Fields Medal

Since its inception in 1936, the Fields Medal has been awarded to 52 of the most exceptional mathematicians in the world under the age of 40. For the first time, that award has gone to a woman: Maryam Mirzakhani, 37, an Iranian-born mathematician who works at Stanford.

She shared the prize — the highest honor in mathematics — with Martin Hairer, 38, of the University of Warwick, England; Manjul Bhargava, 40, of Princeton; and Arthur Avila, 35, of the National Center for Scientific Research, France.

According to The New York Times, 70% of doctoral degrees in math are awarded to males, making the award to Mirzakhani especially noteworthy. In the related field of physics, only two women have ever won the Nobel Prize. Only one has won in economics.

The Fields was presented by the International Congress of Mathematicians to this year’s four winners in a ceremony in Seoul on Wednesday.

Mirzakhani’s research focuses on “understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects,” according to a Stanford release. A text provided by the ICM further explains that she works on so-called Riemann surfaces and their deformations. The ICM praised her for “strong geometric intuition.”

A Huge First For Women: Female Mathematician Wins Fields Medal

Iranian professor is first woman to win “Nobel Prize of maths”

An Iranian-born mathematician has become the first woman to win a prestigious Fields Medal, widely viewed as the Nobel Prize of mathematics.

Maryam Mirzakhani, a Harvard-educated mathematician and professor at Stanford University in California, was one of four winners announced by the International Congress of Mathematicians (ICM) at its conference in Seoul on Wednesday.

“This is a great honour. I will be happy if it encourages young female scientists and mathematicians,” Mirzakhani said in a press release from Stanford University where she is a professor.

Mathematician Maryam Mirzakhani is the first woman to win a Fields Medal. It had been an all-boys club since the prizes were established in 1936.

Mirzakhani, a native of Iran, is a professor at Stanford University. She won for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.“

Here’s how Nature summed up her contributions:

“Perhaps Maryam’s most important achievement is her work on dynamics,” says Curtis McMullen of Harvard University. Many natural problems in dynamics, such as the three-body problem of celestial mechanics (for example, interactions of the Sun, the Moon and Earth), have no exact mathematical solution. Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems’ trajectories “are tightly constrained to follow algebraic laws”, says McMullen. He adds that Mirzakhani’s achievements “combine superb problem-solving ability, ambitious mathematical vision and fluency in many disciplines, which is unusual in the modern era, when considerable specialization is often required to reach the frontier”.

An Iranian mathematician is the first woman ever to receive a Fields Medal, often considered to be mathematics’ equivalent of the Nobel Prize.

The recipient, Maryam Mirzakhani, a professor at Stanford, was one of four scheduled to be honored on Wednesday at the International Congress of Mathematicians in Seoul, South Korea.


The 52 medalists from previous years were all men.

“This is a great honor. I will be happy if it encourages young female scientists and mathematicians,” Dr. Mirzakhani was quoted as saying in a Stanford news release on Tuesday. “I am sure there will be many more women winning this kind of award in coming years.” (New York Times)

We’re delighted for Professor Maryam Mirzakhani, the first female recipient of the prestigious Fields Medal in mathematics. In this long overdue landmark, Professor Mirzakhani has been commended for her work in complex geometry.

The mathematics community is hopeful that this will encourage more girls and young women to pursue careers in the field.

The following articles by Maryam Mirzakhani, published in International Mathematics Research Notices, are free for a limited time:

Image: Maryam Mirzakhani by International Mathematical Union (IMU). Public domain via Wikimedia Commons.

Highest Math Prize Goes to Woman for First Time

An Iranian-born Stanford Univ. professor is the first woman to win math’s highest honor, the Fields Medal. The International Mathematics Union awarded the prize to Maryam Mirzakhani and three others at a meeting in Seoul.

The prize and $13,700 is awarded every four years to mathematicians 40 years old or younger. It was established in 1936. Mirzakhani, 37, won for complex theoretical math on the symmetry of curved surfaces, including spheres and even doughnuts.

Read more:

This man is Cédric Villani. He was born in 1973 in Brive, France.

He received the Fields Medal in 2010 – a prize given to influent mathematicians under age 40 – as well as Elon Lindenstrauss, Ngô Bảo Châu and Stanislav Smirnov.

Let me tell you why this man is awesome.

  • This guy is a professor of maths in the University of Lyons-1.
  • He heads the Henri Poincaré Institute, which is an important research center in mathematics.
  • He works on many complicated (and therefore awesome) things like the optimal transportation theory, or the behaviour of gases.
  • He aired a series of short radio programmes in which he explains math facts, as well as the concrete consequences of mathematics in our daily lives.
  • He always wears a spider-shaped brooch, as well as an ascot tie. Always.
  • He was nicknamed, and sometimes nicknames himself, as “the Lady Gaga of maths” (because of his look).
  • He has such a sweet voice!
  • One day, he traveled by train to go to a folk rock concert. He bought a ticket to go there, but he forgot to buy the return ticket – so he had to hitchhike to go back home!
  • He criticizes the way maths are taught in schools, as well as the way math teachers are prepared.
  • He wishes that maths were taught in entertaining ways, rather than boring ways.

Photo by Espace des sciences [CC-BY-SA-3.0], via Wikimedia Commons.

Memoir of Alexander Grothendieck

Two days ago Alexander Grothendieck passed away, at the age of 86. Grothendieck is commonly regarded as the greatest mathematician of the 20th century and was awarded two of world’s most prestigious math prizes: the Fields medal, in 1966, and the Crafoord prize, in 1988.

