What part does emotion play in the acquisition of knowledge? Does the role of
I think your question presupposes that "emotion" is a fairly simple phenomenon, whereas I suspect that it is extremely complex. But let's sidestep that concern and just try a simple case out.
Scientist A believes that he will very much impress his lover if he unlocks the secret to some phenomenon. Scientist B has no such motivation (and, let us suppose, no other motivator that makes him as eager as A's desire to impress his lover), but works on the same problem.
In this case, it looks to me as if scientist A's success (if he achieves it) will be partly explicable in terms of his emotional motivation, whereas that would not be the case for B. Indeed, it seems reasonable to think that A's emotional motivation might provide stronger motivation than we would find in B. On the other hand, we might worry that A's emotional motivation might also cloud his judgment somewhat, and make him more likely to make mistakes. But this much seems obvious, such an "extrinsic" motivator can certainly function in such a way as to make the acquisition of knowledge more likely.
As a kind of generality, I think it is fair to say that those who have enthusiasm (from the Greek enthusiasmos, which essentially means to be possessed by a divine spirit) are more driven to the discoveries and acquisitions of knowledge than those who are not enthusiastic about their pursuits. I see no reason why this would differ across different disciplines. An excited and enthusiastic mathematician will not necessarily be smarter than a bored one, but I would expect the enthusiastic one to be more likely to advance knowledge. The same, I expect, would be true of historians, scientists, and even philosophers!