I would call them hilariously deluded

Mathematics is
demonstrably true. It necessarily follows from axiomatic definitions of things like sets (though as Gödel proved, such definitions cannot be complete without being inconsistent).
Our observations gave us the beginnings of mathematics, but they don't nail mathematics down as inherently scientific - mathematics is the queen of the sciences, but is not a science herself. It is based on pure logic, not empirical observation.
The highlighted bit is what makes it probabilistic. Relying on mathematical axioms to prove mathematics is circular. It is demonstrably true because it it appears true when we observe its workings. That doesn't mean that it
is true.
Wikipedia suggests that fallibilism leads to a logical contradiction when it says, "This much is certain: Nothing is certain". How do you reconcile this? If you're a 'hard-line fallibilist', doesn't that mean you assert the truth of fallibilism?
Fallibilism seems to create a false dichotomy, where something is either absolutely known to be true or absolutely untrustworthy. And if it doesn't, then I don't see any point in coining a word like 'fallibilism' - isn't it so obvious that unproven human beliefs can be wrong, that it needn't be said?
The wikipedia article is brief and not the greatest. It doesn't adequately respond to that criticism. What you're talking about in the first paragraph is academic skepticism. Fallibilism is essentially a modern form of ancient Pyrrhonism--a school of skepticism that disagreed with the academics. They did not think the academic claim that "Nothing can be known, not even this" (which is basically the same thing as "This much is certain: nothing is certain") was one that could be effectively made, even though they sympathized with it. If one is a fallibilist because they think it is the best/most logical system, not because they think that it must be true, then all of the problems you brought up are avoided. By hard-line fallibilist I mean that I try to not use terminology which
seems to artificially strengthen what I'm trying to say. I bolded "seems" because that's what I mean in that sentence. I'm not trying to say that X is true, but rather that given the knowledge that I have, X
appears true.
Pyrrhonism - Wikipedia, the free encyclopedia
(More on Pyrrho himself here)
http://plato.stanford.edu/entries/pyrrho/
I don't at all see the false dichotomy you are describing and I think you're being rather uncharitable to the position. It's not that either something is certain or completely bunk. The idea is that things can be useful and we should at least work with what we have, but that does not mean that it isn't bunk. In fact, I think that it is entirely possible that we might be able to come across something that is actually true. I'd only add the caveat that I highly doubt we'd be able to be certain of its truth given the way we reason. We might even abandon that truth for something else.
isn't it so obvious that unproven human beliefs can be wrong, that it needn't be said?
That is a common criticism, but, sadly, I do think that people need to be reminded of it. Having faith in scientific claims is dangerous, I think, and completely anathema to the scientific process. Many people find this form of skepticism unsettling. I'm not saying that it isn't unsettling--I think it is. That doesn't make it wrong, though. That also doesn't mean I have to employ it every time someone says something. We can analyze what they're saying on its own without trying to refute it via fallibilism. Fallibilism is more something to be kept in mind.
A lot of this has to do with the problem of induction and the paradox that in order for something to be interesting, it has to be falsifiable. Tautologies aren't very interesting or beneficial to talk about outside of linguistic definitions. All bachelors are unmarried. Really? Cool. But otpinions/preferences are interesting and not really falsifiable, you could say, and I'd agree. It's not very easy to reason about those things, though. People typically turn normative statements into empirical (and therefore falsifiable) statements in order to make cases for them. That is a problem stemming from the is/ought gap.
Problem of induction - Wikipedia, the free encyclopedia
(There's a lot more on the problem here)
The Problem of Induction (Stanford Encyclopedia of Philosophy)
Is–ought problem - Wikipedia, the free encyclopedia