A professor of mathematics at Stanford University, Mirzakhani showed promise in math early: she was accepted as a youngster at the Farzanegan School in Tehran, Iran, where she was born; the school is part of the National Organization for Development of Exceptional Talents. She graduated from Sharif University of Technology, and earned her PhD from Harvard just five years later, where she studied under Curtis McMullen, a Fields Medalist. (The Fields Medal is thought of as the “Nobel Prize of Mathematics” — the most prestigious prize in the profession, though it is only awarded to those under 40 to signify their likely coming achievements.) Upon graduation she was recruited as a professor at Princeton, but four years later she was scooped up by Stanford. OK, but what does she do? In 2014, University of Wisconsin–Madison math professor Jordan Ellenberg explained it to lay people this way: “[Her] work expertly blends dynamics with geometry. Among other things, she studies billiards. But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables. And the kind of dynamics she studies doesn’t directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables … This isn’t the kind of thing you do to win at pool, but it’s the kind of thing you do to win a Fields Medal. And it’s what you need to do in order to expose the dynamics at the heart of geometry; for there’s no question that they’re there.”
And yes, the occasion for explaining this was because Mirzakhani herself had been awarded the Fields Medal: the first woman (and the first Iranian) to be so honored. In less lay language, her recent work was on Teichmüller dynamics of moduli space, where she was able to prove the long-standing conjecture that William Thurston’s earthquake flow on Teichmüller space is ergodic. She also proved that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal. OK… got it? So now you know why I needed someone else’s quote to explain it in more lay terms! In a statement, Stanford University put it this way: her work has “implications” in fields ranging from cryptography to “the theoretical physics of how the universe came to exist.” Dr. Peter Sarnak of Princeton’s Institute for Advanced Study says Mirzakhani “was in the midst of doing fantastic work. Not only did she solve many problems; in solving problems, she developed tools that are now the bread and butter of people working in the field.” Dr. Mirzakhani died July 14, from breast cancer that had metastasized to her bone marrow. She was 40.