- 1982/87: Yao and then later Goldreich-Micali-Wigderson prove the "fundamental theorem of cryptography", which essentially states that any computational functionality can be achieved "efficiently" and securely. I.e., given k parties with one input each and any function F of k inputs and k outputs, the parties can communicate so that each learns their output of the function on all the inputs, and nothing else.
- 2003: Perelman's proof of the geometrization conjecture.
* Green-Tao theorem, and lots of other work involving Terry Tao
* Yitang Zhang's work on prime gaps, and subsequent improvements
* Bhargava and collaborators' work on elliptic curves
* The introduction of algebraic topology methods into algebraic geometry (aka "simplicial"/"derived" stuff, see Jacob Lurie)
* Homotopy type theory
* Mochizuki/ABC stuff
* Peter Scholze's work in arithmetic geometry