>2. Would an equivalent allocation to incentivize human effort have borne the same results?
Unlike their initial massive brute-force run that solved the Navier–Stokes Millennium Prize Problem, most of their subsequent breakthrough results in mathematics have come from a single prompt to a single AI agent, using approximately 3 hours of ChatGPT Pro-equivalent thinking compute per result on average.
[–] gewetensleegte 2 days ago
[–] zamadatix 2 days ago
As a result, I also doubt they'll ever bother to submit these to a journal when they already have the attention and ongoing review of leading mathematicians from around the world.
Perhaps the most salient part of the Millenium puzzles though is the 2 year acceptance period, where we give a time for that review and consensus (the part that matters, not journals or prize claims) to settle before claiming it solved.
[–] gewetensleegte 2 days ago
but that would mean anyone could do it, right?
then why are these results coming from OpenAI all the time?
are you saying they're just better at prompting?
as far as I know they still haven't claimed the prize, but rather stopped just short of it
they produced a Lean certificate for a math problem, but it's not "solving a Millennium Prize Problem" until they get a human readable version approved and published in a Math journal.
that's the rules for the Milennium Prize Problems.
I would personally sooner say they ruined the Navier-Stokes Millennium Prize Problem, because the last part is important. Nobody in fluid dynamics research has any use for the result specifically because the breakdown singularity happens at a scale smaller than molecules, and they were dealing with that already. The Millennium Prize Problems exist to encourage mathematics, not to pull the rug on it.