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 winners honored on Wednesday at the International Congress of Mathematicians in Seoul, South Korea.
The Fields Medal is given every four years, and several can be awarded at once. The other recipients this year are Artur Avila of the National Institute of Pure and Applied Mathematics in Brazil and the National Center for Scientific Research in France; Manjul Bhargava of Princeton University; and Martin Hairer of the University of Warwick in England.
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.”
Ingrid Daubechies, a professor of mathematics at Duke and president of theInternational Mathematical Union, called the news “a great joy” in an email.
“All researchers in mathematics will tell you that there is no difference between the math done by a woman or a man, and of course the decision of the Fields Medal committee is based only on the results of each candidate,” she wrote. “That said, I bet the vast majority of the mathematicians in the world will be happy that it will no longer be possible to say that ‘the Fields Medal has always been awarded only to men.’ ”
Much of the research by Dr. Mirzakhani, who was born in Tehran in 1977, has involved the behavior of dynamical systems. There are no exact mathematical solutions for many dynamical systems, even simple ones.
“What Maryam discovered is that in another regime, the dynamical orbits are tightly constrained to follow algebraic laws,” said Curtis T. McMullen, a professor at Harvard who was Dr. Mirzakhani’s doctoral adviser. “These dynamical systems describe surfaces with many handles, like pretzels, whose shape is evolving over time by twisting and stretching in a precise way. They are related to billiards on tables that are not rectangular but still polygonal, like the regular octagon.”
Dr. Avila, 35, investigated a different area of dynamical systems, including an understanding of fractals. Dr. Bhargava, 40, was recognized for new methods in the geometry of numbers, especially prime numbers, and Dr. Hairer, 38, made advances in the study of the effect of random noise on partial differential equations, capturing the effect of turbulence on ocean currents or the flow of air around airplane wings.
While women have reached parity in many academic fields, mathematics is still dominated by men, who earn about 70 percent of the doctoral degrees. The disparity is even more striking at the highest echelons. Since 2003, the Norwegian Academy of Science and Letters has awarded the Abel Prize, recognizing outstanding mathematicians with a monetary award of about $1 million; all 14 recipients so far are men. No woman has won the Wolf Prize in Mathematics, another prestigious award.
The Fields Medal was conceived by John Charles Fields, a Canadian mathematician, “in recognition of work already done” and as “an encouragement for further achievement.” Judges have interpreted the terms of the Fields trust to mean that the award should usually be limited to mathematicians age 40 or younger.
Dr. McMullen, himself a Fields medalist, did not speculate on why it had taken so long for a woman to be recognized. “I would prefer to look forward and celebrate this occasion,” he said, “and see it as a sign of positive trends in society and in science.”
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Maryam Mirzakhani (Persian: مریم میرزاخانی; born May 1977) is an Iranian mathematician, and a full professor of mathematics (since 1 September 2008) at Stanford University.
Her research interests include Teichmuller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. In 2014, Mirzakhani became the first woman, as well as the first Iranian and the second person from the Middle East (after Elon Lindenstrauss), to be awarded the Fields Medal.
Mirzakhani found international recognition as a brilliant teenager after receiving gold medals at both the 1994 International Mathematical Olympiad (Hong Kong) and the 1995 International Mathematical Olympiad (Toronto), where she was the first Iranian student to finish with a perfect score.
Maryam Mirzakhani was born in 1977 in Tehran, Iran. She went to high school in the city at the Farzanegan School, a school for gifted girls that is administered by the National Organization for Development of Exceptional Talents (NODET). Mirzakhani competed and was recognized internationally for her math skills, receiving gold medals at both the 1994 International Mathematical Olympiad (Hong Kong) and the 1995 International Mathematical Olympiad (Toronto), where she was the first Iranian student to finish with a perfect score.
Mirzakhani obtained her BSc in mathematics (1999) from Sharif University of Technology in Tehran. She went to the United States for graduate work, earning a PhD from Harvard University (2004), where she worked under the supervision of the Fields Medalist Curtis McMullen. She was also a 2004 research fellow of the Clay Mathematics Institute and a professor at Princeton University.
Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Maryam Mirzakhani discovered a formula expressing the volume of a moduli space with a given genus as a polynomial in the number of boundary components. This led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautology classes on moduli space, as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface. Her subsequent work has focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston's earthquake flow onTeichmuller space is ergodic.
Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces". She was congratulated for her win by Iranian President Hassan Rouhani.
She married Jan Vondrak, a theoretical computer scientist. They had a daughter named Anahita.
