A History of Pi, published in 1971, is about two things. The first is pi, the number, and our history struggling with its baffling qualities. The second is fascism and, more broadly, ignorance. Beckmann holds pi like a mirror up to humanity and sees stunning genius and highly confident idiots and thugs. The last line of the book notes that there are more of the latter than the former.
The joining of these two topics makes this book really fun to read. The math is dense, though–denser than most pop math books these days. You can skip what you don’t understand (or don’t want to bother with), but some parts of this story can only be told in mathematics, and if you want to appreciate, say, Newton’s contributions to our understanding of pi, or Euler’s, you need to dig into some math that involves infinite sums and integrals. Even the ancient stuff can be daunting. This book is intended for a numerate audience. If equations make you uncomfortable, I wouldn’t recommend Beckmann. If they don’t, on the other hand, the math is quite thrilling, and elegantly presented. Euler’s derivation of
1/1+1/4+1/9+1/16+… 1/(n squared) + … = (pi squared)/6
is breathtakingly elegant, as is Lindemann’s proof of the transcendence of pi. But, again, I’m afraid much of this will read as opaque to a lay audience.
On the other hand, his uninhibited judgments and thorough historical research make the book strangely thrilling. He compares Archimedes’ writing to Aristotle’s: the first is “science,” the second “prattle.” I’ve never heard Aristotle described as a prattler before, but it’s kind of liberating to hear Beckmann say so. The Romans come off far worse; they are “thugs” to Beckmann, early fascists and forerunners to the Nazis and the Soviets. Their use of pi bears out his judgment: they used 3 and 1/8 as an approximation of pi, which was about 2000 years behind the times. As the Romans empire expands, one soldier comes across as thinker doodling shapes in the sand during the sacking of Syracuse.
“Do not touch my circles!” said the thinker to the thug. Thereupon the thug became enraged, drew his sword and slew the thinker.
The name of the thug is forgotten.
The name of the thinker was Archimedes.
Here is the drama that Beckmann sees played out throughout history: the genius is dispatched by the moron.
There was a series of math books by Lilian Lieber that share the same sense of mathematics (and serious thought, more generally) as being a kind of bulwark against fascism. There’s something I love in this idea. There’s also a delicacy to the whole project: mathematics is the flower and tyranny the backhoe… and yet, if enough of us possess the thoroughness of thought to appreciate the art and beauty of math, perhaps we can prevent that backhoe from ever getting started on its destructive path.
Beckmann is perhaps a bit more cynical than Lieber, but his love and respect for the great thoughts of the giants of mathematics is evident. Science and math march forward, and Beckmann is on its side, even as he bridles against those who push towards darkness. All in all, the book was a pleasure to read, and I recommend it to anyone who won’t be scared off by the denseness of the mathematics.