1. Proving Fermat’s last theorem FLT and lessons on the nature and practice of mathematics

2. The theorem There is no (non-zero) solution where x,y,z are integers and n>2 for: x n + y n = z n Fermat writes in a margin that he has a marvellous proof, but there’s not enough space to present it.

3. It looks like it must be true, but there’s no proof. Why does that matter?

4. Proving FLTFLT Taniyama-Shimura ConjectureConjecture All elliptic curves can be expressed as modular functions.elliptic curves modular functions It doesn’t matter for our purposes if you don’t know what that means!

5. Epsilon conjecture (Frey) – If FLT is false, then there can be non-modular elliptic curves. Bit of logic – if p, then q. q is false. So p is false (modus tollens). So…

6. … if we can prove Frey and then prove the Taniyama-Shimura Conjecture… FLT is true.

7. Lessons about maths Comprehensive knowledge Connections Insight or intuition Authority