Ok, I see what you mean now.

I took your word "invalidate" to mean "be proven false" whereas I meant "valid" as in "logically coherent, even if not true."

> I say the math can’t be invalidated by observations

I meant, isn't a counter-example or proof by contradiction an invalidation by a type of observation?

No, proof by contradiction is a logical construction, has nothing to do with the real world. Proof by counter-example could or could not be observation, depending on whether your example comes from observation or from pure logic.

I suppose even in pure math, if you postulate a set of axioms, then proceed to to prove some theorems, you're still at risk of someone providing something like a counter-example showing that your axioms are not consistent, and that not all of them can be true at the same time.

Meaning that even if the inductive logic is 100% correct, the theory can be incorrect due to using mutually exclusive (in some non-obvious way) axioms.