Modularity theorem: Difference between revisions

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Revision as of 00:40, 16 January 2005

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The full Taniyama-Shimura theorem was finally proved in [[1999]] by Breuil, Conrad, Diamond, and Taylor who, building on Wiles' work, incrementally chipped away at the remaining cases until the full result was proved.

Several theorems in number theory similar to Fermat's last theorem follow from the Taniyama-Shimura theorem. For example: no cube can be written as a sum of two [[relatively primecoprime]] ''n''-th powers, ''n'' ≥ 3. (The case ''n'' = 3 was already known by [[Euler]].)

In March [[1996]] Wiles shared the [[Wolf Prize in Mathematics|Wolf Prize]] with [[Robert 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.