Bjorn Carey at the Stanford website:
“This is a great honor. I will be happy if it encourages young female scientists and mathematicians,” Mirzakhani said. “I am sure there will be many more women winning this kind of award in coming years.”
Officially known as the International Medal for Outstanding Discoveries in Mathematics, the Fields Medal will be presented by the International Mathematical Union on Aug. 13 at the International Congress of Mathematicians, held this year in Seoul, South Korea. Mirzakhani is the first Stanford recipient to win this honor since Paul Cohen in 1966.
The award recognizes Mirzakhani's sophisticated and highly original contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects. Although her work is considered “pure mathematics” and is mostly theoretical, it has implications for physics and quantum field theory.
More here.