In 1935 a young Egyptian woman entered a beauty pageant and set off a national scandal. Fifteen years later, the same woman was leading a uniformed brigade through Cairo and shutting down a branch of Barclays Bank. Doria Shafik was born in Tanta in 1908, earned her baccalaureate at 18 as one of the first girls in the country to do so, and won a rare Ministry of Education scholarship to the Sorbonne, where she took a doctorate in philosophy with highest honors. Her two theses previewed everything that followed: a defense of ancient Egyptian art against Western dismissal, and an unapologetic philosophical case for the equal rights of women. She came home in 1940 wanting to teach at Cairo University. The dean refused to hire her, calling her too liberal.

Locked out of a classroom of a few dozen students, she went looking for an audience of mil ...