No, mathematical knowledge is not scientifically testable. It is an abstract knowledge. But, and this is important, it has very strict standards of proof and there are challenge procedures if a proof is invalid. To be *knowledge*, you have to have *justified* true belief.<quoted text>
Its your prejudice not mine that reduces all "real" knowledge to the scientifically testable. You have only this one form of knowledge, I have philosophy, theology and the like.
Now, how does a belief get justified? Well, if there is a challenging belief, there has to be a way to tell at least one to be *wrong*. In mathematics, the challenge procedure is to use require justification from the rules of inference at each stage of a deduction. The axioms are assumed and not proven. In the science, when there are two different theories, the challenge procedure is to find some observation that they make different predictions for and then test in the real world to see which is correct.
So, the question I have for you: suppose there are two different theologies. How do you determine which one is *wrong*. If there is no way, then the subject of theology cannot be given the term 'knowledge'.
No, I am open to a wide variety of beliefs that are different from mine. To be called 'knowledge', though, there must be some way to justify those beliefs. To justify requires being able to at least determine which beleifs are false. That is a challenge procedure.You have made a catogory error that dissmisses all fields except yours.
On the contrary,there are a great number of very testable hypotheses being investigated; from dark matter and dark energy, to inflation, to theories involving other universes. At this point, the evidence is consistent with a hot big bang with an inflationary period that was seeded by Gaussian fluctuations which then lead to the current distribution of galaxies.tThe fact that the feild of physics has had to combat the questions of the big bang theory as well as the anthropic principles with speculative, untestable hypothesis that fail their own test for "knowledge" is simply one example of history having many ironies in the fire.