THE RIEMANN HYPOTHESIS….I finished my book on the Riemann Hypothesis, and unfortunately I didn’t think much of it. It turns out that I’ve already read another book by the same author, and I didn’t like that book too much either, so maybe I just don’t like his books.

But it goes beyond that, I think, and the problem is one that infects an awful lot of popular books about math: most of them discuss things that require at least some familiarity with topics beyond basic arithmetic. In this case, for example, you really need to know what a complex number is.

So the author has two choices: (a) write the book for an audience that already knows what complex numbers are, which reduces your potential readership to a Very Small Number, or (b) explain complex numbers.

Most authors, including this one, choose option (b). This is annoying to me because I then have to wade through dozens of pages I don’t need to read, something that has to be done with care since these pages invariably also contain details here and there that are important to other parts of the story.

What’s more, I have my doubts that this works anyway. First of all, I wonder just how many non-mathophiles are going to read a book like this in the first place, and of the ones who do, I wonder how many actually end up understanding the kinds of tortured analogies that are usually used to explain difficult concepts. In this case the author analogizes complex numbers to streets and cross streets in New York, and then tries to convince us that the cross streets are somehow related to the square root of -1.

Fair enough, and I don’t know that I could do any better, but does it actually help? Does anyone who didn’t understand the concept in the first place understand it better after reading an explanation like this?

I honestly don’t know, but I can’t help but think that these efforts are doomed. The book has plenty of scary looking equations, and I’m pretty sure that simply saying “don’t be scared!” doesn’t do much to broaden your audience. It might be better to simply assume that anyone interested in a topic like this is already familiar with high school algebra, accept the fact that this will reduce your audience a bit, and be done with it.

POSTSCRIPT: Of course, a lot of this has to do with the skill of the author. For example, a very good book about math that I read a few years ago was The Mystery of the Aleph, by Amir Aczel, a short book about Georg Cantor and transfinite set theory. Aczel did a great job of explaining the math in an understandable way, weaving it seamlessly with interesting historical background and a biography of Cantor himself. My recollection is also that Aczel simply assumed, for example, that his readers knew what an exponent was and didn’t waste time trying to teach basic algebra. It made for a much better book.