From Dreams of Writing to Getting the Fields Mathematics Prize

She is the third child in a family of six. Her father is the head of board of directors of Raad Charitable Training Complex and an electrical engineer who for years has been an encouragement of his children. She finished primary school when the Iran-Iraq war had ended, and she managed to go to Farzanegan School (under the auspices of the National Shining Talents Developing Centre) and continued on to high school there.
As a child she wanted to be a writer. She read any story or book she could get her hands on, and she was more interested in poetry and literature. Their house was near a street filled with bookshops. She was not allowed to look through the books. Because she ended up turning the bookstore upside down until she got the book that she wanted, and would make the proprietor angry. She would usually purchase some books at random. As a child Maryam did not much like numbers and until her last year in high school she never thought about becoming a mathematician. Her brother was the one who got her interested in science. He would tell her what he’d learned in school. One day he told her a story about a German mathematician called Carl Friedrich Gauss who when he was a student had in just a few seconds got the answer to the total of the numbers 1 to 100 in an ingenious way. This was the first time that she found the joy of getting a beautiful answer. Even though she had not been able to find it herself. With the efforts of her school principal who stressed on her students having equal opportunities as the boys, the sewn seeds of interest began to take root in her.
With this start and interest Maryam entered the mathematics Olympiad during her years in high school. In 1994 and 1995 from Farzanegan high school she managed to get gold medal in the national mathematics Olympiad. Also in 1994 she took part in the Hong Kong World Mathematics Olympiad and got 41 out of 42 points and received a gold medal. In the following year with a score of 42 out of 42 she got gold medal in the Toronto World Mathematics Olympiad.
She was the first girl to join the Iranian mathematics Olympiad team to receive a gold medal, she was the first to get gold medals in two years running, and she was the first person to get full points in a world mathematics Olympiad. All these successes gave Maryam further motivation.
She took part in the nationwide university entry exam and began studying mathematics in Sharif Industrial University. In university she got know many new friends and lecturers who showed her good ways in her studies, and she continued on with more interest until in February 1998 while still in university she participated in the students mathematics competition in Ahwaz as part of her university team. But on their return trip from Ahwaz to Tehran her team was involved a crash, leaving her with a sad and bitter memory, because she lost 6of her friends. She was injured and was the sole survivor of the crash.
She got her B.S. and M.S. from Sharif University and went to the United States to continue her studies and by getting a scholarship from Harvard she got her doctorate in mathematics. Following getting her doctorate she continues to researcrh and teach in her field of expertise and at 31 years of age she became a professor and researcher in Princeton and Stanford Universities.
Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Mirzakhani discovered a formula expressing the volume of a moduli space with a given genus as a polynomial in the number of boundary components. This led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space, as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface, generalizing the theorem of the three geodesics for spherical surfaces. Her subsequent work has focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston's earthquake flow on Teichmüller space is ergodic.
Most recently as of 2014, with Alex Eskin and with input from Amir Mohammadi, Mirzakhani proved that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal. The closures of complex geodesics are algebraic objects defined in terms of polynomials and therefore they have certain rigidity properties, which is analogous to a celebrated result that Marina Ratner arrived at during the 1990s.The International Mathematical Union said in its press release that, "It is astounding to find that the rigidity in homogeneous spaces has an echo in the inhomogeneous world of moduli space."
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces". In a message, Iranian president Hassan Rowhani congratulated her for winning this prestigious award.
She is married to Jan Vondrák, a Czech theoretical computer scientist who works at IBM Almaden Research Center. They have a three year old daughter named Anahita.
Some of Professor Mirzakhani’s awards and achievements are as follows:
1 – The first woman to win the most prestigious mathematics award, the Fields Medal in 2014.
2 – Clay Mathematics Institute International Award in 2014.
3 – American Mathematics Institute International Award in 2013.
4 – The IMS Blumenthal Award in 2009.
5 – Becoming a mathematics professor at Stanford University at 31.
6 – International Mathematics Olympiad in Canada 1995.
7 – Gold medal in Hong Kong International Mathematics Olympiad in 1994.
8 – Clay Mathematics Institute Research Fellowship in 2004.
9 – Harvard Junior Fellowship Harvard University, 2003.
10 – Merit Fellowship Harvard University, 2003.
11 – IPM Fellowship the Institute of Theoretical Physics and Mathematics Tehran, Iran 1995-99.
When asked what she found most rewarding or productive, she replied?
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.

Sanaz Moazezi
M.A. in International Law