Solving a 350 year old maths puzzle

Last week, one of the world's largest mathematical prizes was handed out in Norway. It was given to Andrew Wiles for solving what's known as Fermat's Last Theorem a famous 350 year old problem in number theory. We sent our reporter Timothy Revell along to find out who won, and why, and to soak up the mathmosphere!

Timothy - Did you know there's no Nobel Prize for mathematics. Well every mathematician does and they're pretty sure they know why...

Mathematician 1 - Nobel's wife ran off with a mathematician...

Mathematician 2 - Nobel's wife had an affair with a mathematician...

Timothy - I heard this story from so many different sources whilst studying for my degree in maths that I was convinced it just had to be true. But when I looked it up, it turned out that Nobel didn't even have a wife...

Mathematician 3 - The truth is, Nobel just wasn't really interested in mathematics. He didn't believe, as he should have done, that mathematics was a fundamentally important field for mankind...

Timothy - Which means in maths, instead of the Nobel prize, there's the Abel prize, named after the Norwegian 19th century mathematician, Niels Henrik Abel, which was awarded last week...

Compere - As the President of the Norwegian Academy of Science and Letters, it's my pleasure and privilege to announce the winner of the Abel prize 2016 to Sir Andrew Wiles.

Applause!

Timothy - Last week, some of the greatest mathematicians from around the world gathered in Oslo to celebrate this year's Abel prize winner. There was a serious buzz, the champagne flowed, and even the Norwegian Crown Prince attended. And whilst I was there I bumped into author Simon Singh to find out why Sir Andrew Wiles was getting this year's prize...

Simon - 350 years ago, Pierre de Fermat said that he could prove that this equation had no solutions but he never told us what that proof was. It's like having a buried treasure. Somebody says they buried the treasure somewhere but they're not telling you where the treasure is, and so every other mathematician in the world has been treasure hunting - has been looking for this proof, trying to rediscover that Fermat said he had all those centuries ago.

Timothy - Pierre de Fermat was a French mathematician who, in the 17th century, was working through his favourite maths book when he started to think about square numbers and how to split them up.  25 is a square number he thought because it's 5 x 5, but 25 can also be split up into two smaller square numbers - 16 which is 4 squared, and 9 which is 3 squared which, when added together, give back 25.

Carrying on this thought, Fermat wondered if cubed numbers could be split into two cubes or 4th powers split into two other 4th powers, but he could never find an example. Instead he declared that for anything higher than squares, this type of number split was impossible. But then he died, and his proof was never found and proved pretty difficult to reconstruct.

Simon - Every century, mathematicians tried to prove Fermat's last theorem and every century they failed, and the more they failed, the more of a precious problem this became. But still nobody could find the proof until Andrew Wiles came along. He was one of the few people in the world who had the audacity to think he could even try to prove Fermat's last theorem.

Andrew - I'm Andrew Wiles. I'm a Professor at Oxford - the Royal Society Research Professor. When I was a 10 year old I was visiting a public library in Cambridge and just rummaging along the math's shelf and I came across this book by E.T. Bell, and on the cover it described this problem. So I spent my teenage years trying to solve it, and actually had to stop myself when I became a professional mathematician and realised the methods available at that time had really gotten nowhere for a hundred years. So it would have been rather arrogant to devote too much time to it as a professional mathematician.

Timothy - But then, the game changed. Mathematicians proved that there was a completely new way to tackle Fermat's last theorem by connecting it to another completely different unsolved problem. The new mathematics said that anyone that could solve this new problem would solve Fermat's last theorem as well.

Andrew - The moment I heard about that I remember exactly where I was. I was having tea somewhere and someone told me about this, and I was in shock and immediately I started working on the problem. I believed I could solve it but, possibly, not in my lifetime.

Timothy - Wiles then withdrew from the mathematical community opting to work secretly, completely alone for over seven years, toiling away until he eventually solved Fermat's last theorem once and for all. He felt elated but also a certain sense of sadness for his mathematical quest being over.

Andrew - I have to say, there's a tiny feeling of losing something. I'd been a very private enterprise and once you share it with the world, you're sharing it.  And it had been my nonstop companion for years by this point and now I was passing it on.

Timothy - Once Wiles shared his proof with the world, he shot to fame and was even offered a modeling contract as well as having a musical written about him - not bad for just proving a theorem. Wiles has received a lot of prizes for his mathematics over the years and now, he can an Abel prize to his trophy cabinet as well.

Andrew - It is a pleasure to express my deep gratitude to the Norwegian Academy of Science and Letters, and to the Abel Committee for awarding me this prize. Thank you.

Applause!