I often write about women in different time periods, who have struggled, against all odds, to break glass ceilings in numerous fields. Their stories continue to inspire and move us even today. This is a contemporary story of a young woman who scaled new heights in mathematics, in a short life.
Maryam Mirzakhani was born in Tehran, Iran, on 12 May 1977. Her father was an electrical engineer, and she grew up with three siblings. Her parents were always supportive of their children, and encouraged them to work towards something that would be meaningful and satisfying to them, rather than for what society would consider success and achievement. The nineteen-eighties were difficult years for growing up in Iran which was in the middle of the Iran-Iraq war. But Maryam was secure in the love of her family. She loved to read and wanted to become a writer. She would make up stories about a girl who achieved great things, like travelling the world. Science was not her first love; it was her older brother who gradually wakened the spark when he used to tell her what he had learned in school.
The war ended when Maryam finished elementary school, and she joined Farzanegan Middle School in Tehran where she met Roya Beheshti who became a close friend. The two shared an interest in reading and used to spend a lot of time going to bookstores and buying books. Their school which was administered by Iran’s National Organization for Development of Exceptional Talents, aimed to educate the brightest pupils, and the Principal and teachers of the school were keen that their students should get the same opportunities as would students in a boys’ school.
Maryam did not do well in Mathematics in her first year at Farzanegan middle school. Her teacher told her that she was not particularly talented in that subject and Maryam lost interest and confidence in maths. However, in her second year she had a different mathematics teacher who encouraged her. This led Maryam, and Roya, to become excited and engaged with Mathematics.
When the two friends progressed to high school, they found a copy of six Mathematical Olympiad problems and Maryam managed to solve three of them. Encouraged by this, the girls asked their school principal if she could arrange for them to have mathematical problem-solving classes, as boy’s schools had for talented students. The principal was supportive, and classes were arranged for the girls. Later Maryam recalled that this positive mind set was a great influence in her life.
Both Maryam Mirzakhani and her friend Roya Beheshti made the Iranian Mathematical Olympiad team in 1994—the first girls to do so. The international competition was held that year in Hong Kong and Mirzakhani was awarded a gold medal, while Roya bagged the silver. The next year, Mirzakhani, still in high school, was a member of the Iranian Mathematical Olympiad team, and was once again awarded a gold medal in 1995.
In 1995 Maryam joined the Sharif University of Technology in Tehran to study mathematics. She enjoyed the problem-solving sessions and informal reading groups, and also the support and friendship of many professors and students who inspired her, and shared her growing excitement with mathematics. She published several papers while still an undergraduate. After obtaining her degree from Sharif University in 1999, Mirzakhani left for the United States to join graduate school at Harvard University. She earned a Ph.D. from Harvard University in 2004 for her 130-page thesis Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves.
In 2004 she was offered a junior fellowship at Harvard, but turned down the offer. In the same year she was awarded a Clay Research Fellowship and was appointed as an Assistant Professor of Mathematics at Princeton University. This was a great opportunity for her. As she recalled: The Clay Fellowship gave me the freedom to think about harder problems, travel freely, and talk to other mathematicians. I am a slow thinker, and have to spend a lot of time before I can clean up my ideas and make progress. So I really appreciate that I didn’t have to write up my work in a rush.
The fellowship gave her the time to produce some brilliant papers. After completion of her Research Fellowship in 2008, Maryam moved to Stanford University where she was appointed as Professor of Mathematics in 2009. She was 31 years old. Maryam married a computer scientist Jan Vondrak whom she met while at Princeton, who also joined the faculty at Stanford in 2016. Their daughter Anahita was born in 2011. Maryam would spend hours at home with large sheets of paper sketching out ideas, diagrams and formulae; her young daughter would say “Mummy is painting again!”
When once asked what was the most rewarding part of her work Maryam said: 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. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight! I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.
Maryam’s work soon led to her receiving recognition and awards. The most significant was the Fields Medal that Maryam was awarded in 2014.
The Fields Medal, established in 1936, is often described as the Nobel Prize of mathematics. But unlike the Nobel Prizes, the Fields Medals for Mathematics are given only to people aged 40 or younger, not just to honour their accomplishments but also to predict future mathematical triumphs.
Maryam was the first woman, and the first Iranian to win this prize. It was presented to her at the International Congress of Mathematics, held in Seoul, South Korea on 13 August 2014. The award recognized Mirzakhani’s “outstanding contributions to the fields of geometry and dynamical systems, particularly in understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects”.
Even before she got this award, Mirzakhani had been diagnosed with breast cancer. She continued her work, producing not only results of great significance but developing tools that would be used by other researchers in the field. The cancer spread to her liver and bones and she passed away in July 2017. Her death robbed mathematics of one of its brightest stars who, at the age of 40, was at the peak of her creativity.
The little girl who loved to read and to imagine, reached unimagined peaks in a subject that did not initially excite her. As she once said about the pursuit of mathematics: I don’t think that everyone should become a mathematician, but I do believe that many students don’t give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers.
Described as one of the greatest mathematicians of her generation, several mathematics prizes have been named after her, including the Maryam Mirzakhani New Frontiers Prize to be awarded to outstanding young female researchers in the field of mathematics each year.
In 2020 Maryam Mirzakhani was named by UN Women as one of seven female scientists (dead or alive) who have shaped the world. 12 May, her birth anniversary, is now celebrated as International Women in Mathematics Day.