Stanford mathematics professor Maryam Mirzakhani, the first and to-date only female winner of the Fields Medal since its inception in 1936, died July 15 after a long battle with cancer. Mirzakhani was 40 years old.
The quadrennial Fields Medal, which Mirzakhani won in 2014, is the most prestigious award in mathematics, often equated in stature with the Nobel Prize. Mirzakhani specialized in theoretical mathematics that read like a foreign language by those outside of mathematics: moduli spaces, Teichmüller theory, hyperbolic geometry, Ergodic theory and symplectic geometry.
Mastering these approaches allowed Mirzakhani to pursue her fascination for describing the geometric and dynamic complexities of curved surfaces—spheres, doughnut shapes and even amoebas–in as great detail as possible. Her work was highly theoretical in nature, but it could have impacts concerning the theoretical physics of how the universe came to exist and, because it could inform quantum field theory, secondary applications to engineering and material science. Within mathematics, it has implications for the study of prime numbers and cryptography.
Mirzakhani joined the faculty of Stanford University in 2008, where she served as a professor of mathematics until her death.
“Maryam is gone far too soon, but her impact will live on for the thousands of women she inspired to pursue math and science,” said Stanford President Marc Tessier-Lavigne. “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. 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.”
Despite the breadth of applications of her work, Mirzakhani said she enjoyed pure mathematics because of the elegance and longevity of the questions she studied.
A self-professed “slow” mathematician, Mirzakhani’s colleagues describe her as ambitious, resolute and fearless in the face of problems others would not, or could not, tackle. She denied herself the easy path, choosing instead to tackle thornier issues. Her preferred method of working on a problem was to doodle on large sheets of white paper, scribbling formulas on the periphery of her drawings. Her young daughter described her mother at work as “painting.”
“You have to spend some energy and effort to see the beauty of math,” she told one reporter.
In another interview, she said of her process: “I don’t have any particular recipe [for developing new proofs] … 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.”
Mirzakhani was born in Tehran, Iran, and – by her own estimation – was fortunate to come of age after the Iran-Iraq war when the political, social and economic environment had stabilized enough that she could focus on her studies. She dreamed of becoming a writer, but mathematics eventually swept her away.
She attended an all-girls high school in Tehran, led by a principal unbowed by the fact that no girl had ever competed for Iran’s International Mathematical Olympiad team. Mirzakhani first gained international recognition during the 1994 and 1995 competitions. In 1994, she earned a gold medal. In 1995, she notched a perfect score and two gold medals.
After graduating college at Sharif University in Tehran. she headed to graduate school at Harvard University, where she was guided by Curtis McMullen, a fellow Fields Medal winner. At Harvard, Mirzakhani was distinguished by her determination and relentless questioning, despite the language barrier. She peppered her professors with questions in English. She jotted her notes in Farsi.
McMullen described Mirzakhani as filled with “fearless ambition.” Her 2004 dissertation was a masterpiece. In it, she solved two longstanding problems. Either solution would have been newsworthy in its own right, according to Benson Farb, a mathematician at the University of Chicago, but then Mirzakhani connected the two into a thesis described as “truly spectacular.” It yielded papers in each of the top three mathematics journals.
“The majority of mathematicians will never produce something as good,” Farb said at the time. “And that’s what she did in her thesis.”
“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. Kerckhoff is a mathematics professor at Stanford and was one of Mirzakhani’s collaborators. “That was the case starting with her thesis work, which generated several papers in all the top journals. The novelty of her approach made it a real tour de force.”
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.
In recent years, she collaborated with Alex Eskin at the University of Chicago to answer a mathematical challenge that physicists have struggled with for a century: the trajectory of a billiards ball around a polygonal table. That investigation into this seemingly simple action led to a 200-page paper which, when it was published in 2013, was hailed as “the beginning of a new era” in mathematics and “a titanic work.”
“You’re torturing yourself along the way,” she would offer, “but life isn’t supposed to be easy.”
Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita.
The university will organize a memorial gathering in the fall, when students and faculty have returned to campus.