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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