You might want to read more about the history of mathematics. Math describes things we haven't, and can't, observe. It describes other dimensions, various magnitudes of infinity, and all kinds of crazy stuff we can't see. Math goes a bit beyond arithmetic.

within a very short period of time philosophers had the unprecedentedly sudden realization that truth needed to be verified through repeatability

The epistemology underlying science has changed a bit over the years. But science still goes beyond merely what we can observe directly. Much of our knowledge is theoretical, meaning we think we know what we do because of the models we have. We haven't observed the interior of the sun, or of black holes, but we still have equations and models as to what we think happens there.

To me, it's obvious

What you consider obvious isn't much of an argument. The entire history of science and mathematics, or for that matter rationality itself, has been one long sustained lesson that our intuition is a poor guide to the world.

There was no logic, no "creation" of knowledge in the absence of observation

I recommend David Deutsch's book The Beginning of Infinity on that front. He gives a forceful argument that knowledge does not grow from observation itself. To quote Popper, all observations are theory-laden. Observations must be interpreted, and the knowledge we have consists not of facts, but of our explanations for what happened. Facts don't argue for themselves, rather we have to develop and argue for why we think as we do.

Without empiricism, I think it's painfully obvious neither of those fields could exist in any way we'd recognize as knowledge.

What's interesting is that science left empiricism behind long ago. It has moved to Popper's epistemology of conjectures and refutations.