Book Review: 17 Equations That Changed the World

In Pursuit of the Unknown:  17 Equations That Changed the World
By Ian Stewart
Basic Books, New York, 2012

17 Equations That Changed the World:  It’s a greatest hits collection!  17 of your all-time favorite equations from the worlds of mathematics, physics and economics.  Featuring superstar legends from Euler to Einstein, including unforgettable appearances by Newton and his Apple, and Schrodinger and his Cat! 

OK, I admit this is one of the nerdiest books I’ve ever read.  Right up there with Simon Singh’s Fermat’s Enigma.  But, hey, you are what you read, or something like that.

Starting with Pythagoras and ending with Black-Scholes, Stewart takes us through a history of science and mathematics seen through the lens of these most important equations.  For each one, Stewart describes the historical context, the problem the equation was intended to solve and their more far-reaching, often unforeseen applications.  In the chapter on Newton’s Law of Gravity, for example, Stewart describes how NASA uses “gravity tubes” and “Lagrange points.” to plot energy efficient paths through the solar system for its exploratory missions. 

For a book about equations, there’s actually not that much math.  This is more a history book than a math or physics text, so Stewart doesn’t try to prove or derive these equations.  Still he doesn’t shy away from the technical details.  He makes a brave attempt to describe in words how each equation can be applied.  At times this becomes completely impenetrable as in this description of the Schrodinger Wave Equation:

“For a superposition of several eigenfunctions, you split the wave function into these components, factor each into a purely spatial part times a purely temporal one, spin the temporal part round the unit circle in the complex plane at the appropriate speed, and add the pieces back together.”  p. 251

Well, impenetrable for me anyway! 

Still this doesn’t really detract from enjoying the book.  What’s striking is how many of these equations in some way build upon or relate to each other.  Another is how each one tended to upend prior thinking or violate previous assumptions, such as the simplest equation in the book: i2 = –1.  I suppose that’s because they each encapsulate something fundamental about the universe.  

At the end of the book Stewart speculates that future developments may focus more algorithms than on equations, as we find the world becoming more digital, more discrete.  I suppose that means I’ll have to read John MacCormick’s Nine Algorithms That Changed the Future to find out more.   

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