Maryam Mirzakhani

“The beauty of mathematics only shows itself to more patient followers.”

Quick Facts

Nationality: Iranian

Born: May 3rd 1977 in Tehran, Iran

Died: July 14th 2017 in Palo Alto, California, U.S., aged 40

Previous Occupation: Professor of Mathematics at Stanford University

Academic Interests: Moduli spaces, Teichmüller theory, hyperbolic geometry, Ergodic theory and symplectic geometry

Personal Interests: Motherhood, reading, writing, doodling

You may have heard of Maryam, you may not have. I am a little ashamed to admit that until I began my research on STEM role models, I had not. Discovering this inspiring woman and mathematician, I was enlightened – I realised just what a fantastic role model she acts as. Not only could she serve as one for you, but for me too! Less than a week after I found Maryam, she passed away after a long battle with cancer. I feel deeply saddened, not only by the loss of such a hardworking and determined mathematician but also by the loss of such a kind, modest character whom I was just getting to know. The significance of what I would write was immediately clear to me – this mini biography is designed to honour her legacy. So pay close attention, you’re about to read an extraordinary story of accomplishment through the face of adversity.

Childhood and Education

Maryam grew up during harsh times, through both the Iran Revolution and the Iran-Iraq war. As the country was just beginning to restabilise after the war, she enrolled at an all-girls school for exceptionally talented students. She had good teachers who always supported the girls’ learning, encouraging them to pursue and develop their interests in science. Creative in her thinking, Maryam’s ambition was to be a writer. She was one of the brighter students, top of most of her classes apart from – wait for it – maths. Surprising, right? Struggling with the subject and fed up of disappointing test scores, Maryam swore at the age of 11 that she was done trying. However, at the end of her summer break, she had turned a corner and returned with a fresh sense of determination. She knuckled down and studied hard with the faith that one day it would all pay off.

Sure enough, Maryam began to find her passion in what she had previously battled to endure. Her grades improved and with new found self-confidence, Maryam started to enjoy engaging in discussions about mathematics with her classmates. They were often motivated by trying to beat the students in the all-boys school connected to theirs. Maryam was fortunate to have a supportive school principle who encouraged her participation in extracurricular programmes that played an important role in the development of many Iranian mathematicians of her generation. Maryam took part in the International Mathematics Olympiad in 1994 and 1995, winning two gold medals – one for a perfect score! She also attended a summer workshop for high school students run by Sharif University of Technology where she would later study and achieve her bachelor’s degree in mathematics. It was through her enthusiastic involvement in these opportunities that Maryam received recognition for the first time outside of school.

Career

Highly recommended by an Iranian mathematics professor who had noticed her talent, Maryam was accepted into Harvard for her PhD in 1999, aged 22. During a seminar, Maryam presented a paper on an age-old formula related to donut shaped surfaces with one handle (or hole) – it was clear she had a deeper understanding of the topic. Closing her report, she showed how she could use this formula to compute the volume of a certain moduli space of curves on Riemann surfaces – a major challenge in mathematical research. Within weeks, she had extended this idea and proved the same formula for surfaces with any number of handles which was later followed by her use of the formula in calculating volumes of all moduli spaces, rather than just one. With her exceptional knowledge of these volumes, Maryam proved a major problem in string theory – Witten’s famous conjecture – using a completely new approach. Her work very quickly caught attention and she was called to discuss whether her techniques could be used to prove similar conjectures in string theory. Maryam’s thesis had begun simply by counting loops on a donut shape and had concluded with the proof of a major formula relating quantum field theory and gravity which introduced profound new ideas to the world of mathematical physics.

Maryam focused most of her career on the study of billiards. She was fascinated by the dynamical systems at play behind their movement on a polygonal table. Her thesis advisor at Harvard – Professor Curt McMullen – became a Fields Medallist in 1998 for his breakthrough in solving the problem for surfaces with two handles. McMullen was pleased with this result – as you’d expect! He believed he had made a major breakthrough. However, Maryam being the curious student she was, was still discontent and queried why he had only solved it for two handles! Oh Maryam, I am in awe of your spirit.

