A Fields Medal in Mathematics Has Been Awarded to a Woman for the First Time in History

37-year-old mathematics professor Maryam Mirzakhani from Stanford University has become the first woman to receive the Fields Medal, the most prestigious award in mathematics.

The organizing committee recognized Maryam's exceptionally valuable contribution to geometry and dynamical systems. "Her work on Riemann surfaces and their moduli spaces combines several mathematical disciplines – hyperbolic geometry, complex analysis, topology and dynamical systems – and has in turn influenced all of these disciplines. She has gained widespread recognition for her initial results in hyperbolic geometry," the committee said in a statement.

The Fields Medal is awarded once every 4 years at each International Congress of Mathematicians to two, three, or four young mathematicians under the age of 40. Since the Nobel Prize is not awarded to mathematicians, the Fields Medal is often called the "Nobel Prize for Mathematicians."


Stanford University mathematics professor Maryam Mirzakhani

The Fields Medal differs from the Nobel Prize in that it is awarded with an age limit of 40 years. This is because the award should not only be a recognition of merit but also an incentive to continue further work.

According to Mirzakhani's biography, while studying at a school in Tehran, she initially did not have outstanding abilities in mathematics. The teacher did not consider her talented, and she lost interest in the subject. But the following year, a new teacher managed to revive the girl's interest in mathematics, and within a year, she was considered a star.

In high school, Maryam wanted to prove that she could be better than the most talented boys (in Iran, there are still separate girls' schools - Maryam studied in one - and other "discriminations" against the weaker sex). Before her, there were never any girls in the national team for the International Mathematical Olympiad, and young Maryam spent weeks studying textbooks to solve problems from the Olympiad and prove her suitability.


Four-year-old Maryam was not interested in mathematics at all. And later she was more interested in adventure books: she wanted to read all the books in the library

In 1994, at the age of 17, Maryam and her friend Roya Beheshti (now a professor of mathematics at Washington University) became the first girls in Iranian history to be included in the national team for the International Mathematical Olympiad. The team won a gold medal.

After moving to Harvard University, the girl understood practically nothing of what the teachers were saying, but she was so passionate about the subject that she terrorized the teachers with questions. Needless to say, over time she fully mastered the course, and when she turned on her imagination and asked the teacher to determine the correctness of the described models, he did not know what to answer.

Even now, colleagues say, Maryam "gives the impression of a 17-year-old girl who is absolutely fascinated by all the mathematics that is happening around her."

She was most fascinated by hyperbolic planes (Lobachevsky planes) - strange figures with non-standard geometry and saddle-shaped forms. They could not be built in ordinary space; they existed only in abstract form, where distances and angles are described by a set of equations. But Maryam's imagination perfectly drew them.

In the early 2000s, many relatively simple properties of Lobachevsky planes, discovered 150 years ago, remained unknown. For example, what will happen to straight lines (geodesics) on such a plane. In her doctoral dissertation, Maryam elegantly answered this question, so that her solution "begs to be included in a textbook," according to colleagues.

After this enlightening dissertation, Maryam solved several more complex mathematical problems, including offering a one-line solution for a problem that was considered practically unsolvable.

The 37-year-old professor is now continuing her scientific career, conducting research in various fields in collaboration with several colleagues.

Other Fields Medal winners in 2014

Artur Avila, for his profound contributions to dynamical systems theory, which have transformed the field, using the powerful idea of renormalization as a unifying principle.

Manjul Bhargava for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves.

Martin Hairer for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a regularity structures theory for such equations. Source: habrahabr.ru/post/233565/