- #1

screamingman

- 11

- 0

Basically, I see people (and read of people) who think about interesting questions, paradoxes, etc. in mathematics, and would like to do the same. Of course, everyone finds different things interesting, but I think that maths are inherently interesting (that everyone, or at least that I should be able to find areas to think about), and it disturbs me that I waste hours a day that I could be thinking about abstract concepts, letting my mind think about less interesting things. How can I instill passion so that I begin to think about abstract ideas impulsively?

I have a burning desire to be able to think creatively of/on my own mathematical questions, etc., and I do just fine questioning less abstract topics/ideas, but either because of lack of experience/knowledge in/of math (I am a Senior in high school), or my mind only being able to think about less abstract ideas at a deep level, I have yet to do this well. There are people my age who think in a way I desire (at least they project it) in that they think creatively about maths, but I guess I would be too embarrassed to ask someone in person such a question, because it is vague, and almost paradoxically straightforward (just think about these things), yet at the same time, impossible to answer.

The step I have taken to stimulate my mathematical creativity is reading and understanding proofs. I am reading Spivak's Calculus, inspired by the rave posts on the forum, and am greatly enjoying it. Pondering the notion of a limit, etc. is interesting, but I do not ponder the ideas in the text compulsively/passionately all day long. Is this just a problem I need to reconcile on my own (the disconnect between what I would like to think about, and what I do think about)? Any ideas, ranging from branches of mathematics or Physics that one can ponder, to open-ended interesting questions to think about (some place to get me started) etc. would be greatly appreciated.