Maryam Mirzakhani of Stanford University, California, received the Fields medal today at the International Congress of Mathematicians in Seoul, South Korea.
The medal is awarded once every four years to at most four recipients, who must be aged fewer than 40 at the start of that year. All the previous 52 Fields medalists, dating back to 1936, have been male.
Mirzakhani, who is Iranian, studies the geometry of moduli space, a complex geometric and algebraic entity that might be described as a universe in which every point is itself a universe. Mirzakhani described the number of ways a beam of light can travel a closed loop in a two-dimensional universe. To answer the question, it turns out, you cannot just stay in your "home" universe – you have to understand how to navigate the entire multiverse. Mirzakhani has shown mathematicians new ways to navigate these spaces.
Mirzakhani first attracted international attention as a high-school student in 1995, when she was the first Iranian student to achieve a perfect score in the International Mathematics Olympiad.
The three other winners are Brazilian-born Artur Avila of Denis Diderot University in Paris, France, who studies how chaotic systems evolve when constrained by certain rules; Manjul Bhargava, a number theorist at Princeton University; and Martin Hairer, an expert in partial differential equations at the University of Warwick, UK.
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