Trailblazing maths genius who was first woman to win Fields Medal dies aged 40

Maryam Mirzakhani was known for her slow, measured approach to solving problems

The award recognised her highly original work in the fields of geometry and dynamical systems (EPA/Maryam Mirzakhani/Standford University)

The first woman to win the prestigious Fields Medal prize for mathematics, Maryam Mirzakhani, has died at the age of 40.

A professor at Stanford University in California, she had been fighting a four-year battle against breast cancer which had spread to her bone marrow, according to reports.

Born in Iran, she died in a US hospital, and was awarded the Fields Medal – considered the mathematics equivalent of the Nobel Prize – in 2014.

The award recognised her highly original work in the fields of geometry and dynamical systems, citing “her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces”.

Wisconsin professor Jordan Ellenberg described her research in a blog post at the time: “[Her] work expertly blends dynamics with geometry. Among other things, she studies billiards.

“But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables.

“This isn't the kind of thing you do to win at pool, but it's the kind of thing you do to win a Fields Medal.”

Professor Mirzakhani graduated from the Sharif University of Technology in Tehran in 1999.

She went on to complete a PhD on hyperbolic surfaces – theoretical doughnut-like shapes – at Harvard in 2004.

Curtis McMullen, her doctoral adviser, had won the Field Medal himself in 1998.

She later collaborated with American mathematician Alex Eskin on research about the dynamics of abstract surfaces connected to billiard tables.

She doodled three-dimensional shapes constantly while she worked, and was known for her slow, measured approach to mathematical problems.

No other woman has won the prize, which is awarded every four years by the International Congress of Mathematicians to up to four mathematicians under 40, an age at which many women are re-entering the workplace after having children.

She was also the first Iranian to win a Fields Medal.

“The grievous passing of Maryam Mirzakhani, the eminent Iranian and world-renowned mathematician, is very much heartrending,” President Hassan Rouhani.

Growing up in Iran during the Iran-Iraq war, Professor Mirzakhani dreamed of becoming a writer and watched biographies of famous women like Marie Curie and Helen Keller.

She entered the Iranian International Mathematical Olympiad team at 17 in 1994, becoming the first girl to win a gold medal in 1994 and a perfect score the following year.

She had first taken an interest in maths when her older brother told her about how German mathematician Gauss discovered the formula for adding numbers from 1 to 100.

“It was the first time I enjoyed a beautiful solution,” she said in an interview given to the Clay Institute where she was a Research Fellow from 2004 to 2008.

“Of course, the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. Most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.”

Professor Mirzakhani is survived by her husband, an associate professor at Stanford University, and daughter Anahita.