Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer, states that for an elliptic differential operator on a compact manifold, the analytical index is equal to the topological index. Wikipedia
Consequences: Chern–Gauss–Bonnet theorem; Grothendieck–Riemann–Roch theorem; Hirzebruch signature theorem; Rokhlin's theorem
First proof by: Michael Atiyah and Isadore Singer
First proof in: 1963