I'm a mathematician. I have a lot of trepidation about these tools and what they mean for the future of the profession.
That said... most of us are not working on problems as famous as Navier-Stokes. Even if OpenAI could scoop me based on my back-and-forth with ChatGPT, which I presume they could if they threw $15 million worth of compute at it, I highly doubt they'd bother.
I think they spent millions pursuing strategies to attack that particular problem? I don't think it takes 15 million for their model to get trained on your chat logs. This is probably all automated internally. If they did scoop your ideas, it would likely get incorporated into their model without any conscious decision making. And if you're not a high profile academic, nobody will hear about it.
But consider they could decide that they want to scoop more regular research work too. They could automate it with just a few LoC. Even if you opted out in the ToS, you'd have to file a massive lawsuit just to enforce it. And the actual fine would be inconsequential to OpenAI.
I think going forward, any researcher should consider anything submitted to an LLM to be copied/stolen.
ChatGPT can also simple tell your ideas to another user.
The fact that anyone has to make that trade off with that through process shows a company and culture that is untrustworthy. OpenAI isnt open, isnt a non-profit, isnt for the benefit of humanity, and isnt even for the benefit of users at this point, its users are vassals providing training data so their models can reach ASI first.
I am going all in on sovereign ai even if its worse, these companies have shown they not only dont deserve trust but are actively stealing past and present intellectual property from humanity and users.