Fermat's last theorem states that for all whole number $n \geq 3$, the only integer solutions to the equation $x^n + y^n = z^n$ must have at least one of $x$, $y$, or $z$ being zero. Fermat claimed to have a proof of this theorem in the 17th Century, but there is no evidence he did. Andrew Wiles, aided by Richard Taylor, proved Fermat's Last Theorem in 1995. Well before Wiles' proof, there were strong reasons to believe the theorem was true, coming from a different part of Mathematics: geometry. In this talk I will explain the geometry behind Fermat's equation.
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