Completing her PhD at Harvard in 2004, Maryam went to work as an assistant professor at Princeton University alongside her work as research fellow at the Clay Mathematics Institute. In 2009, she took the position as mathematics professor at Stanford University. Collaborating largely with Alex Eskin from the University of Chicago, Maryam studied the trajectories of billiards around a traditional table and made phenomenal discoveries involving the connection between their dynamics and the theory of surfaces with many handles – a problem that had been unresolved for over a century! She deserves some sort of medal for that at least, surely?! Yes – in fact she got the best medal there is – the Fields Medal. That’s right. Maryam became and remains the first and only female winner of the most prestigious award for mathematicians. My goodness Maryam, you are a wonder.

I am sad to say that Maryam’s career was cut tragically short as she battled the illness that eventually took her life. It is true that had she lived longer, she would’ve produced even more amazing work. However, her impact in such a short lifetime has not gone unnoticed. She has left a beautiful legacy – her contribution in the dynamics and geometry of Riemann surfaces and their moduli spaces could open up doors to the theoretical physics of how the universe came to exist! What a parting gift!

I think in all of this, it is really important to remember a message from Professor Cumrun Vafa of Harvard University:

“Perhaps it’s tempting to place (Maryam’s) accomplishments in such an esteemed position that one can only admire it as an unachievable legacy. This would be a grave error. I doubt she would have wanted to be remembered like that. Instead, I believe she would have wanted us to view her achievements as perfectly achievable by anyone regardless of gender, from anywhere in the world by those who are willing to work hard to achieve the highest levels of knowledge.”

Awards and Achievements

  • First female to be on the Iranian team for the International Mathematics Olympiad
  • Gold medallist in 1994 and 1995 at the International Mathematics Olympiad, the latter for a perfect score
  • First and only female winner of the Fields Medal 2014
  • Received 2009 Blumenthal Award for the Advancement of Research in Pure Mathematics
  • Received 2013 Satter Prize of the American Mathematical Society

Trivia

  • Maryam was imaginative with her questions – “they were like mathematical short stories of own invention, sometimes fictional but intriguing… she used to try and craft a narrative to make sense of the mathematical world she would be doing research in.”
  • She didn’t even share the news of the Fields Medal with her parents – they found out later through media – she didn’t think it was a big deal.
  • After moving from Iran to the United States for her PhD, Maryam refused to let any language barrier hold her back in her learning. She would constantly ask questions, conversing in English and writing all the answers and notes down in Farsi.

Video Links

Scientific Papers and Publications

Eskin, A. and Mirzakhani, M., 2016. Invariant and stationary measures for the SL. 2. R/action on moduli space arXiv1302.

Eskin, A., Mirzakhani, M. and Mohammadi, A., 2013. Isolation, equidistribution, and orbit closures for the SL(2,R) action on Moduli space. arXiv:1305.3015

Eskin, A. and Mirzakhani, M., 2013. Invariant and stationary measures for the SL(2,R) action on Moduli space. arXiv:1302.3320

Eskin, A., Mirzakhani, M. and Mohammadi, A., 2013. Isolation theorems for SL (2, R)-invariant submanifolds in moduli space. arXiv preprint arXiv:1305.3015.

More extensive list at: https://scholar.google.com/citations?hl=en&user=FZBjJ4cAAAAJ&view_op=list_works&sortby=pubdate

References

  1. https://kayhanlife.com/extraordinary-life-maryam-mirzakhani-queen-mathematics/
  2. http://news.stanford.edu/2017/07/15/maryam-mirzakhani-stanford-mathematician-and-fields-medal-winner-dies/
  3. http://news.stanford.edu/news/2014/august/fields-medal-mirzakhani-081214.html 
  4. https://www.sciencealert.com/how-maryam-mirzakhani-was-a-role-model-for-more-than-just-her-mathematics?perpetual=yes&limitstart=1
  5. https://www.imo-official.org/participant_r.aspx?id=926
  6. https://phys.org/news/2017-07-maths-genius-maryam-mirzakhani-dies.html#jCp
  7. https://en.wikipedia.org/wiki/Maryam_Mirzakhani