Chris Waring - From 0 to Infinity in 26 Centuries

Rating: 3/5

Review:
A good attempt but flawed

I generally enjoy books of this kind very much and this one does have its merits, but I'm afraid I thought it had some serious flaws, too.

It is presented in a series of brief sections, most of which give an outline of the contribution of an individual to mathematics, from ancient Greek, Chinese, Indian and Arabic mathematicians via people like Descartes, Newton, Euler and so on up to the 20th century where both concepts and people become less familiar. These are generally well written, the concepts on the whole are well explained and the tone is amiable and welcoming with not too much in the way of scary equations, which is excellent for the non-specialist.

However, as a story of maths (which it claims to be) I found it rather lacking because there is no sense anywhere of how the ideas described fit together, and although it is roughly chronological it seemed just a random scattering of stories without any sense of movement through history. And while Chris Waring mentions applications of some of the concepts and techniques, I didn't really get a sense of how it all fitted into the world.

More seriously, some of the explanations are badly flawed. For example, I thought I was losing my mathematical marbles on page 54 because Euclid's Theorem of Infinite Primes is so poorly and inaccurately explained that it seems to be self-evidently false. Waring says "If you multiply all the primes together you generate a number. This next number..." What he means by "this next number" is, "if you then add one to the generated number, this new number..." which is something very different, and even when (or if) you realise this, the explanation still omits a vital step in reasoning. The example of the use of Napier's Bones seems to imply that 5+1=7 until you finally deduce that he has forgotten to tell you to start on the right and that you have to carry over to the next section. And so on.

There are inaccuracies scattered throughout, which in a book about anything other than mathematics probably wouldn't matter but here are significant. For example, "24 is not a weird number because we can add its factors (2,4,6 and 12) together to make 24." What he means is "we can add *some* of its factors together" (leaving out 3 and 8) which, in a section about perfect numbers, is a critical distinction. I'm afraid that there was a good deal of this sort of sloppiness and I found it increasingly irritating because, unlike in fiction, say, small errors in mathematics render it plain wrong, and precision is vital even in a book like this for the general reader.

I am sorry to be critical. Chris Waring deserves credit for attempting to write an accessible book on the history of maths and this isn't terrible by any means, but it is flawed and I can only recommend it with some rather serious reservations.