Popular math books are better than the boring textbooks (Axiom – Theorem – Proof – Exercise). They are motivational, more concrete instead of abstract, philosophical analogy with the Nature (afterall, the math ideas derived from the universe, eg. Pi, e, golden ratio, infinity, limit, …), plus the historical background in which these math ideas were first discovered, and the beauty of these inter-connected ideas such as the Euler’s Identity:
“Proof from the Book” – the name “Book” (God’s Theorem Proof Book) is coined by Paul Erdos the Hungarian ‘vagabond’ (homeless, single, no nationality) mathematician, who had proven 1000+ theorems (some co-operated with his students). He said he had peeped into God’s “Book” to discover these theorems.
My favorite Popular Math book which inspired me in 2005 to re-pick up the fearsome Abstract (aka Modern) Algebra is : “Unknown Quantity” by Prof John Derbyshire, avail at NLB.
Math before university is the “What and How“, whereas the University Math is the “Why” – after WW2 the French Bourbaki Reform in Math Education worldwide based on Set Theory, the post-war Philosophy Trend “The Structurism 结构主义” shaking the basic foundation of Math: Algebraic Structures. eg Group (群) , Ring (环) , Field (域) , Vector Space (向量空间) , Cateogy Theory (范畴论) .
The 70 years of WW1 & 2 taught the world Anarchism (无政府主义) was chaotic & disastrous to society, hence the more orderly “Structurism” Philosophy was born, influencing all Sciences: Chomsky Linguistics, Sociology, IT Structured Programming ‘Pascal’ , Anthropology 人类学, Abstract Algebraic Structure Math…