TITLE: Breakthroughs in mathematics in 2021
QUESTION [112 upvotes]: This is somehow a general (and naive) question, but as specialized mathematicians we usually miss important results outside our area of research.
So, generally speaking, which have been important breakthroughs in 2021 in different mathematical disciplines?

REPLY [7 votes]: Since other answers mention works published in 2021, I think one can add to the list the proof of triviality of the $\phi^4$ quantum field theory in four dimensions:
Michael Aizenman, Hugo Duminil-Copin,
"Marginal triviality of the scaling limits of critical 4D Ising and $\lambda\phi_4^4$ models", Ann. of Math. (2) 194(1): 163-235 (July 2021).