Maryam Mirzakhani

Maryam Mirzakhani (1977–2017) was an Iranian mathematician whose work connected geometry, topology, and dynamical systems. In 2014, she became the first woman and first Iranian to receive the Fields Medal.

Hyperbolic geometry: Geometry of spaces with constant negative curvature, where parallel lines and triangle angles behave differently from Euclidean geometry. Hyperbolic surfaces provide the geometric setting for many of her results.
Simple closed geodesic: A closed geodesic on a surface that does not intersect itself. Counting these curves on hyperbolic surfaces was a central problem in her work.
Simple geodesic counting: The study of how many simple closed geodesics of bounded length occur on a surface. She established precise asymptotic growth laws for these counts.
International Mathematical Olympiad: An annual international mathematics competition for pre-university students. She won gold medals for Iran in 1994 and 1995, with a perfect score in 1995.
Women in mathematics: The historical and contemporary participation of women in mathematical research, education, and institutions. Her Fields Medal made a widely visible milestone in a field with persistent gender barriers.
Riemann surface: A one-dimensional complex manifold that locally resembles the complex plane. Her work studies geometric structures on surfaces that can be treated as Riemann surfaces.
Weil–Petersson symplectic form: A natural symplectic structure on Teichmüller space induced by the Weil–Petersson metric. Its volume calculations enabled her recursive formulas for counting simple geodesics.
McShane identity: An identity expressing a constant as a sum over simple closed geodesics on a hyperbolic surface. She generalized this identity to bordered surfaces and used it to derive volume recursions.
Sharif University of Technology: A public research university in Tehran, Iran, founded in 1966. She studied mathematics there before pursuing doctoral work in the United States.
Breakthrough Prize in Mathematics: An annual prize recognizing major achievements in mathematics. Its 2013 award recognized her contributions before she received the Fields Medal.

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