As a counterpoint, I have decent math chops and even do a lot of computational geometry professionally, and I really wanted to like "Geometry and the Imaginatio

As a counterpoint, I have decent math chops and even do a lot of computational geometry professionally, and I really wanted to like "Geometry and the Imagination"—but for me I was till missing way too much information to figure out what he was saying half the time (much of because of the antiquated style), and after putting lots of work into some section I'd get to the end and be like, "this is kinda neat, but it's not rockin' my world or anything..." (to be fair, I did only make it halfway into the second chapter, on lattices iirc, and the later chapters did look more interesting). I would definitely not recommend it for someone working on high school level math. If I had made an attempt at that in high school, being told it was something I should be capable of then, I probably would have totally given up on any ideas I had about being able to do math well. If you look at a lot of reviews for math books, you'll find there is a major split between folks who, on one side, believe a math book should should be a sort of pure, elegant, perfect thing with barely anything in it but statements of definitions, theorems and proofs. It should be difficult above all. There should be no trace of how the contents within it came to be, just a pure presentation of some set of mathematical truths. The other side values pedagogy. The mathematical results in themselves are not considered sufficient on their own to be good teachers; instead, attention must be paid to the psychology of one's readers, and in consideration of it, the best route for making contact from the reader's knowledge to the author's must be taken. A typical trend is that the presentation includes context on why and how the results were developed. I've seen a similar split in CS, and I can say at least here, that I haven't seen any correlation between those insisting on doing everything the hard/austere way and doing interesting/technically impressive work. That said, I haven't personally done anything particularly impressive in mathematics, so I'll refrain from making too strong a comment about the necessity of any particular pedagogical style in that realm. But I would bet two things: 1) We lose many folks who could have become good mathematicians because they were freaked out by the sort of attitude and presentation making up the first half of the 'split' I describe above 2) It is probably significant that not all excellent mathematicians choose the trial by fire pedagogical approach in their own works.