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Mathematics is an abstract system of logic used to understand the natural world. That being said you cannot "discover" mathematical tautologies. No where in the universe is it apparent that a triangle has 3 sides that must equal 180 degrees, or that 2 plus 2 must equal 4, et cetera. Newton was able to "invent" an entirely new branch of mathematics in order to explain new "discoveries" of the universe by locking himself away.
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The natural world deals with the natural sciences(i.e. physics, chemistry, bio, etc).
Yet, mathematical foundations exists for economics which clearly is not a natural science. Computer science, which is also not a natural science, is actually a form of appiled mathematics. Don't forget about mathematical finance(this branch of mathematics does not fall under economics) because that also exists.
Most pure mathematicians will tell you that mathematics is about discovery. The science itself deals with quantity, structure, size, etc. While it is true that numerous mathematical theorems has come from the natural sciences, most modern mathematics has come from the pure branch.
I actually graduated in electrical engineering in college, but I have enough mathematics courses to goto grad school. I probably will do so in a year.
To me, mathematics is about solving problems, learning new theories, and discovering new knowledge. It's a language used not just to understand the natural sciences, but almost everything existence.
One more thing I would like to point out.
The word "abstract" used in mathematics does not have the same meaning as the word "abstract" in say
"an abstract drawing". Think more along the lines of abstraction in computer science to get an idea of "abstract" mathematics.
Jam it back in, in the dark.
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