Imagining Numbers (Particularly the Square Root of Minus Fifteen), by Barry Mazur, is about the history and mathematics of imaginary numbers, and how mathematical imagination lines up with the more classic, “poetic” imagination.
That’s quite an ambitious undertaking, and I don’t think the book quite lives up to it.
Maybe I just have a really idiosyncratic way of looking at poetry, but most of the poems he brings into play don’t seem very interesting to me at all, and his interpretations of them strike me as too personal to be of much use in this general kind of topic. I could be wrong.
Either way, the bit I bought the book for was, of course, the history of mathematics, and the mathematics itself.
It’s possible there just isn’t a lot of history to imaginary numbers, but I was disappointed to find he only talks about a handful of European mathematicians, and never even mentions similar concepts in other civilisations. Maybe there just aren’t any.
The mathematics themselves are kind of all over the place, too. It’s like Mazur either couldn’t decide between an entry-level book and a “proper” work on mathematics, or he just got tired of explaining things somewhere along the way. He devotes most of a chapter to very tediously explaining the associative and distributive properties of addition and multiplication, and later on just breezes past important concepts with a simple “Here is an exercise for you”.
The various exercises throughout the book are pretty interesting and fun to do, though, but it does mean it’s hard to read it between classes and on the train and whatnot, which I tend to do.
Still, figuring out what equals (and what that means), while not particularly hard, is the type of mathematics I haven’t been able to do in a long time, and it’s a nice change of pace.
So, on the whole, I thought Imagining Numbers was a pretty good book, though I doubt most people would enjoy it much. It’s not as good as some other popular science type mathematics books I’ve read, but still.
I do think it could have been much better if it had been twice as long, though. It’s about 230 pages (not including notes), and it feels kind of superficial and rushed in places.