Frostgage

The way I see it, language is the most important thing humans have created, while mathematics is the most important thing humans have discovered.

of course. This statement presumes that mathematical relationships (e.g "9 > 8" or "the hypotenuse of a right triangle with sides 3 and 4 equals 5") are inherent universal truths - would you agree with that assessment?

Maths in its modern formulation is all-dependent on its axioms, though, which blurs the matter of truth somewhat. 9 > 8 for most definitions of '9', '8', and '>', and one must always remember that the 3-4-5 triangle only contains a 90 degree angle in Euclidean space.

In maths as we currently have it, the only things required for a given statement to be true is for certain axioms to be true and the deductive method to generate the statement from the axioms to be logically valid. If axiom A is true, and a logically valid deduction D can be made from A to a statement X, statement X must be true. The question of whether X is true with respect to the universe is seemingly wholly dependent on the question of whether the axiom A is true with respect to the universe.

The question of truth thus becomes a bit less intuitive - are two sets always the same set if they have the same elements? If X and Y are sets, does there always exist a set which contains X and Y as elements? Is it guaranteed that there exists a set with an infinite number of different members? These are colloquial statements of three of the nine axioms of ZFC, which encompasses pretty much everything normally referred to as maths, and yet they clearly don't refer to anything in the physical universe - indeed, they define purely mathematical concepts. The same holds true of other mathematical concepts like '9' and '8' and '>': they don't refer to anything in the physical universe, so unless there exists some sort of non-physical universe in which these concepts are actualised in some sense, they can't be universally true because they don't refer to anything in the universe - there is no universe fundamentally compatible with the form of truth they have. The closest form of truth that can be found in a purely physical universe is that of physics, where mathematics is augmented with units and interpretations that signify physical concepts in order to give its form of truth something to refer to.

It's all a very curious matter, but the short version is that I indeed agree with that assessment, as I consider there to be a non-physical universe of the right sort to give maths something to refer to. However, now I'm curious about your thoughts on the whole conundrum. 

Very interesting stuff indeed. My thoughts relate to our earlier discussion of the signs of numbers. The linguistic/written content used to express numerical concepts is an arbitrary structure created by humans, best evidenced by the fact that 12, twelve, dozen, XII, doce, etc. all mean the same thing depending on your time and place in history. However, for example, Sir Newton did not decide that the derivative of the concept expressed by "3x^2" equals 6x, he merely discovered it to be true. I can't speak to other universes which I have not yet visited, but I'm willing to put my trust in this mathematical relationship holding true in ours.