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Fermat's last theorem

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Pierre de Fermat
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I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.
—Pierre de Fermat
I have an elegant refutation of your attempted proof, but unfortunately this page is not large enough to contain it.

Fermat's last theorem[1] states that in the equation, A^n+B^n=C^n, if A,B,C are positive integers,[2] n cannot be an integer greater than 2. Fermat wrote in the margin of a book that he had a proof of the theorem, but it would not fit in the margin. He died in 1665 before ever revealing it, and his note was discovered posthumously by his son.[3][4] Fermat must have realized that his imagined proof was flawed, because he later wrote a proof of the special case n = 4 (in which he introduced the method of proof by infinite descent).

In 1994, Andrew Wiles presented a proof of the theorem, using 20th century mathematical principles (modular forms, Galois theory, algebraic geometry). A mistake was discovered, which Wiles repaired after about a year of work with his former student Richard Taylor, with the final proof published in 1995. The theorem built on an earlier theorem of Ken Ribet following a program of Serre. The full modularity theorem was proved in 1998 based on the techniques of Wiles.


  1. Singh, Simon (1997). Fermat's Last Theorem. Fourth Estate. ISBN 1-85702-669-1.
  2. Also known as "counting numbers", to fourth grade mathematicians.
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