The book contains three “interludes”—short chapters that depart entirely from math. Robert explains their presence by drawing a parallel to a Math Circle class.

“There’s a moment when the eyes glaze, and you have to stop,” he says.

“It has to do with the pace at which one reads,” Ellen adds. “Math has to be read at the speed of lyric poetry because it’s that condensed. It provides a smoothness so that you can glide across a philosophical conversation.”

The Kaplans say they understand that mathematics fills many people with dread.

“The written language of it is off-putting, clumsy, medieval,” complains Robert. “You have to be able to see through that to the beauty of the structure, like in music.”

To this end, their book’s treatment of technical notation is very wary, according to Ellen.

“We start in conversational language, speaking qualitatively,” she says. “Then it becomes more precise. You have to make notation you own. It is barbed wire in your face until then.”

The book also addresses the terror of mathematical notation in its appearance. All the diagrams are hand-written by Ellen, who also illustrated The Nothing That Is, and each chapter begins with headings in a whimsical typeface.

That way, explains Ellen, “it doesn’t seem that it was given from above.”

The Kaplans sit in the airy living room of their house off Central Square, sipping tea and nibbling on shortbread. Their conversation ranges from depictions of the crucifixion from the Renaissance to hitch-hiking through Ireland. Ellen’s paintings line the room’s walls. One, a reproduction of a painting she saw in Florence, was the result of the museum not selling a postcard of it, she admits.

Their novel approach to mathematics began on “a Tuesday evening” in 1994, Robert recalls.

Ellen had been teaching at the time, and was sick of “that kind of authoritarianism” so common in math classes.

“Why is math taught so badly,” they lamented at the time, “especially in Cambridge?”

The couple decided to take matters into their own hands. That very Saturday, they gathered about 30 students in the basement of a nearby church.

“They were as randomly chosen as you could get,” Ellen says.