Mirzhakani was one of the most influential geometrists of the 21st century. She was the first woman to ever win the Fields Medal, the Nobel Prize of Mathematics. Mirzakhani worked in dynamical systems, in particular mathematical billiards, which consists of a point particle moving on a frictionless billiard table and hitting the sides of the table without losing momentum. Maryam also worked extensively with manifolds. A manifold is thus a surface that looks flat close-up, but might be an entirely different surface when you zoom out and look from afar.
Mirzhakani was honored with the Fields Medal for her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".
Curtis McMullen, Mirzakhani's PhD adviser at Harvard, noted "She has a fearless ambition when it comes to mathematics". Mirzhakani's doctoral dissertation was on counting loops on hyperbolic surfaces and she contributed significantly to the analysis of dynamics of abstract surfaces connected to billiard tables.
Mirzhkhani completed her undergraduate in mathematics at Sharif University in Tehran, Iran in 1999 and subsequently went to harvard for her PhD in Mathematics. In her doctoral thesis, Mirzhakani developed a formula that related the cardinality of the set of goodseics to their length. At Harvard, Mirzhakani developed an unexpected proof an old conjecture posed by none other than Edward Witten, one of the foremost physicists of the 21st century. Mirzhakani's dissertation resulted in three papers published in the three of the most prestigious journals in mathematics: the Annals of Mathematics, Inventiones Mathematicae, and Journal of the American Mathematical Society. "The majority of mathematicians will never produce something as good -- and that’s what she did in her thesis.", Benson Farb, mathematician at the University of Chicago, notes.
