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. Ratner was a Soviet Union-born Jew who ended up at the University of California, Berkeley, by way of Israel. She had a heart attack at 78 at her home in early July.

Success came relatively late in her career, in her 50s, when she produced her most famous results, known as Ratner’s Theorems. They turned out to be surprisingly and broadly applicable, with many elegant uses.

In the early 1990s, when I was a graduate student at Berkeley, a professor tried to persuade Dr. Ratner to be my thesis adviser. She wouldn’t consider it: She believed that, years earlier, she had failed her first and only doctoral student and didn’t want another.