Her friend Firouz Michael Naderi, an Iranian-American NASA scientist, said on Instagram, "A light was turned off today".
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.
The award was established in 1936.
In a tweet, Gary Lewis, UN Resident Coordinator for the Islamic Republic of Iran, also expressed his sorrow over Mirzakhani's death.
She fought with cancer for four years and was hospitalized lately at a hospital in the U.S.as the cancer had spread to her bone marrow.
"It is fun - it's like solving a puzzle or connecting the dots in a detective case", Mirzakhani said when she won the prestigious Fields Medal in 2014. "Maryam was a brilliant mathematical theorist, and also a humble person who accepted honors only with the hope that it might encourage others to follow her path".More news: Trump Sitting Next to Nieto: 'Absolutely' Want Mexico to Pay for Wall
He then posted: "A genius? Yes. 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".
Mirzakhani joined the faculty of Stanford University in 2008, where she served as a professor of mathematics until her death.
Born in Tehran in 1977, Mirzakhani won two worldwide math awards as a teenager. Kerckhoff is a mathematics professor at Stanford and was one of Mirzakhani's collaborators. She won two gold medals at the International Mathematical Olympiad, bringing home the top honors in 1994 and 1995.
It was at Sharif University of Technology in Iran, where she received her Bachelor of Science, that she discovered her passion for mathematics.
Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita - who once referred to her mother's work as "painting" because of the doodles and drawings that marked her process of working on proofs and problems, according to an obituary released by Stanford.