## How Mathematics Happened: The First 50,000 Years

This book is a weird concoction: popular maths and archaeology? It could be unique...

It tells the (pre)(hi)story of mathematics from the days of Neolithic hunter-gatherers to the time of the famous ancient Greek mathematicians, such as Pythagoras. This means working with very limited data and there are a lot of assumptions, suppositions and intuitions filling in the gaps between the data. Of course that is the nature of all archaeology, which is, after all, the task of reconstructing a culture from a subset of its material productions. Rudman is very good in this territory; he is very clear about what is a fact, what is a hypothesis, what is a theory, what the assumptions are, what is his personal view and what is generally accepted theory.

For me, the book got more interesting as it went along, largely because the maths itself got more interesting; at the outset there is only counting, by the end there is rigorous proof of the irrationality of root 2 and the Pythagoras Theorem (which it turns out was known but not proven well before Pythagoras came on the scene).

I do think the book has flaws, though. There are plenty of "fun questions" through out - but for me most of them weren't fun. Fortunately they are easily ignored. Rudman also "pulls a Dawkins" with several snide remarks about religion and theists that have no place in the book at all and the final chapter on maths teaching methods has some obviously fallacious arguments mixed in with sensible observations - but that chapter is just as out of place in this book as comments about the "intellectual weakness" of theists. Rudman's terminology seems a little obfuscatory on occassions, too: what's a frustrum? What's a truncated pyramid? I bet you can guess what the latter is - but a frustum is the same thing! He also uses "prism" when he means cuboid. That said, the arguments are generally clear.

Overall I feel that an intriguing topic has been poorly but not hopelessly served by this book - a better writer could have improved it greatly.