Maryam Mirzakhani Tames the Shifting Universe

Imagine trying to map the surface of a donut. Now imagine that donut is constantly warping and stretching, and one wrong calculation collapses the entire universe of possible shapes into infinite fractal chaos. That is the world Maryam Mirzakhani lived inside, and she found order in it. This episode is a deep dive into the life of the Iranian mathematician who became the first woman and the first Iranian to win the Fields Medal.

We trace the path: a teenager in Tehran who twice won gold at the International Mathematical Olympiad, a Sharif University undergraduate, a Harvard PhD with Curtis McMullen, and a career at Princeton and Stanford spent on the geometry of moduli spaces, Riemann surfaces, and Teichmüller dynamics. We unpack her landmark work on the volume of moduli spaces, the counting of simple geodesics on hyperbolic surfaces, and her proof (with Alex Eskin) that the earthquake flow is ergodic, which means a shape will eventually visit every possible state in its space.

We also trace her process: sprawling on the floor with enormous sheets of paper, doodling shapes until the hidden structure revealed itself. We close on her early death from breast cancer at 40 and the lesson the episode draws from her style: sometimes the only way to find the clean straight line is to first understand the beautiful shifting curve of the space it lives in.

Subscribe to pplpod for more deep dives into the people who reshaped knowledge. Topics: Maryam Mirzakhani, Fields Medal, moduli spaces, Riemann surfaces, hyperbolic geometry, Teichmüller theory, women in mathematics, Iranian mathematicians, Stanford.

Source credit: Research for this episode included Wikipedia articles accessed 5/3/2026. Wikipedia text is licensed under CC BY-SA 4.0; content here is summarized/adapted in original wording for commentary and educational use.