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).

We won't be running out of hard problems to attack anytime soon, even if we produce a bunch of counterexamples to some of them.

Yeah but the Collatz probably has one of the highest man-hours of actual waste.

Ergo: > “This is a really dangerous problem. People become obsessed with it and it really is impossible,” said Jeffrey Lagarias, a mathematician at the University of Michigan and an expert on the Collatz conjecture.

and

> “Collatz is a notoriously difficult problem — so much so that mathematicians tend to preface every discussion of it with a warning not to waste time working on it,” said Joshua Cooper of the University of South Carolina in an email.

(from https://www.quantamagazine.org/mathematician-proves-huge-res... )