Overview

But one cannot split a cube into two cubes, nor a fourth power into two fourth powers, nor in general any power in infinitum beyond the square into two like powers. I have uncovered a marvelous demonstration indeed of this, but the narrowness of the margin will not contain it.

These words, written by Pierre de Fermat (1601-1665) in the margin of his copy of Diophantus's Arithemetica, have challenged and sometimes haunted mathematicians for more than 350 years. When a successful proof of Fermat's Last Theorem was finally found in 1993, it ended centuries of interesting and often controversial attempts to solve this famous problem.

Background

In modern algebraic terms, the theorem states that the equation xⁿ + yⁿ = zⁿ has no whole number solutions for n > 2. If n = 2, we have the famous...