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Keywords: Popular science, Maths
Title: A Brief History of Infinity
Author: Brian Clegg
Verdict: A good read for all but the maths-phobic
Wrestling with infinity is no easy task. Just when you think you're done you realise that there's an infinite amount still to do. No wonder it helped drive at least two mathematical geniuses over the edge?Author Brian Clegg takes us on an enjoyable trek through the history of infinity, from the earliest concepts through the middle ages and into the modern world of non-standard analysis and beyond. Readers of a non-mathematical persuasion can be assured that they won't be stretched too hard, though some of the ideas are hard to get hold of at first. But don't worry, if you think you've got the idea and then find it slips away you're in good company - infinity is just plain slippery.
As with many such books, the journey is as interesting as the destination. Clegg does a good job of illuminating the subject through the powerful personalities that grappled with ideas of the infinite. From the Newton-Leibniz grudge match to the problems Cantor had with his one-time mentor Kronecker to the weird manias of Kurt Godel and more. But this is more than just a series of interesting biographical sketches, each of the episodes looks at the issues these mathematicians and philosophers were grappling with. From the ideas of fluxions and limits - which moved calculus centre stage in the mathematical, scientific and engineering worlds - to the bizarre realms of Hilbert's hotel and Godel's unravelling of the dream of a mathematics without paradox.
The book is written in a friendly, chatty kind of way. The diversions along the way - for example there is a nice discussion of the geometrical, rather than algebraic or numeric, nature of Greek mathematics - are as interesting as the chapters which deal rather more directly with ideas of infinity. At times I wanted more, particularly in the sections on hyper-real numbers and the ideas of non-standard analysis, but that's partly due to an unnatural attraction to maths that is unlikely to be shared by the majority of readers.
It's a good read and should appeal to all but the most mathematically-resistant.