Proof of Fermat Last Theorem
Demostración del último teorema de Fermat
- Date
- 1994 (anuncio 1993) · confidence high
- Place
- Princeton (New Jersey) and Cambridge (England)
- Credited to
- Andrew Wiles, with Richard Taylor to close the gap
- People
- 👤 Andrew Wiles1953–
- Field
- Knowledge & symbols
What was discovered
A proof of the Taniyama-Shimura modularity conjecture for semistable elliptic curves, which, by Frey, Serre and Ribet, implies Fermat's theorem. It closes a problem that had been open for 357 years using the most advanced machinery of number theory.
The announcement in Cambridge in June 1993 contained an error, corrected in September 1994 with Taylor's help.
What it led to
- the full modularity theorem (2001)
- advances in the Langlands programme
- the Sato-Tate conjecture and the Taylor-Wiles method
Built on
- Early algebra (Diophantus' Arithmetica)c. 250 CE
- Taniyama-Shimura conjecture1955-1957
- Zero-knowledge proofs and elliptic-curve cryptography1985
- Ribet's theorem1986
- modular forms
- epsilon conjecture (Ribet, 1986)
- Iwasawa theory