This shows one of the reasons I love math: mathematicians only say "you can't do that" when they can prove you can't, otherwise they'll say "I don't see how to do it and it would be hard because ..."
In the case of some brutally hard problems there is virtually no difference. When yet another person claims that she proved that P=NP they usually don't read tha paper at all unless they feel that the author is a serious mathematician. Otherwise they should read amateur's papers all day long. To be honest they make fun of these people and basically they say: you cannot do that. And the truth is they are right with a 99.999999999999% probability.
Edit.:
In these extreme cases it may even do good to discourage people to deal with these demonically hard problems. If you are addicted to thinking these problems are dangerous. Such hard problems ruined mathematicians life. You can become addicted to solve the problem, but you cannot solve it so you try harder. There is no sign of success, so you try even harder... When I was thinking about P vs. NP for 1 month I could not sleep well and could not concentrate on my job well. It was terrible. After the dark period it was so good to think about business, software development again where there are problems (or at least subproblems) which you can actually solve or partly solve.
