In the latest (March 2006) edition of Scientific American, Gregory Chaitin writes another article about his number Omega, and also the following (which I paraphrase for copyright reasons):
A traditional view of mathematics is that it is true in any (physical) universe, ie, it is independent of the particular universe you happen to find yourself in. Theorems and mathematical results do not depend on the nature of physical reality. He also mentions how this is not true, of course, for physics.
This traditional view of mathematics struck me as a little strange quite apart from its untestability. To me, mathematics is a human-made set of ideas derived from human experience (including thought). In what sense is it independent of physical reality? Human have not lived (as far as anyone knows) outside this Universe, so the development of mathematics cannot be known to be independent of physical reality.
When I was an undergraduate, I perhaps thought that it did somehow exist outside of physical reality, but now, a few months prior to graduating from my Ph.D., mathematics seems constructed by humans, even if, in some sense, people “discover things” in their research.