> the same probability that seven billion people collectively hallucinated elementary theory
Just for fun, it's not unprecedented that the entire human race is disposed to mislearn basic truths about the universe which have to be unlearned when you get to the point where it matters. See quantum mechanics.
One hopes that conscientious mathematicians are careful to select axiomatizations (such as ZF set theory or the type system of Lean) which faithfully reflect reality. And, within such a system, we can be extremely confident in what we're doing. But the distinct possibility remains that the axiomatization doesn't actually match our universe and, say, admits a proof of false or implies something not physically realizable, such as that a certain computation should terminate, when no real life physical machine obeying the laws of physics can ever do so.
Just for fun, it's not unprecedented that the entire human race is disposed to mislearn basic truths about the universe which have to be unlearned when you get to the point where it matters. See quantum mechanics.
One hopes that conscientious mathematicians are careful to select axiomatizations (such as ZF set theory or the type system of Lean) which faithfully reflect reality. And, within such a system, we can be extremely confident in what we're doing. But the distinct possibility remains that the axiomatization doesn't actually match our universe and, say, admits a proof of false or implies something not physically realizable, such as that a certain computation should terminate, when no real life physical machine obeying the laws of physics can ever do so.