Knots: Mathematics with a twist by Alexei Sossinsky, Harvard University Press, $24.95/拢16.95, ISBN 0674009444 Reviewed by Mike Holderness
POSTMODERN commentators talk about knots on television, observes Alexei Sossinsky, 鈥渨ith all their usual nerve and incompetence鈥�.
So this professor of mathematics at Moscow State University has written a corrective exposition of the mathematics of knots. His aim is to appeal not only to mathematicians, but also to those 鈥渨ho feel they have no aptitude for math as a resultof their experience in school but whose natural curiosity remains intact鈥�.
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He has not entirely succeeded in this laudable aim. I suspect that the later chapters of Knots: Mathematics with a twist, will only make full sense to someone who is familiar with, for example, 鈥淟ie algebras鈥�. But if you鈥檙e not, and are prepared to take a certain amount on trust, you can still pick up an interestingly looping story.
Sossinsky鈥檚 tale begins with the physicist William Thomson鈥檚 1867 vortex model of the atom, whose properties were to be determined by the knottedness of a vortex in some field. That model was superseded by the 鈥減lanetary atom鈥�. The story passes through the 鈥� interestingly unfinished 鈥� attempt to classify knots so mathematicians can be sure whether one is the same as another. And it finishes with Sossinsky鈥檚 strong hunch, shared by others, that the maths of knots will have a lot to say about quantum fields and 鈥渟tring theory鈥�, whatever that turns out to be 鈥� which is what overexcites the postmodernists.