Happy Birthday Andrew Wiles

Happy 60th birthday Andrew Wiles, eminent British mathematician, most famous for his proof of Fermat's Last Theorem.

Andrew Wiles. Image courtesy of Wikipedia.

In the summer of 1986, based on the progress made by fellow mathematicians, Andrew Wiles realised that a proof of a limited form of something known as the modularity theorem might then be in reach, which would be a crucial step to a proof of Fermat's Last Theorem. In secrecy, Wiles dedicated all of his research time to this problem. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. In August that year, it turned out that the proof contained a gap. Wiles tried to fill in this gap, but found out that the error he had made was significant. The key idea for circumventing this problem came to Wiles on 19 September 1994. Together with his former student Richard Taylor, he published a second paper explaining this work-around and in doing so, the proof was complete. Both papers were published in 1995 in a special volume of the Annals of Mathematics.

Fermat's Last Theorem had thwarted and tantalized mathematicians for 350 years. Hundreds of attempts had been made at its proof, both by professionals and amateurs. Until its proof, it was probably the most famous unproven result in all of mathematics. When Fermat published his conjecture, that

has no integer solutions for n>2, he also wrote in the margin of his book that he had discovered a truly remarkable proof, but that he did not have enough space to write this proof down. We still do not know what was going through Fermat's mind at this point, but it is likely his proof was flawed. One thing is certain: it was not the same as Wiles's proof, which relies on an enormous amount of twentieth century mathematics that Fermat had no access to.