“For those of us less versed in the uppermost echelons of mathematics and geometry than Mirzakhani, it’s mind-twisting to understand the abstract accomplishments that got her field’s highest recognition.”

Actually, these are amazing achievements even from the perspective of a research mathematician. That’s why they merit the Fields medal. Edward Witten has a Nobel prize in physics, and she’s advanced the math related to what he was doing.

This is a big day for women. There had been, til now, no woman to score at the uttermost top in any of the cluster of realms of human endeavor such as chess, bridge, mathematics, go…

and of those, mathematics was the Everest.

Way to go.