Since long time ago I have been thinking in two problems that I have not been able to solve. It seems that one of them was recently solved. I have been thinking a lot about the motivation and its consequences. Mostly because people used to motivate one of them with some very interesting implications. My conclusion however, is that there is a mistake in the motivation of the problem, and that, while being a really interesting result, it does not make any sense in the setting in which is formulated. As my opinion is not relevant compared to one of the experts in the area, I do not say anything.

My question is if you can provide me some examples of conjectures that were believed to be interesting in the mathematical community because of a specific reason, but that once having the proof, people realized that the reason to motivate the problem was not truly related to its solution. Or in other words, the solution of the problem gives no clues about the original motivation.

falseillusion, or rather do you just mean "illusion"? To my way of reading, a false illusion would not really be an illusion at all, but real. – Joel David Hamkins Jun 3 '14 at 21:22