Konstantin Kakaes at Quanta:
The technology firm OpenAI has announced the solutions to 377 open questions across nearly every mathematical subdiscipline.
The results are spread over 722 papers, which OpenAI has uploaded to the Github code repository. They were achieved by a new, unnamed internal model that the company intends to release publicly in the near future, once they deem it safe. All of the papers were written by this model; only one, on a zero-free region of the Riemann zeta function, was edited by a person.
The models seem to be growing more capable. Whereas OpenAI’s Navier-Stokes result in September used millions of dollars of computing power spread over a swarm of 10,000 intelligent agents, the computations behind the new results are, according to the firm, “very different in spirit to the Navier-Stokes setup.” With two exceptions — work on the Riemann zeta function and a proof of a particular case of the Hodge conjecture (both advances in pursuit of solutions to Millennium Prize problems) — each proof required only a nominal amount of computing time using the new model.
More here.
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