"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".
Friend Firouz Naderi announced Mirzakhani's death on Saturday on Instagram and relatives subsequently confirmed her death to the Mehr agency in Iran. "It breaks my heart... gone far too soon." in an Instagram posting.
Mirzakhani was born in Tehran, Iran on May 3, 1977, and she quickly displayed an unbelievable talent for math. But her passion and gift for mathematics eventually won out. She liked to read and thought that maybe she would become a writer.
In another interview, she said of her process: "I don't have any particular recipe [for developing new proofs] ..."
In 1999, Mirzakhani earned a bachelor of science degree in mathematics from the Sharif University of Technology in Tehran.
At the time she was praised for the stunning advances she had made in some of the most complicated areas of the mathematics.
Maryam Mirzakhani, the first woman to receive the Fields Medal for mathematics, has died in the United States in Saturday.
The 40-year-old fought the disease for four years and was recently hospitalised in the U.S. as the cancer spread to her bone marrow. Her questions came in English. The prestigious award for is sometimes called the Nobel Prize of mathematics.
Her work has inspired many mathematicians, as she contributed to the dynamics and geometry of Riemann surfaces and their moduli spaces, according to the International Mathematical Union.
"I find it fascinating that you can look at the same problem from different perspectives and approach it using different methods", she said. Kerckhoff is a mathematics professor at Stanford and was one of Mirzakhani's collaborators.
"There are different characters, and you are getting to know them better", she said.
Mirzakhani is survived by Jan Vondrák her husband who is a Czech theoretical computer scientist and associate professor at Stanford University, and a daughter named Anahita.