Maryam Mirzakhani
(born May 3, 1977,
Tehr?n
, Iran?died July 14, 2017,
Palo Alto
,
California
, U.S.) was an Iranian mathematician who became (2014) the first woman and the first Iranian to be awarded a
Fields Medal
. The
citation
for her award recognized “her outstanding contributions to the
dynamics
and geometry of
Riemann surfaces
and their moduli spaces.”
While a teenager, Mirzakhani won gold medals in the 1994 and 1995 International Mathematical Olympiads for high-school students, attaining a perfect score in 1995. In 1999 she received a B.Sc. degree in
mathematics
from the Sharif University of Technology in Tehr?n. Five years later she earned a Ph.D. from
Harvard University
for her dissertation
Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves
. Mirzakhani served (2004?08) as a Clay Mathematics Institute research fellow and an assistant professor of mathematics at
Princeton University
. In 2008 she became a professor at
Stanford University
.
Britannica Quiz
Numbers and Mathematics
Mirzakhani’s work focused on the study of hyperbolic surfaces by means of their moduli spaces. In
hyperbolic space
, in contrast to normal
Euclidean space
, Euclid’s fifth postulate (that one and only one line parallel to a given line can pass through a fixed point) does not hold. In non-Euclidean hyperbolic space, an
infinite
number of parallel lines can pass through such a fixed point. The sum of the angles of a triangle in hyperbolic space is less than 180°. In such a curved space, the shortest path between two points is known as a geodesic. For example, on a sphere the geodesic is a great circle. Mirzakhani’s research involved calculating the number of a certain type of geodesic, called simple closed geodesics, on hyperbolic surfaces.
Her technique involved considering the moduli spaces of the surfaces. In this case the modulus space is a collection of all Riemann spaces that have a certain
characteristic
. Mirzakhani found that a property of the modulus space corresponds to the number of simple closed geodesics of the hyperbolic surface.