[rjrodger]

And the interesting question is, for each of those conceptions, did we call it into being, or was it “there already” in some sense. Consider the case where aliens on the other side of the universe got there first (we consider only possibilities, not probabilities!).

With respect to the debugging of the Euler characteristic, one might ask what truth value formulations during those decades of debugging had, from the perspective of those on the ground at the time. Are we so sure in our present age that there no bugs in Andrew Wiles’s work?

Even if you use automated machine proofs (Mathematica and friends) you still can’t be sure that stray cosmic rays don’t flip a bit every damn time.

Fun times.

[coolgeek]

I already spend more time than I should in considering how to prove that math exists. So if you're talking about physical things in your first paragraph, that's one of those things that I have to prohibit myself from contemplating for reasons of self-preservation.

I will say, though, that acknowledging that math exists independent of its observation makes it more difficult to argue that possible arrangements of atoms do not exist prior to their physical manifestation.

History is, of course, replete with examples of things that we got wrong for thousands of years - the existence of zero, the existence of negative numbers, "real" numbers, as distinct from "imaginary" numbers. These things are now considered trivial, and are taught to children.

I can't imagine Wiles's proof ever being understood by 1% of humanity. I hope, and believe, that there are no catastrophic errors in it, but I wouldn't bet more than $20 that there aren't.