With Snowflakes and Unicorns, Marina Ratner and Maryam Mirzakhani Explored a Universe in Motion

The mathematics section of the National Academy of Sciences lists 104 members. Just four are women. As recently as June, that number was six. Marina Ratner and Maryam Mirzakhani could not have been more different, in personality and in background. . . .

Dr. Maryam Mirzakhani, former Member in the School of Mathematics, was a young superstar from Iran who worked nearby at Stanford University. Just 40 when she died of cancer in July, she was the first woman to receive the prestigious Fields Medal.

I first heard about Dr. Mirzakhani when, as a graduate student, she proved a new formula describing the curves on certain abstract surfaces, an insight that turned out to have profound consequences — offering, for example, a new proof of a famous conjecture in physics about quantum gravity.

I was inspired by both women and their patient assaults on deeply difficult problems. Their work was closely related and is connected to some of the oldest questions in mathematics.

Read more from mathematician Amie Wilkinson on the legacies and far-reaching achievements of Ratner and Mirzakhani at the New York Times.