Maryam Mirzakhani

Maryam Mirzakhani was an Iranian mathematician who in 2014 became the first woman and the first Iranian ever awarded the Fields Medal, mathematics' most prestigious prize, awarded once every four years. Mirzakhani's research centered on the geometry and dynamics of complex curved surfaces called Riemann surfaces and the moduli spaces that describe every possible shape such a surface can take; her doctoral and subsequent work solved long-standing problems about calculating the volumes of these moduli spaces by developing an original method involving counting and measuring the lengths of specific closed loops, called simple closed geodesics, drawn across the surfaces. This work, combining ideas from hyperbolic geometry, complex analysis, topology and dynamical systems, produced precise asymptotic formulas describing how these loops and volumes behave as the complexity of the surface grows, results that other mathematicians later drew on to make progress on further problems in the field. The Fields Medal committee cited her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces. Mirzakhani was a professor of mathematics at Stanford University at the time of her death from breast cancer in 2017 at age 40, and her achievement as the first woman to win the Fields Medal has been widely noted as a landmark moment for the visibility of women in mathematics.