Until the highest levels of university study, math education seems to emphasize the memorization and application of laws and formulas, as far as I know in North America, based on university prerequisites and my past experience. We almost always assume the universality of laws, and, for the most part, they are correctly applicable to most things in life. For example, one apple plus another apple will always equal two apples, for all practical purposes, and that remains the same across all cultures. From our point of reference, objects always have a constant size unless altered in some way.
However, just because something is true, for our purposes, doesn't necessarily mean it is true universally. Bertrand Russell and Alfred Whitehead undertook a tedious process in the early twentieth century to prove that one plus one equals two, published in Principia Mathematica (1910, 1912, 1913, Cambridge: University Press). If something so simple in our everyday use takes so long a process to justify, how many pages will it take to prove everything that we think we know so far about math? Surely, in one of those pages will arise controversies about which law to use or even something as simple as human error. That is not to say that we've been using the wrong principles, but rather, just as in physics where different laws work for different reference frames, those laws could be flexible according to condition.
The Principia Mathematica is a subject of controversy to mathematicians and math philosophers. More recently, Kurt Godel in his On Formally Undecidable Propositions of Principia Mathematica and Related Systems (1962, New York: Basic Books) states that there are axioms (such as the statement that one plus one equals two) which cannot be proved or disproved. So then, how do we know the truth in that basic operation? A possible answer to that would be that the best truth would be its relevance to our purposes in the world, since there is currently no way to prove anything absolutely.
In that case, it would seem as if truths in the area of mathematics is not dissimilar to that of arts in that they cannot be absolutely proven or disproven, but in the area of arts, in a way, the process for defining truths appears to be opposite that of math. Truth in math, it seems, can be summarized as a set of accepted laws as perceived by the general public, and that top scientists and mathematicians are working to come up with proofs to find the scope and limitations of those commonly accepted laws. In art, it seems that the general public is almost always subjective in their judgment of pieces of art, while so-called experts attempt to come up with a set of standards and guidelines as to what makes art good or bad. Another difference noted here is that while truths in art are subjective, in math it appears that they cannot be defined as objective or subjective, only unknown. Perhaps there is a universal mathematical truth yet to be discovered. Or maybe it is also open to interpretation, like art.
While it is almost unanimous that people have very different tastes of art, part of that difference can arguably be attributed to culture. In Western cultures,…