As a child, Maryam Mirzakhani dreamt of being a novelist, at least until she was struck by the spell of mathematics.
Born in 1977, she attended Farzanegan School in Tehran, which has specifically been established by the Iranian state for girls of high aptitude. Mirzakhani was unstoppable. She was the first Iranian woman to bring home several gold medals from the International Mathematics Olympiad for two consecutive years at the early ages of 17 and 18.
After graduating from Sharif University, she headed to Harvard for graduate studies. There, she did her doctoral thesis under the mentorship of Curtis McMullen (a Fields Medalist), before moving to Princeton University as Assistant Professor and the Clay Mathematics Institute as Research Fellow.
At just 31 years of age, Mirzakhani joined Stanford University as a full professor, researching there till cancer consumed her at age 40.
Mirzakhani won more accolades in her short life than many men do in their entire academic careers. She received the Blumenthal Award from the American Mathematical Society in 2009 and in 2013, the Ruth Lyttle Satter Prize in Mathematics.
In 2014, she became the first woman to win the Fields Medal — the highest honour in mathematics, equivalent to the Nobel Prize. In the same year, she was named in the list of 10 most important researchers of the year in the British science magazine Nature.
More than simply a mathematician, Mirzakhani was a gifted artist who could visualise a world beyond what we can see.
Mirzakhani was an expert in Teichmüller and ergodic theory, hyperbolic geometry, symplectic geometry, and moduli spaces.
In simple terms, her work involved different forms of geometry, abstract surfaces, shapes, and structures in higher-dimensional spaces — topics which are a road block for mathematicians.
Her supervisor Curtis McMullen had provided a solution for predicting the path of balls on a billiard table, the table taking an abstract form resembling a torus-doughnut-pretzel-like shape. Mirzakhani’s appetite however, was not satiated by the work of her supervisor.
Undaunted by the complexity of the solution, she went on to extend McMullen’s work to more complex surfaces as part of her doctoral thesis. The three publications that resulted from her doctoral dissertations are distinguished for involving numerous highly-developed considerations.
So, what’s so great about the game of billiards? For decades, mathematicians have been fascinated with the game.
They have tried to predict what happens to the ball on a table. How does one shoot the ball in a way that it returns to its original spot after a number of rebounds/deflections? Will the ball return to the original path at some point? If it does, will it follow the exact path as before? Is the whole space covered by the flight? Or is the system chaotic? Problems like these are particularly relevant in having a better understanding of the universe, such as the role of periodic orbits.
More than simply a mathematician, Mirzakhani was a gifted artist who could visualise a world beyond what we can see. Her world was filled by geometric and dynamic complexities of curved surfaces – spheres, doughnuts and amoebas.
Her work showcases important aspects of geometry, topology and deformation theory of Riemann surfaces, benefiting many other fields of mathematics such as optics, acoustics, classical mechanics, statistical mechanics, prime numbers and cryptography.
Being the first woman to receive a Fields Medal provoked questions on the under-representation of women in science, technology, engineering and mathematics (STEM) jobs. In going through the profiles of successful mathematicians and scientists, one would be hard-pressed to find anyone who is not male and white.
In 2015, women made up one-third or less of the total workforce in STEM fields in the US. In the UK, the figurewas 17% in 2014 when it came to women professors in engineering and technology. Again, very few of these women are non-white or from immigrant backgrounds.
Gender inequality and cultural stereotypes lead to a lack of confidence in women by their peers. When reflecting on my own experiences and speaking to others in my field, I believe that self-doubt is also a common obstacle preventing women, especially from minority backgrounds, from pursuing a STEM career.
This is where Mirzakhani is an inspiration for all of us as a cultural icon. As an immigrant woman of colour, she defied all stereotypes by becoming an exceptional scientist and mathematician, and outdid many of her male colleagues. She can also serve as an example for women in Pakistan, where women are hardly ever employed or engaged in STEM fields due to several cultural restrictions.
Her curiosity and passion for tackling challenges is what made her discover and churn out solutions. She overturned the long-held belief that women can’t be good in mathematics. Mirzakhani was more than good; she was a geniu.