Modular forms: Holomorphic functions on the upper half-plane that transform in a prescribed manner under the action of the modular group, fundamental to modern number theory and mathematical physics.

Scott Ahlgren, Matthew Boylan, Central Critical Values of Modular L-Functions and Coefficients of Half-Integral Weight Modular Forms Modulo l, American Journal of Mathematics, Vol. 129, No. 2 (Apr., ...

By extending the scope of a key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a unifying theory of mathematics.