An unpublished internal model is said to have produced almost all of these results from a single set of parameters. Some of this has been verified using Lean methods, but mathematicians are calling for greater transparency.
On October 6, OpenAI unveiled a batch of 372 results in mathematics and theoretical computer science, presented as solutions or advances on open questions. According to Scientific American, almost all of them come from an internal model that is not yet commercialized, driven by a single agent from a single starting instruction.
Machine-verified evidence
Among the work highlighted are a solution of the Kakeya conjecture in dimension 4, improvements to important algorithms and progress towards the Riemann hypothesis. A good part of the proofs have been formalized in Lean, a language that mechanically verifies each step of a proof, which makes these results almost certain.
The reception remains cautious. Andrew Sutherland (MIT) calls for the community to be able to control everything before validating anything, while Daniel Litt (University of Toronto) welcomes the publication of the results. Terence Tao criticized a pace that he considers excessive. The cost of calculation and the opacity of the model, already criticized by OpenAI when it announced on Navier-Stokes, remain the main points of contention.
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