Maryam Mirzakhani is now the first woman to win a Fields Medal, considered the world's most prestigious math award.
The Stanford University professor won the award for her work in dynamical systems, a complicated area of geometry. As Curtis T. McMullen, her doctoral advisor, explained to the New York Times, "These dynamical systems describe surfaces with many handles, like pretzels, whose shape is evolving over time by twisting and stretching in a precise way."
Mirzakhani's work is "pure mathematics" and often does not have obvious practical applications, according to a release from Stanford hailing her achievement. However, it says her work could inform scholars in fields outside her own:
The work ... could have impacts concerning the theoretical physics of how the universe came to exist and, because it could inform quantum field theory, secondary applications to engineering and material science. Within mathematics, it has implications for the study of prime numbers and cryptography.
The International Mathematical Union awards the Fields Medal every four years, with up to four medals awarded at a time. The purpose of the award is to "recognize outstanding mathematical achievement for existing work and for the promise of future achievement," according to the IMU, and it only goes to people under the age of 40.
Mirzakhani is the first woman winner since the award was first given in 1936. Fifty-four men have also received the Fields Medal, according to the IMU website. (That doesn't include Grigori Perelman, who declined the award in 2006, or Andrew Wiles, who, since he was past the age limit, received a special plaque in 1998 for proving Fermat's Last Theorem.)
Alongside Mirzakhani, three other people received the medal this year: Artur Avila, a researcher at France's Centre National de la Recherche Scientifique; Manjul Bhargava, a professor at Princeton University; and Martin Hairer, a professor at the University of Warwick in the UK.