Date: Aug 14, 2014 4:02 PM
Author: Jerry P. Becker
Subject: The first woman to win the prestigious Fields Medal prize
From The Guardian, Tuesday, August 12, 2014. See
Maryam Mirzakhani: 'The more I spent time on maths, the more excited I got'
The first woman to win the prestigious Fields
Medal prize discusses her life as a mathematician
SIDEBAR PHOTO: Maryam Mirzakhani, professor of
mathematics at Stanford University. She recently
became the first woman to win the Fields Medal.
Photograph: Stanford University
Maryam Mirzakhani has become the first woman to
win the Fields Medal, the most prestigious prize
in mathematics. Mirzakhani, 37, is of Iranian
descent and completed her PhD at Harvard in 2004.
Her thesis showed how to compute the
Weil-Petersson volumes of moduli spaces of
bordered Riemann surfaces. Her research interests
include Teichmüller theory, hyperbolic geometry,
ergodic theory, and symplectic geometry. She is
currently professor of mathematics at Stanford
University, and predominantly works on geometric
structures on surfaces and their deformations.
What are some of your earliest memories of mathematics?
As a kid, I dreamt of becoming a writer. My most
exciting pastime was reading novels; in fact, I
would read anything I could find. I never thought
I would pursue mathematics until my last year in
high school. 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
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. My first memory of
mathematics is probably the time that he told me
about the problem of adding numbers from 1 to
100. I think he had read in a popular science
journal how Gauss solved this problem. The
solution was quite fascinating for me. That was
the first time I enjoyed a beautiful solution,
though I couldn't find it myself.
What experiences and people were especially
influential on your mathematical education?
I was very lucky in many ways. The war ended when
I finished elementary school; I couldn't have had
the great opportunities that I had if I had been
born 10 years earlier. I went to a great high
school in Tehran - Farzanegan - and had very good
teachers. I met my friend Roya Beheshti during
the first week of middle school. It is invaluable
to have a friend who shares your interests, and
it 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. Also, our school principal
was a strong-willed woman who was willing to go a
long way to provide us with the same
opportunities as the boys' school.
Later, I got involved in Math Olympiads that made
me think about harder problems. As a teenager, I
enjoyed the challenge. But most importantly, I
met many inspiring mathematicians and friends at
Sharif University. The more I spent time on
mathematics, the more excited I became.
Could you comment on the differences between
mathematical education in Iran and in the US?
It is hard for me to comment on this question
since my experience here in the US is limited to
a few universities, and I know very little about
the high school education here. However, I should
say that the education system in Iran is not the
way people might imagine here. As a graduate
student at Harvard, I had to explain quite a few
times that I was allowed to attend a university
as a woman in Iran. While it is true that boys
and girls go to separate schools up to high
school, this does not prevent them from
participating say in the Olympiads or the summer
But there are many differences: In Iran you
choose your major before going to college, and
there is a national entrance exam for
universities. Also, at least in my class in
college, we were more focused on problem-solving
than on taking advanced courses.
What attracted you to the particular problems you have studied?
When I entered Harvard, my background was mostly
combinatorics and algebra. I had always enjoyed
complex analysis, but I didn't know much about
it. In retrospect, I see that I was completely
clueless. I needed to learn many subjects which
most undergraduate students from good
universities here know.
I started attending the informal seminar
organized by Curt McMullen. Well, most of the
time I couldn't understand a word of what the
speaker was saying. But I could appreciate some
of the comments by Curt. I was fascinated by how
he could make things simple and elegant. So I
started regularly asking him questions, and
thinking about problems that came out of these
His encouragement was invaluable. Working with
Curt had a great influence on me, though now I
wish I had learned more from him. By the time I
graduated I had a long list of raw ideas that I
wanted to explore.
Can you describe your research in accessible
terms? Does it have applications within other
Most problems I work on are related to geometric
structures on surfaces and their deformations. In
particular, I am interested in understanding
hyperbolic surfaces. Sometimes properties of a
fixed hyperbolic surface can be better understood
by studying the moduli space that parameterises
all hyperbolic structures on a given topological
These moduli spaces have rich geometries
themselves, and arise in natural and important
ways in differential, hyperbolic, and algebraic
geometry. There are also connections with
theoretical physics, topology, and combinatorics.
I find it fascinating that you can look at the
same problem from different perspectives and
approach it using different methods.
What do you find most rewarding or productive?
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.
What advice would you give those who would like
to know more about mathematics - what it is, what
its role in society has been, and so on?
This is a difficult question. 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.
* This interview is republished with the kind
permission of the Clay Mathematics Institute.