Well, for just a singular example from /pol/ (since it isn't a board I frequent much at all given the super low signal-to-noise ratio, I prefer more hobby-specific boards, such as /o/ for car-motorcycle discussions and /mu/ for music-related stuff), people there were looking into and brought upon pedophilic allegations against Peter Bright years before he got actually charged with those (which actually happened just last year[0]). Mind you, not claiming that 4chan had anything to do with the guy getting eventually caught. But the fact that they had those allegations with basic reasoning and evidence before there was even a whiff of it in public is definitely something.

Or when they had "journalists" from big publications trying to go there and interview people on the boards, they got fed so much misleading and obviously bs info on purpose before being chased away, it was definitely entertaining to observe. Especially given how obvious it was that the "journalists" in question came in there with a very specific narrative in mind already, and it all got crumbled pretty much in real time.

Not even mentioning stuff like a solution to a novel math problem (which other commenters have already mentioned), which ended up being cited and is relevant to actual ongoing research in a specific math area.[1]

Do those things count as "gems"? That's purely subjective. But that's the kind of stuff I personally appreciate seeing there.

0. https://www.justice.gov/usao-sdny/pr/former-journalist-convi...

1. https://en.wikipedia.org/wiki/Superpermutation#Lower_bounds,...

I know there was a correct math proof to a novel and nontrivial problem that was put there by some anonymous user (probably not in pol but in 4chan). Forgot details of it