There is no question about it: mathematics has been able to describe reality and predict events better than any human being since the beginning of civilization could see more clearly than anyone else will ever be able again. If you ask a mathematician whether they agree with that statement, almost always, given how good one's ability at math is, the answer is mostly no.
But here's something even stranger: every single question raised in mathematics gets an official yes or no response from it—whether it exists, cannot be proven, or should be accepted without further discussion. And when asked why this matters, there are more than enough reasons to know that one knows how much people genuinely still don't understand about math beyond its own answers.
The reason is deeply philosophical: we have an absolute truth claim that mathematics doesn't hold up against evidence, yet it keeps coming back as the only thing worth knowing. The idea of reality being simply structured by patterns rather than causality or change in some sense became almost universally accepted from around 1900 onward, but nobody could quite put their finger on why, because there was no proof.
And that gap between what is known and what ought to be known sits deeper than just numbers. The modern story of mathematics itself starts with one single question: the Pythagorean theorem—a result that says something about triangles—so central it remains true now every time you measure anything at all. However, proving this alone does not prove the entire structure works properly across everything else; you need to show that it holds for general shapes and sizes.
This was hard to do because people were using essentially arbitrary assumptions until someone finally stepped forward: a mathematician who wrote down his own proof of Hilbert's tenth problem in 1970. This proved something entirely different from the Pythagorean theorem, which is why this particular moment holds special meaning both historically and philosophically.
The reason it matters is that mathematics has been built on foundations so deeply fixed that anyone trying to build anything new would need to accept those assumptions as given—because if there wasn't proof of their existence already written down somewhere else, you could never claim to understand a mathematical object until one had the rules backed by something permanent.
If the axioms were wrong in any obvious sense, it meant mathematics lost its edge and started missing. So that question remains open for decades longer; nobody has found an easy answer yet either way because there is nothing simple about accepting everything on paper as true with absolute certainty at all times. The whole enterprise of mathematics rests squarely against the possibility of a gap remaining between what we think should be known and precisely what it really is.