The ultimate drive for some researches is the pursuit of knowledge. If I'm stuck at some block which prevents me from continuing in some direction that I want, of course I would like some help. I believe we already have nonzero collaborative proofs on math.SE, I can't recall good examples, but I have definitely seen citations to mathSE before.

So for me it sounds quite natural to also share this with AI especially under the privacy assumption. Also there's the assumption of scale -- maybe your problem is not large enough for anyone to care to scoop; and just for blind retraining, how do they know that the proof is even correct to include it into training? I have definitely received a ton of incorrect proofs before. So the SNR of such private chats is also not clear. I'm imagining millions of masters/phd students also trying to solve various random things with various capabilities, but how much real signal is there?

Or start competing with you.

Academic work is based on worldwide sharing, the sharing is not the problem, it's the lack of attribution. Unsurprisingly, these companies neglect standards of academic honor and attribution. Some human researchers also used to do that but in a discipline like mathematics this used to be a small problem because people tend to be so specialized that very few people could just grab someone's research and quickly piggyback on it, and if they do, colleagues will generally understand what happened. Unfortunately, AI is changing this.

LMFTFY:

"Its crazy to me that some people are not egotistical, self-centered, and don't solely care about fame and wealth accumulation".

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