1 / 7

Proving Fermat’s last theorem

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

hester
Download Presentation

Proving Fermat’s last theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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: xn + yn = zn 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 FLT • Taniyama-Shimura Conjecture • All elliptic curves can be expressed as 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

More Related