[g9yuayon]

Can't agree more. Definition-theorem-proof type of textbooks is way too clean. They don't tell you how ideas came to be or why they mattered. In other words, it's hard for students to learn the intuitions behind the ideas. I wish there are list of "XXX from Ground-Up" type of books that show readers a list of problems, struggles of people trying to solve them, and how ideas emerge from the numerous attempts. Leslie's paper Paxos Made Simple was written in that way. A few chapters of Kleinberg's Algorithm Design were written in that way too.

[tnecniv]

I think math classes should be paired with history more. My probability professor often offered historical context (for example, the Poisson distribution first being used to model deaths due to horse kicks in the Prussian army) to the ideas we discussed, and the stories were often both interesting and insightful.

[craigching]

I've been refreshing on Calculus and I found that Kline's book was good at application as well as a bit of history, at least I never got the history part at University and I found it very interesting.

http://store.doverpublications.com/0486404536.html

[jostylr]

Nature and Growth of Mathematics by Edna Kramer is a fantastic book interweaving history and math.

[agumonkey]

I'd love to know all people seriously learning it to tell what they loved. Who like to be stuck on an abstract definition and figure it out on its own (ideal to real), who likes to have gradual build up (real to ideal).

My first AA book was the "European kind", all symbols and definitions, a few proofs every ten pages. It was too dry for me. I never thought other people would think that way.

I love brain teasing but I also need a minuscule amount of inspiration to power my neurons.