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

http://www.theguardian.com/science/2014/aug/13/interview-maryam-mirzakhani-fields-medal-winner-mathematician

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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

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SIDEBAR PHOTO: Maryam Mirzakhani, professor of

mathematics at Stanford University. She recently

became the first woman to win the Fields Medal.

Photograph: Stanford University

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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.

[SEE

http://www.theguardian.com/science/2014/aug/13/fields-medal-mathematics-prize-woman-maryam-mirzakhani

]

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

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. 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

camps.

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

illuminating discussions.

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

areas?

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

surface.

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.

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* This interview is republished with the kind

permission of the Clay Mathematics Institute.

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