Neither can we. We have a lot of theorems ourselves that exist because they are what we consider the most likely solution to either extrapolating existing rules or modeling a set of measurements - but it's unknown as to whether the theory is absolutely true.
a child might see that
1 + 2 = 2 + 1
4 * 3 = 4 * 3
7 + 7 = 7 + 7
They might predict this may apply elsewhere, and that:
8 + 0 = 0 + 8
This is the Commutative Law, which the child can predict exists, even if they don't have the specialty to write proofs and understand the theory, etc. They don't know that this is true, but based on their observations this is a theory that holds true to this situation.
Sure, children can pattern match. But I was thinking more about seasoned mathematicians, who not only create new theorems but can also understand proofs and thus find errors in proofs and decide they are wrong, or can be correct. They can also construct new mathematical structures, which other people may eventually use in novel ways to solve old problems. None of this seems anything remotely like "pattern matching" in any way.
I don't disagree with the notion that "probably 80% of Americans/humans are just glorified autocomplete engines", but what about the people with proper ingenuity that is either provably correct in the mathematical sense, or can build up a tapestry of understanding from which we can build predictions about reality (in the physics sense).
Pretty much everything else I do in life - riding a bike, cooking food, composing/enjoying music, etc - can be done with estimates and pattern matching. But the "correctness" of math proofs seems to me to not fit the approximation/estimations that language models use.