She drew her way to mathematical greatness.

The New York Times | Gareth Cook: Maryam Mirzakhani was a mathematician, but she worked like an artist, always drawing. She liked to crouch on the floor with large sheets of paper, filling them with doodles: repeated floral figures and bulbous, rubbery bodies, their appendages sliced clean away, like denizens of a lost Miyazaki anime. One of her Stanford University graduate students said Mirzakhani portrayed problems in mathematics not as daunting logical conundrums but as animated tableaus. “It’s almost like she had a window on the math landscape, and she was trying to describe how the things living there interacted with each other,” says Jenya Sapir, now an assistant professor at Binghamton University. “To her, it’s all happening at once.”

Mirzakhani grew up in Tehran with dreams of becoming a writer. In sixth grade, she started at Farzanegan, a school for the city’s most gifted girls, and earned the top marks in all of her classes — except math. Near the school year’s end, the instructor returned a math test marked 16 out of 20, and Mirzakhani ripped it up and stuffed the pieces in her bag. She told a friend that she’d had it when it came to math: “I’m not even going to try to do better.” Mirzakhani, though, was constitutionally incapable of not trying, and she soon fell in love with the subject’s spare poetry. As a high school junior, she and her best friend, Roya Beheshti, became the first Iranian women to qualify for the International Mathematical Olympiad, and the next year, in 1995, Mirzakhani took a gold medal with a perfect score.

Mirzakhani moved to the United States in the fall of 1999, for graduate school at Harvard. Her passion was geometry, and she was particularly drawn to “hyperbolic surfaces,” which are shaped like Pringles potato chips. She explored a universe extreme in its abstraction — with “moduli spaces,” where every point represents a surface — and dimensions that exceed our own. Somehow Mirzakhani was able to conjure aspects of such spaces to consider, doodling on a white sheet of paper to try an idea, or remember one, or search for a new one; only later would she transcribe her adventures in the conventional symbols of mathematics. “You don’t want to write down all the details,” she once told a journalist. “But the process of drawing something helps you somehow to stay connected.” Her Ph.D. thesis began with counting simple loops on surfaces and led to a calculation of the total volume of moduli spaces. This allowed the young scholar to publish three separate papers in top mathematical journals, one of which contained a surprising new proof of the famous “Witten conjecture,” a milestone in theoretical physics connecting mathematics and quantum gravity. Mirzakhani’s mathematics is treasured for its great creative leaps, for the connections it has revealed between distant fields, for its sense of grandeur.

MIRZAKHANI’S MATHEMATICS IS TREASURED FOR ITS GREAT CREATIVE LEAPS, FOR THE CONNECTIONS IT HAS REVEALED BETWEEN DISTANT FIELDS, FOR ITS SENSE OF GRANDEUR.

When Jan Vondrak, who would become her husband, met her in 2003, he had no idea, he says, that “she was a superstar.” Mirzakhani was finishing up at Harvard, and Vondrak, now a Stanford mathematics professor, was in grad school at M.I.T.; they met at a party, each recognizing a kindred spirit who didn’t especially enjoy parties. Vondrak introduced her to jazz, and the two went for long runs along the Charles River. Mirzakhani was both modest — Vondrak learned of many accomplishments through common friends — and bracingly ambitious. Vondrak recalls her dreams of future discoveries in moduli space, but also her resolve to explore more distant fields, like number theory, combinatorics and “ergodic theory.” She had, Vondrak said, “100 years of plans.”

Three years ago, Mirzakhani, 37, became the first woman to win the Fields Medal, the Nobel Prize of mathematics. News of the award, and the obvious symbolism (first woman, first Iranian, an immigrant from a Muslim country) sat uneasily with her. She was puzzled when she discovered that some people thought mathematics was not for women — it was not an idea that she or her friends encountered growing up in Iran — but she was not inclined, by personality, to tell others what to think. As she became a major celebrity among Iranians, people would approach her to ask for a photo, which she hated. The Fields Medal was also announced when she had just finished a grueling treatment for breast cancer.

In 2016, the cancer returned, spreading to Mirzakhani’s liver and bones. Everyone who knew Mirzakhani describes her as unwaveringly optimistic; they always left conversations feeling energized. Eventually, though, it became impossible for Mirzakhani to continue with what her young daughter, Anahita, called her “painting.” At a Stanford memorial service, Curtis McMullen, Mirzakhani’s thesis adviser and chairman of Harvard’s Department of Mathematics, said that when she was a student, she would come to his office and pose questions that were “like science fiction stories,” vivid scenes she saw in some unexplored corner of the mathematical universe — strange structures and beguiling patterns, all in motion and interconnected. Then she would look at him with her blue-gray eyes. “Is it right?” she would ask, as if he might know the answer.

Gareth Cook is a contributing writer for the magazine. His most recent article was about a future of policing with no traffic tickets.