Also see my other comment here https://news.ycombinator.com/item?id=49695418
I suggest you go through the SDT wikipedia entry and note in particular how intrinsic and extrinsic motivations are internalised and integrated into a coherent sense of self. This is true for all humans and worth a study to understand what motivates us to do what we do.
To repeat myself from https://news.ycombinator.com/item?id=49680925 "the AI companies behaviour, threatens everybody's Autonomy, nullifies their Mastery/Competence and robs them of Purpose/Relatedness/Belongingness. Nobody should accept this."
Mathematicians will keep doing research with or without AI. But so far they have been doing it in a free environment where there were unsaid-rules/ethics/morals being followed; the most central of which is "do not steal my work; if you use my work give me credit and compensation (if you make money off of it)". This takes care of both one's intrinsic and extrinsic motivation needs which is why all of our scientific practices, societal/economic rules etc. are setup on a system of incentives appropriate to their domain eg. for a researcher doing something original and winning the Nobel Prize/Fields Medal is far more important than making money while for a Business CEO making money is everything.
In the case of Navier-Stokes problem, Name and Fame were everything and Money was a lesser goal. OpenAI with their despicable behaviour have robbed the mathematicians off the above by going behind their backs, without giving them credit and simply throwing a huge amount of resources at the problem. This should not be tolerated.