Fermat's Last Theorem is one of the most famous math problems in history, as it remained unsolved for well over 300 years -- and Fermat himself, before his suicide, had written a margin note claiming he had a solution. Fellow _floss blogger Casey Johnston described FLT like so last year:
In 1637, Pierre de Fermat scribbled a note in the margin of his copy of the book Arithmetica. He wrote (conjectured, in math terms) that for an integer n greater that two, the equation an + bn = cn had no whole number solutions. He wrote a proof for the special case n = 4, and claimed to have a simple, “marvellous” proof that would make this statement true for all integers. However, Fermat was fairly secretive about his mathematic endeavors, and no one discovered his conjecture until his death in 1665. No trace was found of the proof Fermat claimed to have for all numbers, and so the race to prove his conjecture was on. For the next 330 years, many great mathematicians, such as Euler, Legendre, and Hilbert, stood and fell at the foot of what came to be known as Fermat’s Last Theorem. Some mathematicians were able to prove the theorem for more special cases, such as n = 3, 5, 10, and 14. Proving special cases gave a false sense of satisfaction; the theorem had to be proved for all numbers. Mathematicians began to doubt that there were sufficient techniques in existence to prove theorem. Eventually, in 1984, a mathematician named Gerhard Frey noted the similarity between the theorem and a geometrical identity, called an elliptical curve. Taking into account this new relationship, another mathematician, Andrew Wiles, set to work on the proof in secrecy in 1986. Nine years later, in 1995, with help from a former student Richard Taylor, Wiles successfully published a paper proving Fermat’s Last Theorem, using a recent concept called the Taniyama-Shimura conjecture. 358 years later, Fermat’s Last Theorem had finally been laid to rest.
In 1996, Simon Singh and John Lynch made a 45-minute documentary about Wiles and his FLT solution. It's a surprisingly engaging story, with twists and turns and math and problem-solving (also liberal use of Penguin Cafe Orchestra in the soundtrack). Wiles comes across as a genuine mathematician -- he was obsessed with FLT since boyhood, and his joy at its solution is clearly visible in this film. It's all available on Google Video, embedded below. Have a look if you're even vaguely interested in math! (Note: the math discussed in the film is aimed at a mainstream audience; you don't have to be a math whiz to get the human drama of the story.)