From the perspective of the multiverse theory, would maths "work the same" in every possible Universe?

Question

I've had an interesting discussion with a friend recently and I was arguing that in every possible Universe, mathematics would always have to work the same, i.e. $1 + 1 = 2$ would have to be true for every possible Universe, regardless of the laws of physics, number of physical dimensions etc. because in every Universe if you have one thing, and then another, you have two things in total. Another example: every possible Universe would have the same prime numbers and therefore the Ulam spiral would look the same in every possible Universe (with at least 2 dimensions).

Is this true? Is there an example that would prove this false?

Answer 1

AFAIK, there's no reason to think that mathematics would be different in any other universe, nor that it could be different.

Answer 2

Like every statement in natural language, every mathematical statement does not occur isolated but in a certain context. There are also undefinable concepts in any language, whether natural or not. "$1+1=2$" is only meaningful in a context where "$1$" and "$2$" and "$+$" and "$=$" are meaningful. If their meanings are completely determined, then that statement would be true no matter what. So it depends a lot on what exactly you define them to mean! What really is a "thing"?

To give a bit of detail, we could for example say that expressions that have the same value are equal, in which case we can write them down with an "$=$" in between. We could also define "$2$" to be a short-form for "$1+1$", and so both have the same value. Thus we get "$1+1=2$" as long as "$1$" and "$+$" are defined. Notice that I did not define what "value of an expression" means. That again is up to you to decide, but for most reasonable definitions what I said holds.

Also, there is little use for a multiverse theory because there must still be a single over-arching framework that governs what universes are allowed and how they interact. And hence we might as well consider that one single framework as the true universe.