I think that many conjectures from number theory (which I think count as insights) might be more obvious to a computed than a human being since they would have access to a huge amount of empirical data from which to discover patterns and obtain estimates as to the probability that something is true or plausible. This is a very effective way to discover theorems in number theory. The method of discovery is along the lines described by Polya in his books on plausible reasoning in relation to Euler's discoveries.

To obtain the same level of confidence humans need insight and proof which in number theory is often really hard to obtain.

There are some mathematicians like Ramanujan, Euler, Gauss who had similar abilities but this is quite rare.

Also mathematical results that are accessible by humans must be true for a reason i.e. there must be a reasonably short deductive route from known theorems. Work of Chaitlin and others suggests that some theorems are not true for any reason i.e. they are not amenable to any deduction from a set of axioms of less complexity than themselves. On the borderline there must be profound mathematical results that are close to being empirically true in that sense. You would imagine that computers might have a better chance of understanding and perceiving these results since they might be able to reason more effectively from a much wider vantage point empirically speaking given their massive processing power.