From the BBC:
The 40-year-old had breast cancer, which had spread to her bones.
Nicknamed the "Nobel Prize for Mathematics", the Fields Medal is only awarded every four years to between two and four mathematicians under 40.
It was given to Prof Mirzakhani, an Iranian, in 2014, for her work on complex geometry and dynamical systems.
"A light was turned off today. It breaks my heart… gone far too soon," her friend, Nasa scientist Firouz Naderi, posted on Instagram.
Born in 1977, Prof Mirzakhani was brought up in post-revolutionary Iran and won two gold medals in the International Mathematical Olympiad as a teenager.
She earned a PhD at Harvard University in 2004, and later a professorship at Stanford.
More here.