In Pursuit of the Unknown: 17 Equations That Changed the World, Ian Stewart, Basic Books, New York, 2012. $26.99 (342 pp.). ISBN 978-0-465-02973-0
Emeritus professor of mathematics Ian Stewart is a well-known and well-regarded writer on popular mathematics. As a testament to his outstanding expository skills, he succeeded Martin Gardner—a tough act to follow—in writing the Mathematical Games column at Scientific American. Stewart’s new book, In Pursuit of the Unknown: 17 Equations That Changed the World, tackles an equally tough challenge. “Equations that changed the world” is a phrase guaranteed to intrigue the sort of person who, if given a choice between the latest issues of Physics Today and the Economist while trembling in the waiting room of a dentist, would pick the latter. That person may be intelligent and literate, but not a physicist, mathematician, or engineer.
I write that not because In Pursuit of the Unknown is a bad book—far from it, as I’ll soon explain—but because the subtitle is likely to prompt a regular reader of Physics Today to retort, “What do you mean, 17 equations? I can think of at least 50. Maybe even 75 if you give me until lunch!” Stewart, I’m sure, is well aware of that and writes (unfortunately, not until the end of the book), “It took a lot more than seventeen equations to get us where we are today.” In comparison, Dana Mackenzie’s The Universe in Zero Words: The Story of Mathematics as Told Through Equations (Princeton University Press, 2012) covers 24 equations, not all of which overlap with Stewart’s. But given the reality of publishing, one can hardly fault Stewart, or Mackenzie, for not writing the 177 314–page book required to discuss every important equation.
In general, an assessment of equations to include would probably be 50% “No argument with that choice” and 50% “I wonder how that one made the final cut.” In Stewart’s collection, the first category includes the Pythagorean theorem (about which Stewart unfortunately repeats a tasteless joke that no teacher with any sensitivity would ever tell in lecture), Newton’s inverse-square law, and Maxwell’s equations. The second category contains the Navier–Stokes equations, Euler’s formula for polyhedra, and the Black–Scholes equation (with which financial traders nearly destroyed modern banking). The wave equation, Fourier transforms, the second law of thermodynamics, i = √−1, and E = mc2 are in the mix, too. Of course, my selection of which category each of those falls into is as eccentric as Stewart’s. And that’s my point. I can’t help but wonder, however, how Boolean algebra’s wonderful 1 + 1 = 1, which is at the foundation of our modern digital world, failed to make an appearance. Perhaps it was too obvious.
Each equation gets its own chapter, which opens with the equation itself, accompanied by a helpful explanation of what each symbol means. Each chapter is written in Stewart’s easy prose, which never fails to both educate and entertain. The chapters are populated by lots of historical details—a feature of the book I particularly enjoyed. The occasional slips do occur. There’s the temporarily confusing typo (page 26) in a discussion on the invention of logarithms, where we suddenly go from multiplying 2.67 by 3.51 to multiplying 2.87 by 3.41 and then back again. Then there’s the more seriously erroneous statement (page 107) that a probability density function ϕX(x) gives the probability that the value of the random variable X is x. In fact, ϕX(x)Δx is the probability that X has some value in the interval x to x+Δx.
My biggest concern about the book is the huge variation in mathematical expectation that Stewart has made. The logarithm chapter, for example, has a long exposition on how exponents work, whereas the chapters on Maxwell’s equations and the Navier–Stokes equations feature casual uses of vector differential operators to calculate curls, gradients, and divergences. However, for readers who can handle that variance, In Pursuit of the Unknown is an interesting and highly entertaining book. It would make a great gift for a bright high school grandchild who has expressed interest in a technical life, or for a physicist’s own secret reading.
