The story
Proved by Michael Atiyah and Isadore Singer in 1963.
Etymology from Wiktionary, CC BY-SA 4.0.
Atiyah-Singer index theorem
Today it means: A theorem stating that, for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). Full definition →