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Fermat's Last Theorem

Pierre de FermatAndrew WilesRichard Taylor

This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method

For everyone

In 1637 Fermat wrote in the margin of a book that aⁿ + bⁿ = cⁿ has no solution in positive integers for n > 2, and that he had "a marvellous proof". No proof was found for 358 years, until Andrew Wiles published one in 1995.

For specialists

Wiles proved that semistable elliptic curves over Q are modular (the semistable case of the Taniyama–Shimura–Weil conjecture). Via the Frey curve and Ribet's proof of the ε-conjecture (1986) this implies Fermat's Last Theorem. A gap in the 1993 version was closed in joint work with Taylor showing that certain Hecke algebras are complete intersections. The full modularity theorem was completed in 2001 by Breuil, Conrad, Diamond and Taylor.

Claims

Evidence

Supporting

Mathematical proof

The Wiles and Taylor–Wiles papers were published after peer review in the Annals of Mathematics and examined in detail by the mathematical community.[1][2]

Challenging

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Positions

On Fermat's claimed "marvellous proof"
There is no record that Fermat possessed so general a proof; only his proof for the case n = 4 is known.[3]

Connections

Parent

Mathematics

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Sources

  1. ArticleWiles, A. (1995). Modular elliptic curves and Fermat's Last Theorem. Annals of Mathematics 141(3), 443–551DOI 10.2307/2118559archive
  2. ArticleTaylor, R.; Wiles, A. (1995). Ring-theoretic properties of certain Hecke algebras. Annals of Mathematics 141(3), 553–572DOI 10.2307/2118560archive
  3. WebFermat's last theorem. MacTutor History of Mathematics, University of St Andrewsmathshistory.st-andrews.ac.ukarchive

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Cite this page

APA

Athena contributors. (2026). Fermat's Last Theorem. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/fermat-wiles/

BibTeX
@misc{athena_fermat_wiles,
  title        = {Fermat's Last Theorem},
  author       = {{Athena contributors}},
  year         = {2026},
  howpublished = {\url{https://latifkedi.github.io/athena/en/d/fermat-wiles/}},
  note         = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}

Added: September 27, 2026 · Last changed: September 27, 2026 · Page history

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