Fermat's Last Theorem

In about 1630 Fermat was reading a recently published translation of Arithmetica by Diophantus of Alexandria. He was making notes in the margin and at one point he entered:

To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

Today I have seen the documentary about the Andrew Wiles' proof of Fermat's theorem. ( Link to video: [ here ] )