On the other hand, some things really are just impossible, and attacking those problems with youthful zeal will not change that. In my experience, when people

On the other hand, some things really are just impossible, and attacking those problems with youthful zeal will not change that. In my experience, when people take something we all agree is impossible and start doing it, it is usually because they've redefined the problem in such a way that forward effort can be made. Termination checking comes to mind. It isn't that the impossible becomes possible (mostly), it's that we find a smaller or different domain in which progress is possible and useful.