High Quality Content by WIKIPEDIA articles! The modularity theorem (previously known as the Taniyama–Shimura–Weil conjecture and by several related names) in mathematics establishes a connection between elliptic curves over the field of rational numbers and modular forms, both introduced in 19th century mathematics. This represents a significant bridge between two distinct areas of mathematics: algebra and analysis. It was fully proved jointly by Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor in 2001, borrowing many of the techniques used in Andrew Wiles' proof of Fermat's Last Theorem.

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