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.