Three days ago the Breakthrough Prize Foundation announced the recipients of the 2021 Breakthrough Prizes. I focus in this post only on the prizes in mathematics (there are also prizes in life sciences and physics).

**Martin Hairer**is the recipient of the 2021 Breakthrough Prize in Mathematics for*transformative contributions to the theory of stochastic analysis, particularly the theory of regularity structures in stochastic partial differential equations.*

The recipients of the 2021 New Horizons in Mathematics Prize for early-career scientists are:

**Bhargav Bhatt**for*outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development of p-adic cohomology theories.***Aleksandr Logunov**for*novel techniques to study solutions to elliptic equations, and their application to long-standing problems in nodal geometry.***Song Sun**for*many groundbreaking contributions to complex differential geometry, including existence results for Kahler-Einstein metrics and connections with moduli questions and singularities.*

Further, three inaugural Maryam Mirzakhani New Frontiers Prizes were awarded to early-career women mathematicians:

**Nina Holden**for*work in random geometry, particularly on Liouville Quantum Gravity as a scaling limit of random triangulations.***Urmila Mahadev**for*work that addresses the fundamental question of verifying the output of a quantum computation.***Lisa Piccirillo**for*resolving the classic problem that the Conway knot is not smoothly slice.*