Mirzakhani was the first woman and first Iranian to receive the honor since its creation in 1936.
Mirzakhani was diagnosed with breast cancer in 2013, and after fiercely batting this terrible disease for four years, she died on July 15, 2017.
The prize is handed out every four years to honor mathematicians under 40 who make major contributions.
The 40-year-old mathematician, a professor at Stanford University, was the first Iranian woman elected to the US National Academy of Sciences (NAS) in May 2016, in recognition of her "distinguished and continuing achievement in original research".
She received her bachelor's degree from Iran's Sharif University of Technology in 1999 and earned a PhD degree in mathematics from Harvard University in 2004.
"My most exciting pastime was reading novels; in fact, I would read anything I could find", she said in a 2014 interview with The Guardian.
Mirzakhani attended an all-girls high school in Tehran and grew up during the Iran-Iraq war. "Her contributions as both a scholar and a role model are significant and enduring, and she will be dearly missed here at Stanford and around the world".
Firouz Naderi’s post in Instagram in reaction to Mirzakhani’s death
She was also the first Iranian to win the prize. "It breaks my heart [.] gone far too soon", wrote Naderi, a former director of Solar Systems Exploration at NASA.
At the time of her death, she was a professor in the mathematics department at Stanford University.
In short, Mirzakhani was fascinated by the geometric and dynamic complexities of curved surfaces - spheres, doughnut shapes and even amoebas.
She had dreamed of becoming a writer when she was young, she said, but instead pursued her enthusiasm for solving mathematical problems.
"A light was turned off today". Kerckhoff is a mathematics professor at Stanford and was one of Mirzakhani's collaborators.
Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita. Her young daughter described her mother at work as "painting".
Iranian President Hassan Rouhani said Mirzakhani's "doleful passing" has caused "great sorrow", state media reported.
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