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Mathematics World Mourns Maryam Mirzakhani, Only Woman to Win Fields Medal

Maryam Mirzakhani, the first woman and first Iranian to win the Fields Medal, often described as the rough equivalent of a Nobel prize for mathematicians, died of metastatic breast cancer on July 15, at the age of 40. She had been a professor at Stanford University since 2008.

The loss feels personal to many women in mathematics. “My mailbox is full of messages from other women,” says Ingrid Daubechies, a math professor at Duke University. “Women mathematicians all over the world are e-mailing each other, trying to comfort each other. It is heartbreaking that we had to lose a gifted mathematician and wonderful role model so soon.”

Born in Tehran, Mirzakhani studied mathematics at Sharif University of Technology there before coming to the U.S. to get a PhD at Harvard University in 2004. As she told Quanta Magazine in 2014, she did not grow up wanting to become a mathematician. As a child, she loved to read and make up stories and thought she might be a writer. But despite some discouraging classes in middle school, she eventually discovered a passion for mathematics and proved brilliant at it.

Mirzakhani worked on a variety of problems related to hyperbolic geometry, which describes surfaces that are curved like a Pringles potato chip or the curly ends of a leaf of kale. Unlike chips or vegetables, however, these surfaces close up like donuts, usually with multiple holes. If that is hard to visualize, there’s good reason: The surfaces Mirzakhani studied were not bound by the constraints of the real world.

Mathematicians often understand these surfaces by studying curves that sit on them. Simple loops are a particularly important class of such curves. (In this context “simple” refers to a loop that does not intersect itself.) In her thesis Mirzakhani solved a problem that sounds straightforward but which is actually extremely difficult to answer: On a given hyperbolic surface, how many simple loops are there of less than a given length?

Her…

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