[jgrahamc]

I don't know if this will help, but I believe that all of mathematics arises from an underlying fundamental structure to the universe and that this results in it both being "discoverable" (rather than invented) and "useful" (as in helpful for describing, expressing and calculating things).

[rdtsc]

> but I believe that all of mathematics arises from an underlying fundamental structure to the universe and that this results in it both being "discoverable" (rather than invented) and "useful" (as in helpful for describing, expressing and calculating things).

That is an interesting idea. Can you elaborate? As in, us, that is our brains live in this physical universe so we’re sort of guided towards discovering certain mathematical properties and not others. Like we intuitively visualize 1d, 2d, 3d spaces but not higher ones? But we do operate on higher dimensional objects nevertheless?

Anyway, my immediate reaction is to disagree, since in theory I can imagine replacing the universe with another with different rules and still maintaining the same mathematical structures from this universe.

[HackerNewt-doms]

Why do you believe that the same mathematical properties hold everywhere in the universe?

[billforsternz]

Not the person you're replying too, but ... because it would be weird if they didn't.

[rdtsc]

Not OP but I think they are making a slightly different claim — that the universe sort of dictates or guides the mathematical structure we discover. Not whether they hold everywhere or not.