Shape - Jordan Ellenberg ***

I really enjoyed Jordan Ellenberg’s earlier book How Not to be Wrong, so looked forward to Shape with some anticipation. In principle what we have here is a book about geometry - but not seen from the direction of the (dare I say it) rather boring, Euclid-based geometry textbooks some of us suffered at school. Instead Ellenberg sets out to show how geometry underlies pretty much everything.

Along the way, we are given some nice turns of phrase. I enjoyed, for example, Ellenberg’s remark on the philosopher Thomas Hobbes, where Ellenberg remarks Hobbes was ‘a man whose confidence in his own mental powers is not fully captured by the prefix “over”’. Whether or not what we read about here is really all geometry is a matter of labelling (as is the ‘number of holes in a straw’ question that Ellenberg entertainingly covers). Arguably, for example, there is some material that is probability that can be looked at in a geometric fashion, rather than geometry that produces probabilistic results - I find the probability viewpoint a lot simpler and more interesting. In the end, despite his efforts, unless you are a mathematician, some aspects of geometry (and maths in general) feel laboured and uninteresting. But the marvel of this book is that he does make a surprising amount of it quite the opposite. 

Unfortunately, Ellenberg can go into far too much detail sometimes (which may be why the book is a bit of a doorstop at 463 pages) - for example, a story that starts with the mosquito’s random walk seems to go on and on for ever and I rather lost the will to continue, in a topic that interests me a lot more than geometry does. In a different way, I struggled to get my head around the lengthy section on US electoral district gerrymandering which seemed only of interest to someone with in-depth enthusiasm for US politics, while some of the final meandering final chapter should certainly have been lost in the edit.

I do wonder if the success of the earlier book meant this one was not given the editorial scrutiny it needed. Although Ellenberg failed to convince me that geometry is the foundation of many of the topics he discusses, there is material to interest the reader here - and it’s certainly a far cry from those laborious proofs and QEDs.

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Review by Brian Clegg