Do you ever miss math class?
Not timed drills or column after tedious column of long division problems. But those moments between the drudgery when the concrete and the abstract seem to coalesce. When the table in front of you dissolves into a plane that you can both see and see through and contemplate it extending to Venus, and beyond.
Looking back, it sometimes feels like the best moments in math class where those flashes of imagination and searching inspired by 2,000-year old theorems or equations we handle with the same tools as people separated from us by continents and millennia. Who were the people who worked this out? What were they building, or measuring? What did they have for breakfast? What happens if we do this?
In “Hidden Harmonies: The Lives and Times of the Pythagorean Theorem,” math professors Robert and Ellen Kaplan indulge in exactly this sort of playful curiosity. Their whole book would be a mildly amusing side issue back in geometry class, where even the best instructors and students are focused on the next text and mastering the next stage. Even if you are fortunate enough to have a teacher who doesn’t allow you to use a theorem until you have mastered the proof of that theorem, there is still little time for the curvy, asymmetric details of life outside the diagrams and equations.
So what a pleasure to sit down and amble through the proofs and explanations of math students and scholars over centuries, without the imposition of a project deadline , no pyramid to build, no exam to worry about .
If you don’t remember your math, or if it gives you a belly ache, be easy. You don’t have to linger over the pages of proofs and diagrams and equations. You can just take the Kaplans’ word for it, and the rest of the book will be a quick and enjoyable read about people and cultures dating back thousands of years. You’ll find the Babylonians counting by the joints of each finger, which means you can count to 15 on each hand and base 60 seems a lot more manageable.
There is Pythagoras’ colony of smarties at Samos, of course, and all those other big, old, accomplished cultures — Egyptians, Indians, Arabs, Chinese. But the reader also meets a blind girl in 19th century Massachusetts and a high school kid in Milwaukee in the 1920s. They were all working with and playing with math, trying to master or say in a new way or discover more insights in the relationship among the sides of a right triangle.
I once knew a physicist who complained that Stephen Hawking’s book “A Brief History of Time” was fine as far as it went, but it included none of the math that demonstrated the explanations of black holes and other ideas about space.
“It’s like having the words but none of the music,” the physicist said.
If you are that guy, then the Kaplans will not disappoint you. The music is all there.