Maryam Mirzakhani has become the first woman to win the Fields Medal, the most prestigious prize in mathematics. Mirzakhani, 37, is of Iranian descent and completed her PhD at Harvard in 2004. Her thesis showed how to compute the Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces. Her research interests include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. She is currently professor of mathematics at Stanford University, and predominantly works on geometric structures on surfaces and their deformations.