"You must learn to distinguish between what is true and what is real." See: http://www.edge.org/q2005/q05_8.html#kay
I think most mathematicians would disagree with your assertion that math is about "definitions". (I'm no math geek, just a programmer, so take with an appropriately sized grain of salt.)
> I think most mathematicians would disagree with your assertion that math is about "definitions".
An analogy: math is about definitions in the same sense that go is about placing stones on a grid.
There's certainly an abstract similarity, but etymologically, constructing a proof is very different from running an experiment. A proof declares a statement as True. An experiment (at best) shows that reality behaves as your model hypothesized it would. Experiments can provide evidence of something, not prove it as True. As Alan Kay says (following former link):
When we guess in science we are guessing about approximations and mappings to languages, we are not guessing about "the truth" (and we are not in a good state of mind for doing science if we think we are guessing "the truth" or "finding the truth"). This is not at all well understood outside of science, and there are unfortunately a few people with degrees in science who don't seem to understand it either.