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 the International 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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