In summary, the conversation delves into the concept of mathematics being the same in different universes. While some argue that math is independent of physical laws and will remain the same everywhere, others bring up the possibility of different foundational assumptions and the potential for higher-level results to differ. Ultimately, the definition of mathematics plays a crucial role in determining whether it remains constant across universes.
Over the years, I've come to appreciate the philosophy from quantum mechanics: only observable, measurable quantities are relevant. So I never worry about what happens in other universes, or what happened before the Big Bang. We are unable to detect any effect from those scenarios, so it doesn't matter.
BUT, I think that the foundational assumptions will be different, so higher-level results still might not match. 100 years ago Frege's set theory was all the rage, and now ZFC is pretty well accepted. In a hundred years I doubt either will have a major place in math. And that's just this planet. :D
Spontaneously one may regard it axiomatic, that mathematics is the same independently
of external circumstances.
But is this really true? For instance the fundament of mathematics, the axioms, is resting on basic experiences of our physical world - our laws of physics and also our way of thinking and perceive things,
the logic qualities of our brains. These fundamentals may be different in an "other world".
Perhaps you may regard the fundamental logics (and consequently also mathematics resting on logics) as in fact basic physics.
A given set of mathematical statements may be consistent also in an other worlds - but may be interpreted in a different way.
What is mathematics though? We need a definition of mathematics before we can ask whether or not it is the same everywhere.
For instance, if I say that it is proven truths that hold in the theories that we have examined (such as in Set Theory or in Number Theory or something), then yes, these are true everywhere since the things that we have proved are independent of everything except for themselves (whether or not there is anything that they can be applied to though is a different question)
If you defined mathematics to be the theories that have any kind of regular application, then I'd say no. You might end up in some weird place where you can't find any things to add together, so addition doesn't make any sense. For instance, maybe you're in a universe where every looks the same (maybe some kind of uniform distribution of stuff) all around you, as far out as you can see, and it still looks exactly the same if you look closer or further out. Then there are no things to add; it doesn't make any sense to try to measure things, etc. So the real numbers are not applicable. People in this universe would probably not think to invent them because they have nothing in their world that they'd think to apply them to.