The theorems of mathematics are all rigidly proven....
I fully agree that proof is possible in mathematics. Mathematics deals with formal systems. Natural science deals with nature. Demonstrative proof is possible in the former case because we know the rules that govern the system in advance. In the case of nature we do not know all the rules. (Indeed a purpose of science is to discover those rules.) This is one of the reasons that scientific propositions can never be proven.
Something which can never be disproven is by definition pseudoscience and not science. The normal definition of a pseudoscience is that it be non-falsifiable, but it appears to me that demonstrating that something could never be proven should do just as well. The basic quality you're looking for is guaranteed perpetual inability to get any sort of a handle on something. Witchcraft is still as good an example as anything else; how could you prove or disprove the existence of witches? Does that not make witchcraft a science by your definition?