The death of the Teheran-born Mirzakhani, pictured, who specialized in theoretical mathematics, came three years after she received the Fields Medal at an event in Seoul.
She received the medal for her work in understanding the symmetry of curved surfaces, said officials at Stanford University, California, where she taught.
Growing up in Iran, she attended an all-girls high school and gained recognition as a teenager in the 1994 and 1995 competitions of the International Mathematical Olympiad.
She graduated in Teheran and then headed to Harvard University in Massachusetts, to obtain her doctorate in mathematics.
In recent years, she worked with Alex Eskin at the University of Chicago to investigate the trajectory of a billiard ball as it bounces around a polygonal table. Mirzakhani is survived by her husband, Jan, and a daughter, Anahita.