But the Kaplans realized that they had touched a nerve, and enrollment grew—purely through word of mouth. They now teach nearly 200 people every semester.

The Kaplans have never repeated a curriculum.

“Each semester starts from scratch, so veterans and novices move together,” Robert says.

They try to find topics which are “mysterious and accessible at the same time,” Ellen says.

The results are often so creative that last year one class had its findings published in FOCUS, the Mathematical Institution of America’s most widely distributed periodical.

But the Kaplans never considered themselves math whizzes in their younger days.

“I am the poster child for the mathematics failure,” Ellen says.

She describes her elementary school as a progressive school “where you only learned what you wanted.” At age 10, she could add numbers under 20, subtract without borrowing, but knew no division.

“And my mother was a mathematician,” she says with a laugh.

Ellen’s parents had her switch schools, but she never developed an interest in math and never took a math class in high school beyond Algebra 2.

After high school she attended Radcliffe Collge, where she studied classical archeology and steered clear of math classes.

But several years later, after she was hired at a local high school teaching biology, she found out that she would be teaching math as advanced as calculus.

It was then that, with the help of summer lunch hours with colleague Barry Mazur she learned “everything from long division on.”

Robert also admits experiencing the “standard terrible teaching” as a student, learning math from the football coach. He says he rediscovered mathematics by way of philosophy, which he studied as a graduate student at Harvard.

“They are intimately related,” he explains. “If you want to know how things are and what they are, in my belief you’re asking a question of structure. Mathematics is not only the art of the infinite, but also the science of structure.”