Professor Timothy Gowers starts with the need for models and ends with the usefulness and necessity of estimation. The body of the book gives the flavor, the value and the connectedness of Proofs, the calm resolutions of infinity and the impact of changes in dimension and Geometry.
No. Not a problem-based course. Not a history lesson. No sexy examples. Little mention of the titans. Yet the point of doing math, its constraints and pathways, would strike anyone who reads the book. Whether high school students would get it. I'm not sure. The maturity in the words and the totality of the immersion within its few pages is sublime. In knowing that exact answers are rarely found, but knowing the boundaries of the answers and their closeness to actual mimics our own lives.
This would be a must read in a non-ADHD world.
Gowers also wrote the Princeton book on Math. The professor is a Fields medal winner.