Modularity theorem: Difference between revisions

Revision as of 00:22, 26 January 2003

Revision as of 00:29, 26 January 2003

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:"all [[elliptic curve]]s are [[modular form|modular]]"

This [[theorem]] was first [[conjecture]]d by [[Yutaka Taniyama]] in September 1955. With [[Goro Shimura]] he improved its rigor until 1957. Taniyama died in 1958. In the 1960s it became associated with the [[Langlands program]] of unifying conjectures in mathematics, and was a key component thereof. The conjecture was picked up and promoted by [[Andre Weil|André Weil]] in the 1970's, and Weil's name was associated with it in some quarters. Despite the interest, some considered it beyond proving.

It attracted considerable interest in the 1980's when [[Gerhard Frey]] proposed that the '''Taniyama-Shimura conjecture''' implies [[Fermat's last theorem]]. In 1995, [[Andrew Wiles]] proved a special case of the '''Taniyama-Shimura theorem''' which was strong enough to yield a proof of '''Fermat's Last Theorem'''.