I used to be a young mathematician sometime at the turn of the century...

"waste their time trying to prove it" is the MBA approach, where you should spit out results and articles.

Outside the MBA-thinking box, attacking hard problems, even unsuccessfully, is the way to gain deeper insight into various results and tools that you can later apply to other problems, i.e. no waste of time at all, unless you go to the extremes (like spending years on a single problem and nothing else).