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Infinite Powers - Stephen Strogatz ****

I missed this one when it came out, possibly because the cover looks somewhat amateurish. Stephen Strogatz starts by exploring the prehistory of calculus - arguably the most widely applied mathematical tool in physics and engineering. We tend to think of calculus starting with Newton and Leibniz, but there was a long prehistory stretching back to the Ancient Greeks. This involved using methods that might, for instance, mentally cut something up into smaller and smaller pieces, then rearranged those pieces in order to work out, for instance, the relationship between the area of a circle and its circumference. This background is delightfully introduced.

Strogatz takes us through some, though not all, of the intervening history before the real thing bursts on the scene, but oddly then gives up on the historical context, so we don't hear about Newton and Leibniz until we have absorbed a whole host of detail, including where necessary some equations, ranging from functions to the natural logarithm and its exponential function before we get on to the basics that lie behind differentiation.

Uncovering the fundamentals of the mathematics is the kind of thing Strogatz does brilliantly. He can really dive into what makes calculus tick. Things are less effective on the history front. We do eventually get both Newton and Leibniz's side of the story, but I found the way it was mixed up with mathematical detail made it difficult to absorb the message. Again we then lose the historical structure - no Bishop Berkeley and not much on the way that limits were introduced to fix the problem of infinitesimals (though this is touched on early on in the book). Partial differential equations get an introduction but with less detail, as does Fourier analysis. Along the way, Strogatz introduces a wide range of real world applications, and finally looks at future possibilities.

I had a couple of problems with the book. Strogatz sometimes gets carried away with floridity. For example, when talking about dividing a circle into quarters and arranging them in a line: ‘It’s certainly not a rectangle, so its area is not easy to guess. We seem to be going backward. But as in any drama, the hero needs to get into trouble before triumphing. The dramatic tension is building.’ He also commits the science writer's heresy of telling us 'During the Inquisition, the renegade monk Giordano Bruno was burned alive at the stake for suggesting that God, in His infinite power, created innumerable worlds.’ Not only was Bruno a friar, he was burned for conventional religious heresy, not his (often pseudo-) scientific views.

This was a book that couldn't decide what it was supposed to be. It started off as history of maths, but that petered out to be replaced by random historical snippets mixed in with an excellent exploration of what calculus is all about. I think it would be better to have either taken the historical approach throughout, fitting in the explanation of the maths, or to have based it purely around the maths with just passing references to the historical context. Yet despite that strange hybrid approach, there is so much to like in Strogatz's ability to bring the maths alive.

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Review by Brian Clegg - See all of Brian's online articles or subscribe to a weekly digest for free here

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