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I suspect you're wrong; I get the sense that the majority of the projects worked on by today's most productive research mathematicians have been very significantly disrupted by OpenAI's public releases. You can get a sense of the scope of these results by skimming the collection of mathematicians' reactions compiled here.
Again, I suspect you're wrong; I expect the most important math journals will all pivot now to publishing primarily expositions of computer-generated results, which is a major shift. Soon, the expositions themselves will be computer-generated, too. As far as academia, the entire systems of reward, hiring, and promotion for research math will be unsettled (each of these systems is currently focused on the ability of individuals to develop proofs of mathematical statements).
I think you're making the point here that research math isn't solely about problem solving (proof development), and that exerting social influence over (e.g.) area focus and direction is similarly important. That's clearly true. Gauss wrote: "I confess that Fermat's Last Theorem, as an isolated proposition, has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of" - which I take as suggesting that the prominence of Fermat's Last Theorem owes as much to historical and social factors as it does to any inherent importance of the statement. But so what? Yes, the emphasis placed on particular problems emerges as a consensus across the work of mathematicians operating as a community. But this emphasis has no real bearing on whether humans or machines are better-positioned to tackle such problems, which was previously only ever the work of individual humans.
I think this is a fair point. At least right now, a lot of the success of the models in solving major math problems may owe to effective interactions with human experts in the form of seasoned prompting. We honestly don't know how significant the human collaboration was to generating these results. Many mathematicians have called for OpenAI to share these details.
I don't understand this point. Certainly we don't deride great (human) mathematicians this way (look at all the problems Gauss couldn't solve). Maybe you're suggesting that humans today can still more effectively resolve certain types of math problems than machines can? If so, what evidence do you think supports this idea?
This does not contradict my point. The journals still exist and are selective and important, but with AI playing a bigger role. But the vast majority of content, ai or not, will be rejected. AI has the effect of raising the bar of quality because now people can use AI for help.
My point was there are tons of prompts that fail to yield sought solutions. so no one reports it or write papers about negative results.
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