Maryam Mirzakhani

Her success, for mathematics and for women, drew acclaim from President Rouhani. Professor Sir Tim Gowers, from the University of Cambridge, said that he hoped that her win would “put to bed many myths about women and mathematics, and encourage more young women to think of mathematical research as a possible career”.

While much of Mirzakhani’s work was theoretical — described as “esoteric, abstract and impenetrable” to outsiders — it had implications for physics and quantum field theory.

One contribution concerned the dynamics of abstract surfaces connected to billiard tables and the trajectory of billiard balls. “It’s fun. It’s like solving a puzzle or connecting the dots in a detective case,” she said of her research. “I felt that this was something I could do, and I wanted to pursue this path.”

Maryam Mirzakhani was born in Tehran in 1977, two years before the overthrow of the Shah. She was one of four children of Ahmad Mirzakhani, an engineer. “As a kid I dreamt of becoming a writer,” she once said, adding that her maths grades at school had been poor. “I never thought I would pursue mathematics before my last year in high school.”

She was educated at Farzanegan School in Tehran, starting just as the Iran-Iraq war ended, opening opportunities for students. “I think I was the lucky generation,” she said. “I was a teenager when things got more stable.”

At home her older brother would tell her what he had learnt in maths each day and her first memory of the subject was his description of a famous problem solved by Carl Gauss, the German child prodigy. Asked to add up the numbers between one and 100 while his teacher was taking a nap, Gauss realised that the numbers could be broken up into 50 pairs, each of which added up to 101, and so the answer must be 5050. “The solution was quite fascinating for me,” Mirzakhani said. “That was the first time I enjoyed a beautiful solution, though I couldn’t find it myself.” In 1994 she was the first female Iranian to win a gold medal in the International Mathematical Olympiad, held in Hong Kong, returning to the competition the next year to achieve a perfect score and collect two gold medals in Toronto.

Her school was close to a street full of bookshops. “I remember how walking along this crowded street, and going to the bookstores, was so exciting for us,” she said, adding that her childhood ambition had been to read every book that she could find. There was no browsing; she and her friends simply bought random books and took them home. She was also inspired by television biographies of women such as Marie Curie and Helen Keller.

Mirzakhani entered the Sharif University of Technology in Tehran and, after graduating in 1999, won a fellowship to complete her PhD studies at Harvard in the US. There, to her frustration, she often had to explain that attending university as a woman in Iran had not been a problem. Curtis McMullen, her doctoral supervisor who had won the Fields Medal in 1998, recalled how she was captivated by the beauty of hyperbolic geometry. “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.”

Alex Eskin, a mathematician at the University of Chicago who collaborated with Mirzakhani, added that he found her optimism infectious. “When you work with her, you feel you have a much better chance of solving problems that at first seem hopeless,” he said.

She was appointed professor of mathematics at Stanford, California, in 2008. Friends recalled how she was constantly doodling, drawing images related to her research and spending hours working with huge pieces of paper scattered all over the floor. She described her work as slow, gravitating gradually towards deep mathematical problems that she could chew on for years. “Months or years later, you see different aspects” of a problem, she told Quanta magazine, adding that there were some mathematical problems she had been thinking about for more than a decade, “and still there’s not much I can do about them”.

In 2005 she married Jan Vondrák, an applied mathematician from the Czech Republic who also teaches at Stanford. He described how the slow and steady approach of her work was apparent in other areas of her life such as when, in their early days together, they went for a run. “She’s very petite and I was in good shape, so I thought I’d do well, and at first I was ahead,” he recalled. “But she never slows down. After half an hour I was done, but she was still running at the same pace.” Vondrák survives her with Anahita, their seven-year-old daughter who would describe Mirzakhani’s mathematical sketches as “mummy’s painting”.

Although she worked in the US, she remained a significant figure in Iran — so much so that, reporting her death, several Iranian newspapers broke with custom and printed front page images of her without a head covering.

Despite being small, Mirzakhani was indomitable in character. Holding questioners with her steady, grey-blue eyes and speaking carefully in a low voice, she would insist that there was no “particular recipe” for solving new mathematical problems. “It is the reason why doing research is challenging as well as attractive,” she said. “It is like being lost in the 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.”

Maryam Mirzakhani, mathematician, was born on May 3, 1977. She died of breast cancer on July 15, 2017, aged 40