Introduction to Fermat's Last Theorem and the idea of proof
The background to Fermat's Last Theorem is explored, beginning with and building on Pythagoras' theorem. Andrew Wiles and others explain that Fermat set out his problem, but was unable to write his proof down. The concept of mathematical proof is then explained, showing that you'd need to try an infinite number of numbers to be able to check Fermat numerically. This is not satisfactory to mathematicians, who want rigorous proof.