I will get downvoted for this but I can't help thinking that billions of dollars have gone into chatgpt over a period of years and an LLM can direct all its "attention" (in a metaphorical sense) on one problem. I think if you gave top mathematicians a few million (so a fraction of a percent of chatgpt budget) to solve this problem over four years, they probably would have at least made significant progress. I don't think chatgpt has solved thousands of similar problems (even stretching that across all ham disciplines). Basically my thesis is that universal basic income could have had a similar impact, and also encouraged human flourishing elsewhere.

There are literally millions of people who receive incomes from states which don't restrict them from spending 90% of their waking hours studying mathematics proofs, if that is what they wanted to do. Most of them do not and overwhelmingly could not, even if we took the opposite tack and made their welfare or pensions or even university fees contingent upon them solving mathematics problems. Topping up the global welfare budget by a couple of hundred billion might meaningfully improve some people's lives, but even with the most sceptical take on AI usefulness it's hard to imagine it producing more research than went into and came out of ChatGPT....

We also actually do devote millions in public funds to enable top mathematicians to spend much of their time studying mathematical problems, but it turns out that there are a lot of problems, solving them is hard, and sometimes they like to spend their time devising new problems instead. Perhaps some people currently dedicating their efforts to writing trading algorithms would also prove adept at devising novel proofs to more abstract mathematics problems, but I don't think UBI is changing their personal priorities...

sam altman already did a scaled pilot of UBI, unfortunately it had disappointing results which led to almost no one talking about UBI these days.