Are the laws of mathematics 'absolute' in this universe?

Question

We observe that almost all physical phenomena (which has been explained) can eventually be explained by the laws of mathematics. Mathematics seems ubiquitous- for example the form of the differential equation that governs the simple harmonic motion of a helical spring has the exact same form to explain the current in a RLC circuit. The parallels are endless virtually. But it does not mean necessarily that the 'next to be discovered phenomenon' has to follow the laws of mathematics provided that there is a theorem out there which proves that every physical mechanism has to abide by the laws of maths.

Could anyone answer with a philosophical insight on this matter and has the Godel's Incompleteness theorem anything to say on this?

Answer 1

If you haven't already read Eugene Wigner's essay "On the unreasonable effectiveness of mathematics in the natural sciences". It addresses most of what you mentioned.

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Answer 2

Your question seems to be based on an assumption that the laws of mathematics are out there and the physicists are busy trying to apply them to understand the laws of physical reality, but actually the relation is often the opposite: certain physical phenomena often lead physicists to develop new mathematics that the mathematicians themselves may have been powerless to develop, lacking the necessary physical intuitions. A spectacular example of this was the development of Seiberg-Witten theory that was used to almost "trivialize" previously spectacular (and complicated) mathematical develoments; see this article for a more detailed account.

Answer 3

I think they are not. Consider, for any consistent first-order theory S in any language L, the set S* of consistent theories of greater provability strength. The incompleteness theorems tell us that if S is incomplete, then S* can be arranged in an upside-down pyramid, where each S' in S* can be extended with at least con(S') and not con(S'), giving an upwards branching structure of incompatible extensions.

If mathematics was absolute, then there would be a subset T(L) of first-order theories in S* that is the "true" tower without branching structure that traces out this absolute mathematical reality for the language L.

Is there such an absolute mathematical reality for any meaningful language L? I don't think we have a universally accepted methodology for getting T(L) for arithmetic or set theory.