Abel prize for ‘stunning proof

Andrew Wiles, British mathematician, has won the 2016 Abel prize for his “stunning proof of Fermat’s last theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era of mathematics,” (to quote from the citation). Awarded by the Norwegian Academy of Science and Letters, the Abel prize is an international award given for outstanding scientific work in the field of mathematics, including mathematical aspects of computer science, mathematical physics, probability, numerical analysis, scientific computing, statistics and also mathematical applications in the sciences.

Fermat’s last theorem, which looks deceptively simple, is the statement that the equation xⁿ + yⁿ = zⁿ, where x, y and z are positive whole numbers, has no solution for n larger than 2. In what can only be described as tenacious, Professor Wiles worked on this single problem for nearly a decade before making a breakthrough, in the process having to develop a lot of mathematics. Efforts to solve the problem go back 350 years: Pierre de Fermat first formulated the theorem in the 17th century, and he himself proved the claim for n = 4; Leonhard Euler proved the case of n = 3 and Sophie Germain generalised it to infinitely many prime exponents. While Ernest Kummer’s attempts led to major revelations, the bounty of a full proof eluded all concerned until Professor Wiles proved it in 1994. R. Balasubramanian, a well-known number theorist and former director of Institute of Mathematical Sciences, Chennai, declares his happiness at the award to professor Wiles: “He more than deserves the award, and I can’t think of anyone else who is better qualified [for the award]. It is a herculean task and he worked on this problem alone for the last ten years!... he proved the Shimura-Taniyama-Weil conjecture to the extent needed and for this he had to develop a lot of mathematics… which has applications to the Diophantine equations,” he says.

A story of Wiles' pursuit of thesolution, well known among mathematicians, can be narrated: While at Princeton, Andrew Wiles started his work on this problem and for seven years worked alone, in his attic, without telling anyone and after seven years, announced that he had solved it, in a conference in Cambridge, U.K., only to have a serious mistake pointed out by a colleague a few months later. He was not to be outdone and with help from his former student Richard Taylor, he patched up the gap and proved it successfully a year later. “Many people believe that if only he had been less than 40 years , he would have surely won the Fields Medal. This is a fantastic proof,” says Prof. Balasubramanian. According to an article in Nature, the two papers he published on this work in 1995 took up the entire issue of Annals of Mathematics.

“His work has made it easier to study elliptic curves and modular forms. It is a step ahead towards the Langlands programme,” says Prof. Balasubramanian, naming some sought-after areas of mathematics. Professor Wiles now aims to work on the Birch and Swinnerton-Dyer conjecture — a problem which has a million dollar prize attached. It is one of the seven millennium problems, only one of which, the Poincare conjecture, has been solved by Grigori Perelman, so far.

One cannot help but recall John Nash here who won the prize last year, and also that once the prize has gone to an Indian-origin mathematician Srinivasa Varadhan.