"It breaks my heart. gone far too soon".
"A light was turned off today", NASA scientist Firouz Michael Naderi wrote on Instagram. "But also a daughter, a mother and a wife".
Professor Mirzakhani, who was also the first Iranian national to win the award, passed away after a four-year battle with breast cancer.
Her work focused on the complexities of curved surfaces, such as spheres and doughnuts.
The death of the Tehran-born Mirzakhani, who specialized in theoretical mathematics, came three years after she received the Fields Medal at an event in Seoul.
"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. "I felt that this was something I could do, and I wanted to pursue this path".
"I will be happy if it encourages young female scientists and mathematicians", Mirzakhani said at the time. She became a professor at Stanford University in 2008.
Mirzakhani is survived by her husband, Jan Vondrak, and her 6-year-old daughter, Anahita.
Iranian President Hassan Rouhani saluted Mirzakhani in a message in Farsi, posted to Twitter.
He praised the "unprecedented brilliance of this creative scientist and modest human being, who made Iran's name resonate in the world's scientific forums, (and) was a turning point in showing the great will of Iranian women and young people on the path towards reaching the peaks of glory.in various global arenas".
A year later, she became the first Iranian student to achieve a ideal score and win two gold medals at the Olympiad.
Mirzakhani completed her PhD at Harvard in 2004, then accepted positions as a research fellow at the Clay Mathematics Institute and an assistant professor at Princeton, accruing awards and acclaim along the way.
Maryam Mirzakhani, a professor at Stanford University who was the first and only woman to win the Fields Medal in mathematics, has died.