Maryam Mirzakhani becomes the first woman to win the Fields Medal - the Nobel Prize of mathematics

When Maryam Mirzakhani, a professor of mathematics at Stanford, was awarded the 2014 Fields Medal today, she created history by becoming the first woman mathematician to have achieved this prestigious honor. Mirzakhani is also the first Iraninan and second Stanford recipient (Paul Cohen in 1966 was first) to win the prize, widely regarded as the “Nobel Prize of mathematics,” since it was established in 1936. She was awarded the Fields Medal for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.

Officially known as the International Medal for Outstanding Discoveries in Mathematics, the Fields Medal was presented by the International Mathematics Union today at the International Congress of Mathematicians, held this year in Seoul, South Korea.

In the official blog of Stanford University, she has expressed her immediate reactions on receiving the honor,

This is a great honor. I will be happy if it encourages young female scientists and mathematicians. I am sure there will be many more women winning this kind of award in coming years.

Earlier, in an interview with Erica Klarreich she had accepted that when an email arrived in February saying that she would receive what is widely regarded as the highest honor in mathematics — the Fields Medal, she assumed that the account from which the email was sent had been hacked.

Fields Medal was conferred to Mirzakhani for her sophisticated and highly original contributions to the fields of geometry and dynamical systems. In simple terms, she has been working towards understanding the symmetry of curved surfaces, such as spheres, the surfaces of doughnuts and of hyperbolic objects. Although her work is considered “pure mathematics” and is mostly theoretical, it has implications for physics and quantum field theory.

From a writer to a mathematician

Mirzakhani was born and brought up in Tehran, Iran. At first she was more interested in reading and writing fiction than doing mathematics. She just wanted to read every book she could find. She watched television biographies of famous women such as Marie Curie and Helen Keller, and later read “Lust for Life,” a novel about Vincent van Gogh. However, by high school, her affinity for solving mathematical problems and working on proofs had shifted her sights.

Mirzakhani won gold medals at both the 1994 and 1995 International Math Olympiads finishing with a perfect score in the latter competition. Mathematicians who would later be her mentors and colleagues followed the mathematical proofs she developed as an undergraduate. She spoke about her interest,

It is fun – it’s like solving a puzzle or connecting the dots in a detective case. I felt that this was something I could do, and I wanted to pursue this path.

After earning her bachelor’s degree from Sharif University of Technology in 1999, she began work on her doctorate at Harvard University under the guidance of Fields Medal recipient Curtis McMullen. She possesses a remarkable fluency in a diverse range of mathematical techniques – including algebra, calculus, complex analysis and hyperbolic geometry. By borrowing principles from several fields, she has brought a new level of understanding to an area of mathematics called low dimensional topology.

Research Work and its Impact

Mirzakhani’s earliest work involved solving the decades-old problem of calculating the volumes of moduli spaces of curves on objects known as Riemann surfaces. These are geometric objects whose points each represent a different hyperbolic surface. These objects are mostly theoretical, but real-world examples include amoebae and doughnuts.

In general, her work can best be described as pure mathematics – research that investigates entirely abstract concepts of nature that might not have an immediately obvious application.

Steven Kerckhoff, a mathematics professor at Stanford and one of Mirzakhani’s collaborators mentioned,

What’s so special about Maryam, the thing that really separates her, is the originality in how she puts together these disparate pieces.

Maryam’s work is an example of curiosity-driven research. The work, however, could have impacts concerning the theoretical physics of how the universe came to exist and, because it could inform quantum field theory, secondary applications to engineering and material science. Within mathematics, it has implications for the study of prime numbers and cryptography.

Mirzakhani spoke about her approach to developing new proofs,

I don’t have any particular recipe. It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.

What defines Maryam Mirzakhani?

Mirzakhani likes to describe herself as slow. Unlike some mathematicians who solve problems with quicksilver brilliance, she gravitates toward deep problems that she can chew on for years. She said,

Months or years later, you see very different aspects of a problem. There are problems I’ve been thinking about for more than a decade and still there’s not much I can do about them.

Mirzakhani doesn’t feel intimidated by mathematicians who knock down one problem after another. She said, “I don’t get easily disappointed. I’m quite confident, in some sense.”

What’s next

Mirzakhani has expressed that she has no desire to be the face of women in mathematics. Her ambitious teenage self would have been overjoyed by the award, she said, but today, she is eager to deflect attention from her achievements so she can focus on research.

She has started working to try to develop a complete list of the kinds of sets that translation surface orbits can fill up. Such a classification would be a “magic wand” for understanding billiards and translation surfaces.

It’s no small task, but Mirzakhani has learned over the years to think big. She said,

You have to ignore low-hanging fruit, which is a little tricky. I’m not sure if it’s the best way of doing things, actually — you’re torturing yourself along the way. But life isn’t supposed to be easy either.