Back in 1997, Simon Singh – science writer extraordinaire and occasional Uncaged Monkey – directed a documentary about Fermat’s Last Theorem that went on to win the ‘Best Documentary’ award at the BAFTAs and an Emmy Award nomination in the States.

The documentary tells the story of the British mathematician Andrew Wiles, who devoted the best part of 10 years of his life to solving this theorem and fulfilling his childhood dream. One particularly moving passage sees Wiles on the verge of tears as he recounts the moment that the proof finally clicked:

For those who are yet to be acquainted with Monsieur Fermat (rhymes with ‘grandma’, not ‘cat’), he was a French lawyer and mathematician who lived during the 17th century. Although Fermat did a lot of other very useful maths during his lifetime, his most enduring legacy is his ‘Last Theorem’, which states that no three positive integers a, b, and c can satisfy the equation a^{n} + b^{n} = c^{n} for any integer value of n greater than two.

This means that there are solutions for a^{2} + b^{2} = c^{2} (otherwise known as Pythagoras’ theorem, that stalwart of GCSE maths), but that there are no solutions for a^{3} + b^{3} = c^{3}, or a^{4} + b^{4} = c^{4}, or a^{5} + b^{5} = c^{5}, and so on until infinity. The theorem itself is therefore remarkably simple – the proof less so. Scribbling in the margin of one of his textbooks, Fermat claimed that he had found the proof but that it was too lengthy to write down, unwittingly banishing his theorem to the Dingy Dungeons of Unsolved Problems.

Andrew Wiles presenting his proof of Fermat's Last Theorem during a lecture in 1993

Andrew Wiles’ proof came 358 years after the theorem was first conjectured by Fermat. Interestingly, because Wiles used mathematical techniques developed in the 20th century, his proof must have been different from that of Fermat. In fact, most mathematicians today doubt that Fermat had a full proof of his theorem (i.e. for all values of n).

The story of Wiles, his colleagues, and their relentless drive to understand one of math’s greatest mysteries is worthy of a Hollywood blockbuster, encompassing heroes, rivals, treasure, a suicide, and plenty of (non-evil) geniuses. The full 45-minute documentary can be viewed online here, and if anyone knows of any equally awesome maths-themed documentaries/books out there, I’m all ears!

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