His main mathematical contributions were to the field of algebraic geometry, linking together algebraic concepts of equations and numbers with geometric ideas of shapes and curves. In the 1960s, Grothendieck and his contemporaries revolutionized the subject by establishing a powerful and abstract foundation, which became the main set of tools and led to countless discoveries in the field in the last half century.

In 1970, at the age of 42, Grothendieck started to desolate mathematics and society in general, radically turning to the problems of environmental protection and ecology, and fighting nuclear power and military buildup.

In 1991 he left his home in the Pyrenees after burning thousands of pages of manuscript. His concealed his new address and became a recluse, even trying to eradicate all traces of his past life in 2010, demanding his entire catalogue be removed from libraries and refusing republications.

On 13 November 2014, Grothendieck died in Saint-Lizier in France.

Maryam Mirzakhani: ‘The More I Spent Time on Maths, The More Excited I Got:

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 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.

• This interview is republished with the kind permission of the Clay Mathematics Institute.
Indian-origin wizard wins 'Nobel Prize' of Mathematics

Mathematicians of Indian- and Iranian-origin are among the four winners of the 2014 Fields Medal, widely considered the Nobel Prize for maths that has been broadly dominated by white males since it was instituted in 1936.

The award going to Princeton University’s Manjul Bhargava, a Canadian-American maths wizard was no surprise; although he is the first person of Indian origin, he was the hot favorite in pre-award polls among peers.

The sensational co-winner is Maryam Mirzakhani, a female Iranian mathematician who teaches at Stanford University. It is the first time a female mathematician has won the Fields medal; all 52 previous winners have been men in a field traditionally dominated by the male of the species.

Expectedly, it created a ripple in the rarefied maths world.

Mirzakhani’s success was “hugely symbolic and I hope it will encourage more women to get into mathematics because we need more women. I am very happy that now we can put to rest that particular ‘it has never happened before’,” Ingrid Daubechies, herself the first female president of the International mathematical Union (IMU), said while announcing the award.

The two other winners this year are Artur Avila from Brazil and Martin Hairer from Austria. Avila is also the first Brazilian and Latin American to win the medal.

One to four Fields Medals are awarded once every four years to mathematicians under the age of 40 years at the International Congress of the International Mathematical Union (IMU), which meets every four years. The presentation will take place in Seoul on Wednesday at the quadrennial IMU Congress (Hyderabad hosted it in 2010).

Although the prize money ($15,000) is chump change (approximately 1/100th) compared to the Nobel Prize, the award, long dominated by Americans, Russians, French, and Britons (38 medals between them), is the highest recognition in the world of mathematics.

Canadian mathematician John Charles Fields instituted it at a time mathematicians felt short-changed that they had no Nobel recognition. The Nobel Prize is awarded for literature, peace, economics, physiology or medicine, chemistry and physics — but not for mathematics.

Legend — or the apocryphal story — goes that Swedish chemist Alfred Nobel, who instituted the Nobel Prize, disdained maths after someone he loved cheated on him — with a mathematician. But there is no historical basis to the story. More likely fact is that Nobel didn’t care much for maths because it was not considered a practical science from which humanity could benefit (a chief purpose for creating the Nobel Foundation).

All that has changed, of course. Mathematics offers solutions to everyday issues from airline scheduling to Internet security, even though many practitioners pursue esoteric problems described in dense language incomprehensible to the layman. Bhargava’s PhD thesis, for instance, is said to have helped in the “determination of the asymptotic density of discriminants of quartic and quintic number fields.”

Although a Canadian-American who was born in Hamilton, Ontario, Bhargava is no stranger to India or to Indian mathematicians. Indeed, his mother, Mira Bhargava, is herself a rare female mathematician, teaching at Hofstra University (another well-known female Indian-American mathematician is Bhama Srinivasan at the University of Chicago).

Manjul has also collaborated with many Indian mathematicians, and his work with fellow Princeton scholar Arul Shankar, his PhD student, won them the Fermat Prize in 2011. Manjul’s own PhD advisor was Andrew Wiles, famous for proving Fermat’s last theorem.

Bhargava was awarded the 2012 Infosys Prize in mathematics for his “extraordinarily original work in algebraic number theory, which has revolutionized the way in which number fields and elliptic curves are counted.” That came on top of almost every other top prize in maths, from the SASTRA Ramanujan Prize in 2005 to the American mathematical Society’s Cole Prize in 2008. So the Fields Medal comes as no great surprise to the mathematical community in the US or in India.

Last week, as speculation heated up about possible 2014 winners of Fields Medal, an online poll put Bhargava on top with 516 votes, with Avila coming second with 486 votes. Apparently, his peers pretty much expected it. Which is not surprising for someone who became a tenured full professor within two years of finishing graduate school, an Ivy League record, and the second youngest full professor in Princeton’s history.

That’s not all. Before you think all he does is crunch numbers, Bhargava is also an accomplished tabla player (tutored by Zakir Hussain) and has the number on Sanskrit, which he learned from his grandfather Purushottam Lal Bhargava, was the head of the Sanskrit department of the University of Rajasthan, during family visits to Jaipur. He sees close links between his three loves noting how beats of tabla and rhythms of Sanskrit poetry are highly mathematical.

Such recognition came to him early. In past interviews, he has often recounted how in Grade 3, he became curious about how many oranges it takes to make a pyramid. Just as well his mathematician mother and chemist father were well-to-do: they indulged him with oranges till he figured out the answer, which was not long coming. Now he’s at the pinnacle of his calling.

The Fields Medals are commonly regarded as mathematics’ closest analog to the Nobel Prize (which does not exist for mathematics), and are awarded every four years by the International Mathematical Union to one or more outstanding researchers.


“Rise above oneself and grasp the world.”


“The mathematicians assembled here from all over the world
pay tribute for outstanding work.”