So technically, in math we refer to the core "ideas" from which all mathematics is derived as axioms, which we hold to be true until found to be false/self-contradictory/redundant. We arrive at these by describing the world, so it's more like - "if you agree to the following statements, then you must also agree to the entirety of mathematics".
Continuing with the occupational pedantry, I think there is some confusion lies in conflating "fact (repeatable observation)" with "fact (tested causal mechanism)"
So, kinda not really, but kinda? This is more philosophy but i think the idea is that as long as we can ensure that "there exists a statement for which there is a piece of evidence that can prove a statement false, but no evidence exists after significant testing and experiments" IRL we can use this interchangeably with "I have found a causal mechanism that causes this phenomena and can replicate the effect while controlling for confounding variables". Statements under both are true and correct to the best of our understanding.