Fermat's last theorem
| Part of a|
convergent series on
“”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 states that in the equation, , if are positive integers, 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. 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.
- Singh, Simon (1997). Fermat's Last Theorem. Fourth Estate. ISBN 1-85702-669-1.
- Also known as "counting numbers", to fourth grade mathematicians.