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Is mathematics something real like something so correlated in our universe which would be different in other theoretically universes or is it just an abstract universe-independent layer/framework we came up to with our minds for describing our universe?

Could the second Gödel's Incompleteness Theorem, the taking as axioms something we can not prove like Continuum hypothesis or the semidecidability of Hilbert system (K-Theory) inference be an hint to definitly say that it's just a working abstraction and not something real?

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    Possible duplicate of Was mathematics invented or discovered? – Eliran Nov 13 '18 at 18:24
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    Are traffic laws real? They're purely social conventions. But if you violate them you can die. So abstractions ARE real. Does a property owner own a piece of the earth? How can that be? There's no law of physics that says anything about it. Purely a convention. But you have to stay off other people's property unless you have permission, else you go to jail. Our entire civilization is about abstractions made real by social convention. A Martian physicist can use wavelengths to distinguish red from green. But she can't tell you which one's go and which one's stop. That's a social convention. – user4894 Nov 13 '18 at 18:29
  • ps See Searle, the Construction of Social Reality. amazon.com/Construction-Social-Reality-John-Searle/dp/… – user4894 Nov 13 '18 at 18:30
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    Hi, welcome to Philosophy SE. Please visit our Help Center to see what questions we answer and how to ask. Generic questions such as yours are not really suitable for our format. There is no answer, rather a centuries long philosophical controversy, which is best addressed by reading encyclopedias, see e.g. SEP's Philosophy of Mathematics. We take more pointed questions that can be more or less objectively answered within reasonable space. – Conifold Nov 13 '18 at 21:51
  • Thank you all for your answers, even if it was a question you didn't have to answer. – Dev01 Nov 13 '18 at 22:35
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No, math, per se, isn't physically real. You can't measure "1", or hold it in your hand, etc. But you can measure 1apple, 1orange, etc. That is, you have to add units to mathematical abstractions in order to refer to reality. Those are typically meters, kilograms, seconds, etc, rather than apples and oranges, but it's fundamentally the same idea. Units added to math is typically called https://en.wikipedia.org/wiki/Dimensional_analysis

And then your "framework...for describing our universe" is exactly correct. Ordinary English is yet another such framework — English wouldn't be very useful if it couldn't describe the real world. But it turns out mathematical language is extraordinarily better at that than any natural language. Wigner famously calls this https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences Why is math so extraordinarily effective? Beyond the discussions in that link (or other googling on that phrase), let me know when you figure that out.

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