Book review: How Not to Be Wrong

As signalled in a post a few days ago, I've been reading How Not to Be Wrong - The Power of Mathematical Thinking by Jordan Ellenberg, which I just finished. Writing an accessible book about mathematics for a general audience is a pretty challenging ask. Mostly, Ellenberg is up to the task. He takes a very broad view of what constitutes mathematics and mathematical thinking, but then again I can't complain, as I take a pretty broad view of what constitutes economics and economic thinking. The similarities don't end there. Ellenberg explains on the second page the importance of understanding mathematics:

You may not be aiming for a mathematically oriented career. That's fine - most people aren't. But you can still do math. You probably already are doing math, even if you don't call it that. Math is woven into the way we reason. And math makes you better at things. Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world... With the tools of mathematics in hand, you can understand the world in a deeper, sounder, and more meaningful way.

I think I could replace every instance of 'math' or 'mathematics' in that paragraph with 'economics' and it would be equally applicable. The book has lots of interesting historical (and recent) anecdotes, as well as applications of mathematics to a variety of topics as broad as astronomy and social science (as noted in my post earlier in the week). I do feel that mostly the book is valuable for readers that have some sensible background in mathematics. There are some excellent explanations, and I especially appreciated what is easily the clearest explanation of orthogonality I have ever read (on page 339 - probably a little too long to repeat here). Just after that is an explanation of the non-transitivity of correlation that provides an intuitive explanation for how instrumental variables regression works (although Ellenberg doesn't frame it in that way at all, that was what I took away from it).

There are also some genuinely funny parts of the book, such as this:

The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we'd now call mathematics, things we'd now call religion, and things we'd now call mental illness.

However, there are some parts of the book that I think Ellenberg doesn't quite get right. For instance, there is a whole section on geometry in the middle of the book that I found to be pretty heavy going. Despite that, if you remember a little bit of mathematics from school, there is a lot of value in this book. It doesn't quite live up to the promise in the title, of teaching the reader how not to be wrong, but you probably wouldn't be wrong to read it.