each. The winning designs will be printed as A1 posters and sent to schools and colleges registered with the Further Mathematics Network, and others with which FMN centres are in touch, for display in the mathematics department, potentially reaching over 2000 schools and colleges.

Last year's winner, Michael Manfredi, was presented with his prize by Charlie Stripp of the Further Maths Network at the Rolls-Royce Learning and Career Development Centre in Derby (Michael's the one in the picture receiving the cheque!). You can see Michael's winning poster on cryptography on the Further Maths Network Website.

If you want to take part, then email your entry to Janice Richards, including your name(s) and full contact details, with the poster attached as an editable file. For more information, contact Richard Browne.

And if you prefer writing to designing posters, don't forget the Plus new writers award 2009. Anyone can enter, and there are special categories for university and school students. Winners will achieve everlasting fame through publication in Plus, and receive iPods and books. Closing date is the 31st of March 2009.

posted by Plus @ 12:01 PM

November 1, 2008
Saturday, November 01, 2008

### Election questions

Gaffes, murder plots, and hockey mums — the US election circus is in full swing. Personality politics is partly a consequence of the first-past-the-post system — but what are the alternatives? Can any system guarantee to represent the will of the people? Do opinion polls manage to capture its voice? The following selection of Plus articles provides mathematical answers, insights and paradoxes.

posted by Plus @ 1:24 PM

November 1, 2008
Saturday, November 01, 2008

With US election week upon us, we thought you might appreciate a look at alternatives to the first-past-the-post system used to elect the US President and Congress, as well as the UK government, and many others around the world.