Maryam Mirzakhani: gifted mathematician and only female winner of Fields Medal, the ‘maths Nobel prize’

Her doctoral thesis was of such brilliance that it solved two longstanding mathematical problems

Mirzakhani’s research interests included Riemann surfaces and Teichmüller theory, both related to the geometric and dynamic complexities of curved surfaces (EPA/Maryam Mirzakhani/Standford University)

Maryam Mirzakhani, who has died of breast cancer aged 40, was a gifted mathematician and the first woman ever to win the coveted Fields Medal, one of the highest awards in the subject. Iran’s President, Hassan Rouhani, spoke of the “unprecedented brilliance of this creative scientist and modest human being, who made Iran's name resonate in the world's scientific forums”.

Mirzakhani was born in Tehran in 1977 and attended Farzanegan School, a girls-only establishment in the capital. Her abilities were recognised early when she won gold at the 1994 International Mathematical Olympiad in Hong Kong, following up with another gold and a perfect score in 1995, in Canada.

On leaving school she had initially wanted to be a writer but soon found her direction in the world of maths. She obtained her BSc at Sharif University of Technology in Tehran, graduating in 1999, and went on to study at Harvard under Curtis McMullen, receiving her PhD in 2004. Her doctoral thesis was of such brilliance that it had solved two longstanding mathematical problems. “The novelty of her approach made it a real tour de force,” noted Professor Steven Kerckhoff of Stanford.

From 2004 to 2008 she was a Clay Mathematics Institute Research Fellow and an assistant professor at Princeton University, New Jersey. She had latterly worked as a professor at Stanford University, California. Her research interests included Riemann surfaces and Teichmüller theory, both related to the geometric and dynamic complexities of curved surfaces.

But amid the abstract, theoretical work she had also found time to collaborate with Alex Eskin at the University of Chicago on what might appear to be an altogether more prosaic question: how does a ball travel around a billiards table? That work resulted in a 200-page paper, published in 2013. Mirzakhani summarised her personal approach to her research as “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”.

The Fields Medal is given every four years to mathematicians aged 40 or younger who excel in their area of research. Awarded by the International Congress of Mathematicians, it is the maths world’s equivalent of a Nobel Prize. In 2014 Mirzakhani became the first and so far only woman winner of the Fields Medal in recognition of her “outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces”.

She had been diagnosed with breast cancer four years ago and was being treated for a recurrence of the disease. Stanford University president Marc Tessier-Lavigne said in tribute: “Maryam was a brilliant mathematical theorist, and also a humble person who accepted honours 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.”

Maryam Mirzakhani, mathematician, born 3 May 1977, died 14 July 2017