I think that when we answer such kind of questions we may follow next simple rule:

*Mathematics can in general represent a potential realization of a local universe, but not all math objects have necessarily a physical correspondent in our local universe.

Or in other words:

*Maths can explain all available local universes, but for our one we have to search by using Physics!

See more here:

https://www.researchgate.net/publication/264537258

Article A new cosmological paradigm: universal locality

Mathematics is the backbone of all sciences including natural sciences.   Knowledge of mathematics is essential for all scientists; it is the language with which we formulate theories and natural laws and express our ideas. Mathematical concepts have applicability far beyond the context in which they were developed.  Some examples are the following.

Calculus is used to evaluate rates of change and cumulative effects and to evaluate simple expressions involving derivatives and integrals. In physics, calculus and differential equations are used in order to study complex relationships between one property and another. Simple statistical tests are performed for verifying the significance of the experimental findings.  Algebraic equations are widely used to make statements about physical quantities and their relations.

The list does not ends here.  Some of the interesting articles are attached here.

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

http://www.sfu.ca/~rpyke/cafe/reasonable.pdf

http://web.stanford.edu/dept/SUSE/SEAL/Reports_Papers/RelationshipMathScience.pdf

Wigner's observation of the unreasonable and even miraculous applicability of mathematics in the natural sciences was hinged on a number of important, yet (at least today) controversial philosophical underpinnings: Wigner expressed a strongly formalist ideal of mathematics and a realist position concerning physics, and he took mathematics to be a body of knowledge much rather than a historically developed notion. All of these assumptions are today heavily debated, and I would particularly like to draw attention to the work of fellow historians of mathematics like Ivor Grattan-Guinness or Jesper Lützen who have successfully argued that mathematics, in particular during the nineteenth century, developed in close connection with physics in order to address concerns from other disciplines. Thus, mathematics is not, on this view, to be seen as much as a "tool" but rather as a set of techniques and questions developed over time, often from particular concerns. This seems to transfer the question into new, also interesting ones: How did mathematics attain the status of the preferred "language", "tool" or technique for doing physics? How about the cases where no prior knowledge of a particular piece of mathematics was claimed by a scientist when it was later discovered that the use was equivalent to said piece of mathematics? How do collaborations (in person or over time) involving mathematics progress? etc.

In theoretical physics, all the basic concepts absolutely need to be expressed through mathematical concepts.  These fundamental theories have multiple mutually compatible mathematical embodiements.  But physics is mostly about the smallest and the biggest natural entities and it is there that the effectiveness of mathematics and the accuracy of theories is most impressive.  But this has been achieve by eliminating all that do not fit this very narrow focus. In chemistry, the next scale of nature, the effectiveness of theories is way down.  At the next scale up in biochemistry, the theoretical approach become even less effective and at the micro scale of cellular life, the effectiveness of mathematic is ridiculously low. The answer to the question ''what is life?'' does not seem to be theoretically reducible.  At the level of humans and our culture, mathematic is usefully punctual in effectiveness but globally dismally small.

Miodrag -

To say that we are governed by the laws of physics seems synonymous with saying that we are governed by the laws of mathematics. We continually find that mathematics appears to describe all of nature, and that the consistency built into math is reflected by the consistency we may see in the natural laws.  If math were not consistent, it would not function, and neither would nature. They parallel each other. Thus it is appealing to believe that "all is number."

If physical laws are different in other space-time, I would suppose math to reflect that as well.

Cheers - Jim 

Dear Miodrag,

I think Wigner's essay titled" the unreasonable effectiveness of mathematics " is an ecstatic state of mind in which his appreciation to mathematics  in describing the natural universe has no bound, to the extent of equating it's effectiveness to magic - that I think is what unreasonable is.

It is not that mathematics is unreasonable in describing physical sciences or nature effectively  but in fact it is the reasonable effectiveness of mathematics that has to be the case, the rationality and reasonableness of the building axioms of mathematics that somehow been developed from our perceptions of reality give its power of effectiveness.  

Things in nature start out from simplicity and grow up to be complex structurally in repetitive nature of increasing orders and symmetry of some sort without losing basis of simplicity.  That is why very simple mathematical equations describe fundamental laws of physics/ nature universally.

Therefore Wigner  should have said " The  reasonable and rational effectiveness of mathematics". Any physical phenomena has to be described by its properties to be identified and be declared it exists and that property(s) is (are) written only in mathematics.