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modus_tollens · #2 (**permalink**) 26th October 2006, 07:45 PM

Hi RunicSage

You're asking questions that have perplexed scholars for a long time. Try googling under philosophy of mathematics for their take on it.

A question, related to your final question, I find myself asking is whether math is created or discovered.

I don't think it is a simple answer; some math is created and has little to no bearing on the physical manefestation of reality whereas other math is discovered: deeper not neccessarily seen aspects of physical reality.

Take conic sections (parabola, hyperbola, ellipses). The Greeks spent a lot of time investigating their properites. Did the Greeks [or other ancient culture in parallel] invent conic sections or did they discover them?

Little did they know that parabolic dishes would be used for satellite receivers and headlights...or maybe they suspected their investigations would later be "useful."

I'm not anti-pure math. I think that whether or not math is "useful" is to the mathematician doing it, like beauty is in the eye of the beholder. Some math is about as "useful" as an abstract painting but the mathematical artist doing his/her math is the same thing.

Little to none of this answers your questions, I know... Sorry...