This excerpt - "what he really liked was solving problems. The text of each chapter was just some advice about solving them. He said that as soon as he got a new textbook he'd immediately work out all the problems—to the slight annoyance of his teacher, since the class was supposed to work through the book gradually." is literally me. I did that. Every year at my school I did exactly that. Once I actually turned in m…
I thought I was absolutely the worst person in the world at math. Turns out, crappy teachers and a teaching methodology that is diametrically opposed to one's optimal learning style count for a lot in school.
However what was amazing to me was how I went from zero confidence in my math skills to actually being excited about math when I took geometry. I never studied once in that class--just absorbed and immediately internalized what the teacher said. I could look at a proof and it just sort of visually made sense to me and clicked and I could step through it because of the pattern recognition. To this date I've never experienced anything intuitive in that fundamentally primal manner.
What has been great lately is Khan Academy and a growing interest in teaching myself software development has rekindled my interest in math. I also owe a huge debt of gratitude to Kalid @ BetterExplained.com (he frequents HN) for getting me past my fear that higher-level maths were beyond my capabilities. They weren't--I just needed to find a way of applying them in an intuitive manner that I could easily internalize vs. staring at equations and their definitions.
I wouldn't be surprised if I would have ended up as an engineer if I hadn't had such a poor experience with math when I was younger. I am pretty resentful of it. Fortunately I can take steps to change that, and I am.