# Fermat's Last Theorem

- kind: problem
- status: solved (evidence tier V3)
- year: 1637
- authors: Pierre de Fermat, in a margin

**Statement.** No positive integers $a, b, c$ satisfy $a^n + b^n = c^n$ for any $n > 2$.

For 358 years it produced whole fields of mathematics as by-products, from Kummer's ideal numbers onward. The end came indirectly. Frey, Serre and Ribet showed that a counterexample would give an elliptic curve that could not be modular. Wiles then proved enough of the modularity conjecture to rule that curve out. The theorem itself was a corollary of a much larger structure.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1637, Pierre de Fermat, in a margin. Closed 1995, Andrew Wiles, with Richard Taylor.

## Related problems

- Progress here drew on [Modularity theorem](/wiki/Problem:modularity-theorem.md), whose resolution the original curation lists as unlocking it; the argument for the link has not been written yet.

## Sources

- [Wikipedia: Fermat's Last Theorem](https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem)

[Number theory](/wiki/Space:number-theory.md) · [Mathematics](/wiki/Continent:mathematics.md)

## Relations

- uses [modularity-theorem](/wiki/Problem:modularity-theorem.md) — Progress here drew on Modularity theorem, whose resolution the original curation lists as unlocking it; the argument for the link has not been written yet.

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Revision 10, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Problem:fermats-last-theorem?action=history. Edit: POST /api/wiki/page/Problem:fermats-last-theorem {source, summary, base_rev: 10}.