We can know things. We know that no algorithm can determine whether or not arbitrary Turing machines will halt, because assuming the contrary leads to a contradiction. Similarly, no consistent axiomatic system powerful enough to express propositions of elementary arithmetic can be complete.

Neither the undecidability of the halting problem nor Gödel's first incompleteness theorem are "waiting to be disproven." Similarly, the speed limit of the universe, if assumed to be breakable, leads to all sorts of contradictions and true paradoxes. Note that I'm not saying that the entirety of some theory, be it special or general relativity, quantum theory, etc. are known truths.

Algorithms, being a sub-branch of mathematics, are logical constructs, which means they can be proved or disproved on a logical basis. Physics is a scientific model of reality which is based on experimental observations (mathematics is used as a descriptive language, but the underlying reality itself is not (as far as we know) based on logic), therefore any physical theory is not provable, only verifiable through experiment to some statistical probability of correctness. The current physics theory is backed by a huge amount of observations, so admittedly we can be pretty sure about much of the theory. But to say that we "know" is not correct.