Curious about this: do you expect that Claude science will also scoop interesting directions looking at anonymous usage, to publish posts like this before the original author (similar to the Navier Stokes debacle)?
I think so, yes; anything we type here (or any other social media) will eventually turn up in the LLMs' memories and become avenues.
There's no evidence that's what happened with navier stokes. By all appearances some employees heard a (somewhat inaccurate) rumor which led them to believe it was solvable and they proceeded to throw utterly absurd amounts of compute at the problem. The ethics of that are still questionable but for an entirely different reason than they were accused of.