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I used to think I was terrible at math until I actually tried it a few years after finishing high school. Turns out when you apply it to real life problems it's actually interesting. Still, I have my area of study and a few other interests and I'm not interested enough to get into math as well.
What I like is language. Once you get into details it's interesting how you can play with words, how the same sentence rephrased but containing the same information can elicit a different responce due to different connotations. Interestingly this seems to have a greater effect on women than men.
Attempt to listen to your native tongue without hearing what they are saying - the same way you listen to foreign tongue without hearing what they are saying.
I've only done it once and I was in a very odd mood.
A bit of both and kind of depends on how you look at it. In essecenses its a discorvery but you could say that people invent mathmatical "tools' (no not calculators I mean processes).
I enjoyed maths at uni (except fourier transforms ARGHGHAH!!!) Also at my uni it was taught with all of the theory behind it all which was good.
I would say that the mathematical language is an invention used to make discoveries. The Pythagorean Theorem is a discovery, but the language in which it is usually stated is an invention.