[tremon]

I don't think that's true. Mathematics can model every conceivable universe; you cannot derive the values of c or G in our universe from a purely mathematical model. Even if there were a proof that the current values for cosmological constants are the only possible values, that proof would necessarily have to rely on lemmas from physics.

[ordersofmag]

It could be that once we truly understand math in a complete way it would lead inexorably to the definition of one and only one possible universe with only one possible set of rules and c and G would simply fall out naturally. I'd agree it seems unlikely given our current understanding of math and physics (and their relationship to each other). But given both are incomplete it remains a possibility. The one theme that seems to hold true as we dig deeper and deeper into how the world works is that the fundamental rules seem to get more and more unified.

[jeremyjh]

Please tell us more about this. I’m not familiar with any definition of mathematics that would support the idea that it can prove statements about our universe without access to observed facts.

Are there any papers where this possibility is explored? What does it mean to have a complete understanding of mathematics?