I know the answer is that philosophy is bad and thinking more than mechanistically like a wind-up clock is invalid, but why does is not bother more math type people that there is a vast infinity of non-computable real numbers?

It is one of the few math proofs I can understand well (like many of the fundamental ones, it is not that hard in either common variant). I know that it doesn’t have many if any consequences for the real world or math as constructed (as Gödel’s incompleteness theorems also do not), but still it seems like something fundamentally broken in how reality as we perceive it is ordered.

Other than my complete lack of ability — such as spending three years trying to learn to do quadratic equations and failing — one of the reasons I could never pursue math is that it seems to be a house built on ghosts of broken, vanished universes.

These philosophical concerns are minor to non-existent for most people I know, but for me they aren’t and never could be just a quibble.

They are — to borrow the title of a decent sf novel — a reality dysfunction.