Echoing similar view, Mirzakhani's friend from NASA, Firouz Naderi, said, "A light was turned off today".
Professor Mirzakhani, who was also the first Iranian national to win the award, passed away after a four-year battle with breast cancer.
Born on May 3, 1977, in Tehran, Mirzakhani showed her knack for numbers from an early age, winning back-to-back gold medals in the 1994 and 1995 International Mathematical Olympiads.
The world-renowned Iranian mathematician and Stanford professor died from breast cancer at a hospital in the United States.
After her doctorate at Harvard, Mirzakhani accepted a position as assistant professor at Princeton University and as a research fellow at the Clay Mathematics Institute before joining the Stanford faculty.
The award was established in 1936.
Stanford president Marc Tessier-Lavigne said Mirzakhani's impact will live on for the thousands of women she inspired to pursue math and science careers.
Firouz Naderi’s post in Instagram in reaction to Mirzakhani’s death
Mirzakhani enjoyed pure mathematics because of its "elegance and longevity", she said.
As a teenager, she gained worldwide attention when she won gold medals in two global Mathematical Olympiads, achieving a flawless score in one. But her passion and gift for mathematics eventually won out. "It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out".
When she won in 2014, the IMU called Mirzakhani's accomplishments in complex geometric forms such as Riemann surfaces and moduli spaces "stunning".
The paper she completed based on that exercise was published in 2013.
As a professor and scholar, Mirzakhani's pictures helped her write stories with her math.
In a message issued on Saturday, President Rouhani said the demise of "the well-known mathematical genius" has caused deep sorrow for him.
She is survived by husband Jan Vondrák, a Czech theoretical computer scientist, and their daughter Anahita.