Seventeen Equations that Changed the World

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If Ian Stewart had published this book pre-2003, maybe I wouldn't have skipped so many lectures after booze-induced somnolence. This isn’t a mathematical theorem but rather it’s true for physical reasons in that it fits the observations. The final non-Mathematics equation is the Black-Scholes equation, which is hard to fuck up in that that equation is just smoke and mirrors to obscure the fact that the assholes running the financial sector don't outperform random number generators. For example, the base 10 logarithm of 1 is log(1) = 0, since 1 = 10 0; log(10) = 1, since 10 = 10 1; and log(100) = 2, since 100 = 10 2.

I was a little disappointed in the discussion of Maxwell's Equations, as he tried to get a little technical, but then said a couple times that it would be too hard to explain correctly in this book. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today. The Black–Scholes equation changed the world by creating a booming quadrillion-dollar industry; its generalisations, used unintelligently by a small coterie of bankers, changed the world again by contributing to a multitrillion-dollar financial crash whose ever more malign effects, now extending to entire national economics, are still being felt worldwide.

Also, towards the end of the book, chapters started losing that element of excitement that kept you going through the first chapters. History: Michael Faraday did pioneering work on the connection between electricity and magnetism, and James Clerk Maxwell translated it into these equations.

Surveying, navigation, and more recently special and general relativity – the best current theories of space, time, and gravity. For certain values of k, the map shows chaotic behavior: if we start at some particular initial value of x, the process will evolve one way, but if we start at another initial value, even one very very close to the first value, the process will evolve a completely different way. By 1615 the Dutch mathematician Willebrord Snellius (Snel van Royen) had developed the method into essentially its modern form: triangulation. In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. He explores how Pythagoras's Theorem led to GPS and Satnav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrödinger's cat.

If, however, your maths is more limited or, like mine, rather rusty, you'll find you don't need to follow all the mathematical details. The populist banker bashing this chapter represented made me seriously question the accuracy of the detail in the other chapters. Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration — and explanation — of life on earth. The stories behind them — the people who discovered or invented them and the periods in which they lived — are fascinating.