Mathematics and the Universe

[Purple Rabbit]

So are you saying that mathematics is no different to a language, it is purely human made? We choose symbols to depict values etc. 'Language' needs a giver and a receiver in order for it to have a purpose or be understood. We decide what the values are and the meanings, but surely this is not the case with mathematics. Are you saying that pi for example or Einstein's famous equation isn't really out there waiting to be found, rather we have 'created' these equations? Sorry, I'm struggling to convey what I'm thinking. I hope you see where I'm leading...

By the way, have you read much of Kurt Gödel?

Rereading your post triggered some other thoughts on this. Your question is not only about mathematics but about it's application to the real world. Assuming that there is a real world out there, it does not necessarily follow from it that mathematical concepts are relevant in the real world. Always the application to the real world needs validation. Reality does not follow from mathematics. Euclid's Geometry shows this. Assuming Euclid's axioms as true thus has two meanings that should be distinguished sharply: 1) are Euclid's axioms true in mathematices, and 2) are Euclid's axioms true in the real world. It seems essential to me that these are separate questions.

But what does it mean to apply mathematics to nature? For instance we have no way on deciding if perfect circles in nature exist, because that would mean that physical objects can be arranged with random precision to form a perfect circle. But validating this requires measurement with random precision. This is not possible, not practically (we would need perfect tools), and not theoretically (due to Heisenberg's Uncertainty Principle). So it seems to me that anyway you look at it, by saying that a certain geometry (whatever geometry!) is applicable to reality is already an assumption on the nature of reality. It's a model of reality and again it follows that mathematics has no necessary implications on reality.