Originally published elsewhere on August 21, 2014.
This was discussed a bit on Hacker News recently: 2014 Fields Medal Announced
I happened to put together a bunch of links that day. Today, I thought maybe other folks would like to see it all collected together. So here is what I have, with a small amount of commentary and quoting but mostly just the links and title:
The Quanta Profile of her: A Tenacious Explorer of Abstract Surfaces has the best laymen's explanation of her work that I could find:
Mirzakhani became fascinated with hyperbolic surfaces — doughnut-shaped surfaces with two or more holes that have a non-standard geometry which, roughly speaking, gives each point on the surface a saddle shape. Hyperbolic doughnuts can’t be constructed in ordinary space; they exist in an abstract sense, in which distances and angles are measured according to a particular set of equations. An imaginary creature living on a surface governed by such equations would experience each point as a saddle point.
It turns out that each many-holed doughnut can be given a hyperbolic structure in infinitely many ways — with fat doughnut rings, narrow ones, or any combination of the two. In the century and a half since such hyperbolic surfaces were discovered, they have become some of the central objects in geometry, with connections to many branches of mathematics and even physics.
The article also makes the very astute observation:
Mirzakhani is the first woman to win a Fields Medal. The gender imbalance in mathematics is long-standing and pervasive, and the Fields Medal, in particular, is ill-suited to the career arcs of many female mathematicians. It is restricted to mathematicians younger than 40, focusing on the very years during which many women dial back their careers to raise children.
I am a big believer in the idea that the fact that women are the child-bearers and are usually also the child-rearers is the single largest reason we have a glass ceiling at all. So I was really pleased to see that observation.
She is not only the first woman, she is also the first Iranian:
Journal Article: Weil-Petersson volumes and intersection theory on the moduli space of curves
Original tags on previous site:
Hacker News; likeagirl; Math