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

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.

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

There are legitimate questions if physical constants are constant everywhere in the universe, and also whether they are constant over time. Just because we conceive something "should" be a certain way doesn't make it true. The zero and negative numbers were also weird yet valid. How is the structure of mathematics different from fundamental constants, which we also cannot prove are invariant.

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The constants don't have to be the same everywhere. It is sufficient that everywhere in the universe follows some structure and rules, that's all.

Otherwise we have a random universe, which does not seem to be the case.