Showing posts from May, 2011

Fermat’s Last Theorem

[Concrete/Interesting] A while back I saw a BBC Horizon programme about Fermat’s Last Theorem and the mathematically heroic work by Andrew Wiles in raising the Taniyama-Shimura conjecture from a mere conjecture to a theorem and using this to show a contradiction between the predictions of the epsilon conjecture and Wiles’ proof that all such elliptic curves must be modular. This contraction implies there are no solutions to Fermat’s equation, hence Fermat’s equation is true.   Like many, I was excited about this proof and although difficult to follow (Elliptic Curves are hard to understand, no kidding), the proof was without a doubt a clever piece of late 20th century mathematical wizardry, full of deep insight and imagination. But something was wrong. It was all to clever, all too complex, all to contemporary. So to mark the birth of my new baby boy, Khaliq, I decided to provide a simple proof, maybe not complete in mathematical rigor and probably nowhere near robust enough for