While many people who become preoccupied with "problems" like these are operating in bad-faith and can't be swayed otherwise, I would be very surprised if a lar

While many people who become preoccupied with "problems" like these are operating in bad-faith and can't be swayed otherwise, I would be very surprised if a large number of them (if not most of them) weren't just lay people who were simply curious, who had poor experiences learning math or technical subjects growing up, and for once read about some mathematical "problem" that was accessible to them, were excited by it, and set about exploring it not realizing it was actually a red herring. And unfortunately, if you lack a good foundation, you won't be able to realize the "problem" you're working on is actually a red-herring, and the rabbit holes you wander through when researching these "problems" will just teach you further bad habits and crankery. For the sake of those people, I don't think it's fair or right to immediately assume bad faith and take the attitude of "run for the hills" when met with anyone who's gone down such a path. And I don't think it's right to make a mockery of them either (except of course for the ones that start trying to write books, teach seminars, or submit papers about their "discoveries" without ever getting it right). Instead maybe we can point them towards resources so they can fix their faulty foundation and find more productive ones? No need to engage them further. Just give them something -- even something canned -- to sate the obvious curiosity that they have and give them a little direction. At the very least we can not mock them and assume bad faith -- there's nothing wrong with being curious.