I grew up in a family with three siblings. My parents were always very supportive and encouraging. It was important for them that we have meaningful and satisfying professions, but they didn't care as much about success and achievement. In many ways, it was a great environment for me, though these were hard times during the Iran-Iraq war. My older brother was the person who got me interested in science in general. He used to tell me what he learned in school.

I met my friend Roya Beheshti the first week after entering middle school. It is invaluable to have a friend who shares your interests, and helps you stay motivated. Our school was close to a street full of bookstores in Tehran. I remember how walking along this crowded street, and going to the bookstores, was so exciting for us. We couldn't skim through the books like people usually do here in a bookstore, so we would end up buying a lot of random books.

The principal of the school was a very strong character. If we really wanted something, she would make it happen. Her mindset was very positive and upbeat - that "you can do it, even though you'll be the first one." I think that has influenced my life quite a lot.

I met many inspiring mathematicians and friends at Sharif University. The more I spent time on mathematics, the more excited I became. At Sharif University, we had problem-solving sessions and informal reading groups with my classmates. The friendship and support of all the people I met there ... helped me a lot in many different ways.

She had a sort of daring imagination. She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, "Is it right?" I was always very flattered that she thought I would know.

... closed geodesics on a hyperbolic surface. These are closed curves whose length cannot be shortened by deforming them. A now-classic theorem proved more than50 years ago gives a precise way of estimating the number of closed geodesics whose length is less than some bound L. The number of closed geodesics grows exponentially with L ... Mirzakhani looked at what happens to the "prime number theorem for geodesics" when one considers only the closed geodesics that are simple, meaning that they do not intersect themselves. The behavior is very different in this case: the growth of the number of geodesics of length at most L is no longer exponential in L but is of the order of$L^{6g-6}$L6g−6, where g is the genus.

[Mirzakhani is honoured] for her exceptionally creative, highly original thesis. This work combines tools as diverse as hyperbolic geometry, 'classical methods' of automorphic forms, and symplectic reduction to obtain results on three different important questions. These results include a recursive formula forWeil-Petersson volumes of moduli spaces ofRiemann surfaces, a determination of the asymptotics of the number of simple closed geodesics on a hyperbolic surface in terms of length, and a new proof ofWitten's Conjecture(originally established byKontsevich) establishing the KdV recursion for the intersection numbers on moduli space.

[The Clay fellowship] was a great opportunity for me; I spent most of my time at Princeton which was a great experience. 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.

Mirzakhani, together with Alex Eskin and, in part, Amir Mohammadi, made a major breakthrough in understanding another dynamical system on moduli space that is related to the behaviour of geodesics in moduli space. Non-closed geodesics in moduli space are very erratic and even pathological, and it is hard to obtain any understanding of their structure and how they change when perturbed slightly. However, Mirzakhani et al have proved that complex geodesics and their closures in moduli space are in fact surprisingly regular, rather than irregular or fractal. It turns out that, while complex geodesics are transcendental objects defined in terms of analysis and differential geometry, their closures are algebraic objects defined in terms of polynomials and therefore have certain rigidity properties.

She is very optimistic, and that's infectious. When you work with her, you feel you have a much better chance of solving problems that at first seem hopeless.

Sometimes there were setbacks, but she never panicked.

If we knew things would be so complicated, I think we would have given up. I don't know; actually, I don't know, I don't give up easily.

... for her outstanding contributions to the dynamics and geometry ofRiemann surfaces and their moduli spaces.

Maryam is gone far too soon, but her impact will live on for the thousands of women she inspired to pursue math and science. 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 was a wonderful colleague. She not only was a brilliant and fearless researcher, but she was also a great teacher and terrific PhD adviser. Maryam embodied what being a mathematician or scientist is all about: the attempt to solve a problem that hadn't been solved before, or to understand something that hadn't been understood before. This is driven by a deep intellectual curiosity, and there is great joy and satisfaction with every bit of success. Maryam had one of the great intellects of our time, and she was a wonderful person. She will be tremendously missed.