Some time around 1637 Pierre de Fermat made the most famous marginal note in the history of mathematics:
'To resolve a cube into the sum of two cubes, a fourth power into two fourth powers, or in general any power higher than the second into two of the same kind, is impossible; of which fact I have found a remarkable proof. The margin is too small to contain it.'
This statement came to be known as Fermat's Lost Theorem.
On Wednesday 23 June 1993 Andrew Wiles announced a proof, which was widely acclaimed by experts. Early in 1994 a number of difficulties emerged among them a subtle logical gap. By the autumn of 1994 some experts were estimating that it would take at least three years of hard work to complete the proof, and others thought the gap might not be filled at all. Then, in October 1994, Wiles announced that he had overcome this final stumbling block.
This lecture will describe the history of Fermat's Last Theorem from ancient Greece to the present day, discuss Wiles' methods, and examine the current status of his proof.