epistemology has little or nothing to do with how untrained people gain confidence in their beliefs as knowledge, etc.
Epistemology is about how to acquire beliefs correctly. How untrained people actually acquire beliefs is some kind of social science. Just like rocketry is distinct from investigating how untrained people imagine rockets work.
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The point is very well-made. But it's not a philosophy-specific one. Mathematicians with a preferred ontology or axiomatization, theoretical physicists with a preferred nonstandard model or QM interpretation, also have to face up to the fact that neither intuitiveness nor counter-intuitiveness is a credible guide to truth — even in cases where there is no positive argument contesting the intuition. Some account is needed for why we should expect intuitions in the case in question to pick out truths.
I think a semantic check is in order. Intuition can be defined as an immediate cognition of a thought that is not inferred by a previous cognition of the same thought. This definition allows for prior learning to impact intuition. Trained mathematicians will make intuitive inferences based on their training, these can be called breakthroughs when they are correct. It would be highly improbable for an untrained person to have the same intuition or accurate intuitive thoughts about advanced math.
Intuition can also be defined as untaught, non-inferential, pure knowledge. This would seem to invalidate the example above since the mathematician had a cognition that relied on inferences from prior teachings. Arriving at an agreement on which definition this thread is using will help clarify comments.