Modularity theorem
>
The modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough... Wikipedia
Consequences: Fermat's Last Theorem
Field: Number theory
First proof by: Christophe Breuil; Brian Conrad; Fred Diamond; Richard Taylor
First proof in: 2001