And there is no mathematical proof of Bayesian epistemology. Bayes' theorem itself is a bit of math/logic which everyone accepts (including Popper of course). But Bayesian epistemology is an application of it to certain philosophical questions, which leaves the domain of math/logic, and there is no proof that application is correct.

Incorrect. E.T. Jaynes book Probability Theory: The Logic of Science gives a proof in the first two chapters.

Replied here:

http://lesswrong.com/r/discussion/lw/54u/bayesian_epistemology_vs_popper/