"There is no algebraic formula for the roots of a general quintic polynomial." R: "That we KNOW of." "No, we can confirm that one does not exist." R: "But that's according to our current knowledge." I just changed the topic since the quintic thing was an analogy, but this misunderstanding troubled me. What would be a fitting response? I suppose a response is that all of our "current knowledge" is also developed through mathematical proof, and thus any result derived from our "current knowledge" cannot be nullified by "further knowledge" as this would require that our axioms have an underlying inconsistency. But I suspect this response would not satisfy someone who did not study mathematics. Statements of nonexistence in math seem to be taken as "we haven't found it yet" by the general populace. Why is that?