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

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Presentation transcript:

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

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.

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

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!

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…

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

Lessons about maths Comprehensive knowledge Connections Insight or intuition Authority