I’m not sure why it took 17 years for me to catch up with John H. Conway and Richard Guy’s The Book of Numbers. I don’t even recall hearing about it until I came across it in a local library.
It is, I’m sorry to say, not as good as I’d hoped. They would have written a better book had they chosen about half as many topics, or written about twice as many pages. As it is, there’s far too many steps left out, too much unexplained, too many terms undefined. To pick just one example, in the section “Lagrange’s Numbers, Markov’s Numbers, and Frieman’s Number” in Chapter 7, the last paragraph is about the Lagrange spectrum, the Markov spectrum, and Frieman’s number. One paragraph? It needed more. I would guess that people who already learned about these things once might read Conway and Guy’s discussion, nod, and say, “Oh yes, I remember that.” For me, who’d not encountered them before, the paragraph was opaque. There simply wasn’t enough information conveyed to promote any understanding. Omitting that paragraph, or perhaps that entire section, would have been an improvement, if they didn’t want to expand the discussion to a page or so.
There should have been better proofreading, as well. In the caption to Figure 10.8, to pick one of several problems I noticed, the fraction 6/14 should be 1/64.
It’s a shame. Conway and Guy could have written a much better book had they not been in such a rush to get through so many subjects.