"A light was turned off today. far too soon". Later he twitted: A genius? Yes.
Mirzakhani fought breast cancer for the last four years of her life, which eventually spread to her bone marrow.
Mirzakhani was born in Tehran in 1977 and brought up in the Islamic Republic.
Mirzakhani is survived by Jan Vondrák her husband who is a Czech theoretical computer scientist and associate professor at Stanford University, and a daughter named Anahita.
Stanford University in a statement said Mirzakhani was "ambitious, resolute and fearless in the face of problems others would not, or could not, tackle".
Stanford President Marc Tessier-Lavigne calls Mirzakhani a brilliant theorist who made enduring contributions and inspired thousands of women to pursue math and science.
In another interview, she said of her process: "I don't have any particular recipe [for developing new proofs] ..."
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Prof Dame Frances Kirwan, a member of the medal selection committee from the University of Oxford, said at the time, "I hope that this award will inspire lots more girls and young women, in this country and around the world, to believe in their own abilities and aim to be the Fields Medallists of the future". But her passion and gift for mathematics eventually won out.
She earned a doctoral degree from Harvard University in 2004 and became full professor of mathematics in 2008 at Stanford at a very young age of 31.
As a teenager, she gained worldwide attention when she won gold medals in two global Mathematical Olympiads, achieving a flawless score in one.
Mirzakhani was lauded for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.
Mirzakhani, who described herself as a slow mathematician, was drawn to big, hard questions in her field, a trait that made her a revered figure within the mathematics community. "Her questions came in English".
As a professor and scholar, Mirzakhani's pictures helped her write stories with her math.
The resulting paper, now more than 200 pages in length, was published in 2013.