I found this article, “Math 101: A Reading List for Lifelong Learners”, via Hacker News. I’m only familiar with one book on the list (A Tour of the Calculus) and my experience with it was a bit disappointing. It might not be the books fault, my expectations may have been unrealistic. I know there are limitations to how much you can learn about math by just reading, you have to engage through project related work or just churning through the problem sets.
Which is too bad, since reading is easy and doing problems is hard. Maybe that accounts for the lack of people with deep mathematical skills.
However, shortly after seeing the Math 101 reading list another conversation popped up on Hacker News, How or where to begin learning mathematics from first principles?. The first set of responses were excellent. If you have an interest please take a look at them, although the thread is a bit long. The first respondent in particular talks about the poor quality of math textbooks. In particular citing the fact that textbooks “read like a laundry list of theorems and proofs, with some discussion inserted as an afterthought”. They give two examples of math texts which were “crafted to be read, internalized, and meditated on”, Real Analysis by Pugh and Calculus by Spivak.
I”m a bit suspicious that a different math book could really change my approach. I suspect that there is still some level of commitment that I need to make above and beyond picking up a book and reading it. I suspect I’ll only find out though if I pick one of them up and give them a try. It would be niced to be engaged by some math again.
As a side note there is probably a good tie in to “Lockharts Lament” (also a book), but I’m not familiar enough with it to try to draw out the relationship. If any of these topics resonate with you I’d say at least go and read the shorter version.