Ask HN: How can I discover math?

So I've been trying to teach myself K-12 math using www.khanacademy.org now after reading http://www.maa.org/devlin/LockhartsLament.pdf I feel like I should be discovering math, playing with numbers asking more questions. The problem is that from up to this point in my life all I have been taught was to memorize a formula, plug in some numbers, get an answer. I want to learn math well, I want to enjoy the beauty of it, but I don't know where to begin that journey or how to start.

Get "The Princeton Companion to Mathematics" - http://press.princeton.edu/titles/8350.html

Soviet textbooks and the Princeton Companion (recommended by others) are likely to be pretty brutal for you. I suggest problem-solving as a better way in.

Take a look, e.g., at Project Euler (http://www.projecteuler.net/); find some books aimed at K-12 students doing mathematical contests (there are lots; what's best depends on how much you already know) and online resources aimed at the same audience (e.g., http://amc.maa.org/, http://www.mathcomp.leeds.ac.uk/); there are other sources of not-too-routine mathematical problems online, such as http://nrich.maths.org/.

This pretty much guarantees that you'll be doing as well as passively absorbing (one of many problems with which is that it's easy to think you're absorbing when actually you're not). There's a very wide range of levels of difficulty. And it's likely to be fun, if mathematics really suits you at all.

Check out this previous post: http://news.ycombinator.com/item?id=1449799

And also, I'd highly recommend art of problem solving. http://www.artofproblemsolving.com/

Honestly, the best way to discover math is the Hacker's way i.e. find problems to work on and then start working on them even in you don't know how initially. The very digging in process will lead to further discovery and further learning. Now, be sure to check out art of problem solving forums, people ask questions there and there are very good detailed explanations available.

Be also sure to check out Street Fighter math (http://ocw.mit.edu/courses/mathematics/18-098-street-fightin...) and fermi questions (e.g: http://mathforum.org/workshops/sum96/interdisc/classicfermi....)

And remember to print out these questions and carry them with you along with tons of scrap paper. Sometimes, it helps just to read a problem and let it sink in over days...

Seriously? Your reply to "I'm trying to teach myself K-12 math" is "find out what mathematicians think about, instead"? My guess: you are trolling or have never read the Princeton Companion.