When I applied for a PhD student position I had an interview with two professors. Somehow we touched the problem if $P$ is $NP$ and, once we got there, for some reason both professors made it clear that in their opinion there is absolutely no point attacking such a hard problem. Of course this is the case for a starting student, it is more fruitful to build the basis first. But they basically stated that the problem has been studied by so smart researchers that no mortal could do better anyway.

This makes me wonder should one attack such hard problems at all? If one should, why and when? Will studying hard problems span new ideas? Is it even a necessity to understand some hard problems and, especially, why they are hard to solve? Or is it just pure waste of time? Or is it that one should learn some hard problems to educate oneself but not spend time attacking them?