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.