{"id":"fermats-last-theorem","domain":"named-results","also_in_domain":"number-theory","type":"Theorem","title":"Fermat's Last Theorem","slug":"fermats-last-theorem","url":"/mathematics/named-results/fermats-last-theorem/","statement":"No positive integers a, b, c satisfy a^n + b^n = c^n for any integer n > 2.","conjectured":"1637, Pierre de Fermat","proved":"1994, Andrew Wiles (published 1995)","summary":"Conjectured by Fermat in a margin note in 1637; proved by Andrew Wiles in 1994 after 358 years, via the Modularity Theorem connecting elliptic curves and modular forms.","timeline":[{"year":1637,"event":"Fermat states conjecture"},{"year":1770,"event":"Euler proves n=3"},{"year":1825,"event":"Legendre and Dirichlet prove n=5"},{"year":1839,"event":"Lamé proves n=7"},{"year":1850,"event":"Kummer proves regular primes"},{"year":1994,"event":"Wiles completes proof (with Taylor fixing 1993 gap)"}],"added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Wiles, A. (1995). Modular elliptic curves and Fermat's Last Theorem. Annals of Mathematics, 141(3), 443–551."},{"tier":1,"citation":"Taylor, R. and Wiles, A. (1995). Ring-theoretic properties of certain Hecke algebras. Annals of Mathematics, 141(3), 553–572."},{"tier":2,"citation":"Cornell, G., Silverman, J.H. and Stevens, G. (eds.) (1997). Modular Forms and Fermat's Last Theorem. Springer."},{"tier":3,"citation":"Singh, S. (1997). Fermat's Enigma. Walker & Company."}],"relationships":[{"type":"special_case_of","target":"pythagorean-theorem","label":"n=2 has infinite solutions"},{"type":"uses","target":"galois-theory","label":"Galois representations"},{"type":"key_person","target":"wiles-andrew","label":"Andrew Wiles"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.3"}