# A legacy of firsts: How an Iranian mathematician transcended boundaries

## The Stanford mathematics professor is the only woman to have won Fields Medal

*** Originally published on September 23, 2019.*

Maryam Mirzakhani was a woman of many firsts. She was the first woman to compete on the Iranian math Olympiad team and the first to achieve a perfect score. She was also the first woman — and the first Iranian — to win the "Nobel Prize" of mathematics, the Fields Medal in 2014.

Like the mathematics she studied, Mirzakhani was complicated and complex. Her untimely death has led people to wonder what other astonishing things the gifted mathematician could have achieved.

Born in Iran, Mirzakhani didn't start out particularly interested in mathematics.

"I was more excited about reading novels and I thought I would become a writer one day," Mirzakhani once told the Simons Foundation in an interview.

"I got excited about (math) just as a challenge, but then I realized that it's really nice and I enjoy it."

Mirzakhani credited good schools, caring teachers, and supportive mentors for her success.

## Making sense of 'clever' math

When she was in high school Mirzakhani went on to join the Iranian Mathematics Olympiad team. At the time, one of her mentors, Kasra Rafi, now a professor at the University of Toronto, was an undergraduate. Rafi recalls an unforgettable moment with Mirzakhani that happened early on in a study session.

"As a high school student you are not supposed to know advanced mathematics. I gave them some problems and she came to me with a solution that she had written down. I tried to read the solution and I couldn't understand what was going on," Rafi told IDEAS.

"I mean, I can see that it's mathematics. I can see that it has some logic to it and it's complex analysis and I can follow it. [But] I'm thinking there's no way this makes sense."

Rafi realized he had to first learn the math Maryam was using before he could evaluate her answer, which turned out not only to be correct but "extremely clever."

When he spoke to Maryam about her solution, she said she didn't quite understand all the math involved but she had read several math papers that described the same sort of problem.

"I was very impressed and I was very surprised," Kasra said with a laugh.

Fast forward many years to 2004, when she completed her Ph.D at Harvard University and began teaching at Princeton University. By this time, Mirzakhani had already made a name for herself among mathematicians and accepted a position as a mathematics professor at Stanford University.

Her colleagues cited her quick thinking and complex analyses as attributes that set her apart in a field where slower paced thinking is often the norm. She was also known for her style of writing that many people in the mathematics field describe simply as beautiful.

Caroline Series, an emeritus professor of mathematics in Warwick, UK, says Maryam's math stood out for its creativity and simplicity.

"She doesn't waste energy, and on every half page there'll be some other new point that she just so cleverly turns around," said Series.

"She looks at things from many different angles and each angle will tell her something and at the end she says, poof! And something is true."

## A legacy of infinite inspiration

By the time Mirzakhani accepted her Fields Medal in 2014, she was already quite ill. Cancer had taken its toll on both her health and energy. She made it to the ceremony, but was not able to give a speech. Organizers also shielded Maryam from the media, giving her a chance to make her exit from the proceedings quietly.

Ingrid Daubeschies recalls she was in her office when she heard Mirzakhani had passed away: "Everything seemed fine. And then we heard that she had cancelled conferences. I heard that she had a relapse."

Ultimately, she says, Maryam's story was an inspiring one, that she was an immensely talented young woman in a field where women are not common.

But the news of course also stung: Maryam was leaving behind a young daughter.

"The whole women mathematical community felt touched by it."

**Guests in this episode:**

**Kasra Rafi**is from Iran and a professor and associate chair (Graduate Studies) in the department of mathematics at the University of Toronto. Rafi was also Maryam's math Olympiad teacher in Tehran, Iran in 1994.**Keivan Mallahi Karai**is from Iran and is a university lecturer in mathematics and postdoctoral fellow AG Diederich in mathematics & logistics at Jacobs University in Bremen, Germany.**Caroline Series**is a professor of mathematics at Warwick University and is president of the UK mathematical society.**Ingrid Daubechies**is a Belgian physicist and mathematician and the James B. Duke professor of mathematics and electrical and computer engineering at Duke University in Durham, North Carolina.

*** This episode was produced by Samira Mohyeddin and Naheed Mustafa.*