"What's so special about Maryam, the thing that really separates her, is the originality in how she puts together these disparate pieces", said Steven Kerckhoff, at the time of her Fields Medal award.
Mirzakhani, a professor at Stanford University in California, died after the cancer she had been battling for four years spread to her bone marrow, Iranian media said.
She received the Fields Medal in 2014 for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.
Born in Tehran in 1977, Maryam was twice awarded the International Mathematical Olympiad's gold medal in her youth.
In 2008, Mirzakhani joined the faculty of Stanford University, where she served as a professor of mathematics until her death.
"Maryam is gone far too soon, but her impact will live on for the thousands of women she inspired to pursue math and science", Stanford University President Marc Tessier-Lavigne said.More news: Houston Nutt files lawsuit against Ole Miss' athletic foundation
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"On behalf of the entire Stanford community, I congratulate Maryam on this incredible recognition, the highest honor in her discipline, the first ever granted to a woman", said Hennessy.
"The more I spent time on mathematics, the more excited I became", she told The Guardian. She went on to win the 2009 Blumenthal Award for the Advancement of Research in Pure Mathematics, and the 2013 Satter Prize of the American Mathematical Society.
Mirzakhani was also a two-time gold medal victor in the International Mathematical Olympiad, a victor of the 2009 Blumenthal Award for the Advancement of Research in Pure Mathematics and the 2013 Satter Prize of the American Mathematical Society. Her parents had traveled to the U.S. on Monday, according to the Persian-language daily Haft-e-Sobh. In 2008 she became a professor of mathematics at Stanford. A colleague speculated that perhaps she organized her thoughts like this because the "problems she is working on are so abstract and complicated, she can't afford to make logical steps one by one but has to make big jumps".
"There are different characters, and you are getting to know them better", she said.
Mirzakhani is survived by her husband, Jan Vondrak, and her 6-year-old daughter, Anahita.