Andrew Wiles

Andrew Wiles is an English mathematician whose proof of Fermat’s Last Theorem established a major link between elliptic curves and modular forms.

Gerhard Frey: Gerhard Frey is a German mathematician whose proposed elliptic curve connected Fermat’s Last Theorem to modularity. His curve suggested the route from a hypothetical Fermat counterexample to a contradiction with modularity.
Modularity theorem: The modularity theorem states that every elliptic curve over the rational numbers is associated with a modular form. Wiles proved enough of this broader result to establish Fermat’s Last Theorem.
Fermat's Last Theorem: Fermat’s Last Theorem states that no positive integers satisfy xⁿ + yⁿ = zⁿ for any integer n greater than two. Wiles encountered the problem as a child and later made its proof his central research goal.
Isaac Newton Institute: The Isaac Newton Institute is a mathematical research institute in Cambridge, England. Wiles first announced his proof during a series of lectures there in 1993.
Jean-Pierre Serre: Jean-Pierre Serre is a French mathematician whose conjectures shaped modern number theory and the study of Galois representations. His conjectures helped formulate the modularity conditions that Wiles’s strategy required.
Elliptic curve: An elliptic curve is a nonsingular cubic curve with a specified point, equipped with an algebraic group structure. Frey’s construction converts a hypothetical Fermat solution into an elliptic curve with impossible modular behavior.
University of Oxford: The University of Oxford is a research university in Oxford, England, with origins in the medieval period. Wiles studied mathematics at Oxford before pursuing doctoral research in Cambridge.
Nature: Nature is a scientific journal first published in 1869. Its 1993 report brought the announcement of Wiles’s proof to a broad scientific audience.
Kenneth Ribet: Kenneth Ribet is an American mathematician who proved a theorem linking Fermat’s Last Theorem to the modularity of elliptic curves. His 1986 theorem made a proof of Fermat’s Last Theorem follow from a sufficiently broad modularity result.
Modular form: A modular form is a highly symmetric complex function that transforms predictably under a group of fractional linear transformations. Wiles’s argument established that certain elliptic curves correspond to modular forms.

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Pierre de FermatRelated: Wiles completed the proof Fermat claimed to have found, using modern number theory.