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.

Professor Maryam Mirzakhani was the recipient of the 2014 Fields Medal, the top honor in mathematics.

The quadrennial Fields Medal, which Mirzakhani , 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.

In short, Mirzakhani was fascinated by the geometric and dynamic complexities of curved surfaces - spheres, doughnut shapes and even amoebas. Despite the highly theoretical nature of her work, it has implications in physics, quantum mechanics and other disciplines outside of math. She was ambitious, resolute and fearless in the face of problems others would not, or could not, tackle.

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.’

A self-professed ‘slow’ mathematician, Mirzakhani 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.

College at Sharif University in Tehran followed and then 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. Her questions came in English. Her notes were jotted 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.’

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 take on another of the most-vexing problems in the field: the trajectory of a billiards ball around a polygonal table. The challenge began as a thought exercise among physicists a century ago and had yet to be solved.

The resulting paper, now more than 200 pages in length, was published in 2013. It has been hailed as ‘the beginning of a new era’ in mathematics and ‘a titanic work.’ Through it all, Maryam Mirzakhani never settled for the low-hanging fruit, but for the brass ring.

‘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.

*Editor’s note: A high-res photo of Maryam Mirzakhani is available here.*