[omnicognate]

"That human intelligence involves processes that algorithms cannot emulate" is the conclusion of his argument. The premise could be summed up as something like "humans have complete, correct perception of mathematical truth", although there is a lot of discussion of in what sense it is "complete" and "correct" as, of course, he isn't arguing that any mathematician is omniscient or incapable of making a mistake.

Linking those two is really the contribution of the argument. You can reject both or accept both (as I've said elsewhere I don't think it's conclusively decided, though I know which way my preferences lie), but you can't accept the premise and reject the conclusion.

[saltcured]

Hmm, I am less than certain this isn't still begging the question, just with different phrasing. I.e. I see how they are "linked" to the point they seem almost tautologically the same rather than a deductive sequence.