Jacketing in terms of Physics and Maths is trivial. Its all natural science. And that's why you see people from pure Maths and Physics background work interchangeably with each other. GR comprises Physics and Maths (Riemann Geometry) equally!

Ahmida> if we have the sum x=1+1 then every body will say that x=2, but is that an absolute fact (x=2) ?

I thought everyone knew that 1 + 1 = 10 ;-D

There isn't anything like relativity, of course; but there is the idea of correspondences, between, apparently different topics, which, in mathematics, is epitomized in the Langlands program. A very nice introduction, that stresses the implications for physics, can be found here: https://math.berkeley.edu/~frenkel/houches.pdf

There are, sort of, but it's a little bit of a false correspondence since most of these mathematical concepts emerged as solutions to physics problems like relativity. One thing you might find interesting is the theory of Lie algebras and fibre bundles.

Example: if we wish to work with a gauge theory on a spacetime with some isometry group (simple example is spherical symmetry), then we are considering actions of a group G on a bundle E. However there is no 'preferred action' of the isometry group on a principal bundle, hence we need to consider all possible conjugacy classes of automorphisms of G on E - getting between those classes amounts to choosing a different basis for the roots of the g, Lie algebra of G.

Thus replacing words like 'preferred isometry action' with 'preferred frames of reference' and 'choosing a basis of the Lie Algebra' with 'choosing a local co-ordinate system' etc, gauge theory looks a lot like relativity. Spoiler though - relativity is itself a kind of gauge theory (think 'frame bundle over spacetime' - i.e. the fibre is the group GL(N)), which is why the correspondence is so close :) 

Always remember that maths is invented; therefore you often find that with extremely technical maths like this, the reason those kinds of maths exist and are popularised is by-and-large because of the physics - they do not evolve independently. Hence I would say that it is equally correct to describe relativity as both a physical theory and also as a mathematical theory - the difference is the treatment you give it, whether experimental or theoretical.

However, if what you are asking is "Does maths have a concept where a fact is not absolute", then not really, because the entire foundation of logic is based on each statement being either true or false. There is such a thing as 'fuzzy logic', but there's a reason it's not generally used in proofs - maths is the tool we use to sort out truth from falsehood. If you want a system that is more flexible than this, you are no longer doing maths, by definition.

In maths, it is certainly not true that there are no facts. Again, always remember this: reality is the territory - maths is just the map. We have no reason to want maths to contain very much uncertainty, any more than we'd want a hammer to randomly go soft every now and then. For different jobs, different tools are needed.

@ Erik

Totally agree! Well said!

My answer should be no. Mathematics is just logics, starting from some basic assumptions you apply just logics to come at the results. So, there are two possible relativities. The first one is lying in the basic assumptions, the postulates or axioms. A change of the postulates may give a different mathematics. An example is of course the mathematics needed for the general relativity. The other possibility lies in logics. Logics is connected with what our brain thinks are the right argumentations. At this moment I do not see any deviations from that

Relativity = mathematics + causality principle - nothing else.

My opinion would be yes, in certain sense as will be explained below.

In essence, relativity in physics states the fact that laws about nature should be irrelevant to human choices, in particular, of coordinate frames. In mathematics, there is also a field which concentrates on mathematical properties which are independent of coordinate choices, i.e. geometry.  That said, it will be no surprising that the relativistic physics is best described in mathematical terms of geometry. 

Of course, there is some differences between the two disciplines. In physics, relativity implies a Lorentzian signature of the spacetime metric, so only Minkowski manifold or pseudo-Riemannian manifolds are relevant. In mathematics, however, all manifolds with any signature may be of interests from purely geometric perspective. I hope the above constitutes a useful answer to the original question.

The answer is no.

Of course, Liu Zhao is right when he states that there are similar concepts in Mathematics which are used to clearify your statements and specify the objects you are working with, but I think the author of the question meant something different.

The beauty of Maths is its ultimate verity. Every proven mathematical statement is a statement of pure truth. It is deduced from a set of axioms and once proven, we can be sure that the theorem holds true for all eternity (of course it was true all along, but it just took us so long to prove it). Wether you talk about Lie-Algebras, Zeta-functions or DIfferential Geometry - these relations hold true wether this planet, humanity our galaxy exists. They literally don't care if even our universe exists because they are metaphysical - not bound to our mere existence. You may use Lie-Algebras for Gauge-Theory and the Riemann Zeta-Function as a partition function for your system, but all you do is *applying* these relations for describing and predicting our reality.

Here is the difference to Physics: It explicitly does not need the strictness needed for a mathematical proof, au contraire: Applying pure mathematical strictness would mean the inevitable death for Physics. It only works because we approximate, and approximations are the nemesis of Mathematics. We Physicists set up theses which are then scrutinized, validated and after some time discarded in favor of a new thesis which descibes our reality better (hopefully). There may be other universes where the laws of physics look differently and where we would need a different set of Mathematics to describe what is happening there (and if we believe the esoterics behind the Multiverse Theory, this is most likely the case). But a mathematical statement hold true regardless.

Summa sumarum: There is no relativity in Mathematics as the one you witness in Physics. This is because a scientific proof and thesis is works entirely differently than a mathematical. In Physics, there is a little bit of falsehood in every statement we make, in some more than others - simply because you cannot describe the laws of physics *exactly* for a system of 10^23 particles and so you are forced to approximate. But that is okay for us, this works wonderfully. In Mathematics, a statement or a thesis is either right or wrong - and it is this for all eternity and beyond. This property of being absolute, being eternally is the beauty of Mathematics. It is the opposite of Physics and its relativity.

P.s.: And no, 1 + 1 = 2 holds true in every Universe, even if there is no universe with a mathematician in it to make that statement. Of course, the equation 1 + 1 = 10 equally holds true - it is the same statement, merely differently worded.

Robin> P.s.: And no,.. 1 + 1 = 2 ... 1 + 1 = 10

Finally one who got my point! I hope(?)

There is no more relativity in relativity theories than in mathematics; it is all about the possibility that there may be different ways of expressing invariant truths.

1+1 = 1

If I were a god I'd forbid sentient beings to believe that everything is just an illusion. Consider, yes. Believe, no.

Entire field of mathematics exists due to relativity. Laws of mathematics can operate only where there is multiplicity. In snaskrit there are two words. Dvaita (Duality) and Advaita (non-duality). Mathematics cannot be used to explain non-duality. Advaita deals with a concept of "one without a second." It describes the entire universe as one without a second and the multiplicity seen within it as an illusion. More details in following article.

Article Unified field of consciousness