Modularity theorem: Difference between revisions

Revision as of 00:04, 26 January 2003

Revision as of 00:22, 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 [[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'''.

The full '''Taniyama-Shimura theorem''' was finally proved in 1997 by a team of a half-dozen mathematicians who, building on '''Wiles''''s work, incrementally chipped away at the remaining cases until the full result was proved.

In March 1996 Wiles shared the [[Wolf Prize]] with Langlands. Although neither of them had originated nor finished the proof of the full theorem that had enabled their achievements, they were recognized as having had the decisive influences that led to its finally being proven.