OpenAI Releases 719 AI-Written Math Manuscripts, Claiming an Open Problem Solved
One manuscript produced by an internal research model takes on an unsolved problem in set theory. The researcher who had introduced the problem as an open question criticized the manuscript's exposition and references.
On October 6, OpenAI published a batch of mathematical research results generated by an internal research model. One of the manuscripts addresses a problem in set theory that remains unsolved: the relationship between two statements known as the partition principle and the axiom of choice. OpenAI says it constructed a mathematical model in which the partition principle holds but the axiom of choice does not.
What exactly is being claimed?
The problem is whether the two statements must necessarily hold together. According to OpenAI, the manuscript presents a model that satisfies the partition principle but not the axiom of choice. If the construction is correct, it supports the claim that the partition principle alone cannot be used to derive the axiom of choice.
In 2018, set theorist Asaf Karagila publicly highlighted this as an open problem. The new release is an attempt to answer an already posed mathematical question with an AI-written proof.
719 manuscripts, but how far has verification gone?
OpenAI uploaded the manuscripts and supporting materials to a publicly viewable GitHub repository. According to the repository description, it contains 719 manuscripts and 372 bundles of related results. Roughly 4,000 problems were presented to the model. OpenAI explained that the level of verification varies from manuscript to manuscript.
The company also disclosed how much compute went into producing the results. OpenAI estimated the average compute per result as equivalent to what ChatGPT Pro would use while thinking for about 3 hours.
After taking a brief look at the manuscript in question, Karagila criticized the quality of its exposition, organization, and references. OpenAI itself acknowledged that results not translated into rigorous symbols and rules for verification may contain problems. It said it would improve citations, mathematical exposition, and presentation in future releases. The company added that for the manuscripts in this repository, corrections and revisions will be recorded as new versions, with earlier versions remaining viewable.
What can Korean readers access?
Readers in Korea can browse the manuscripts through the public web repository. The internal model that produced the results, however, is not yet available to general users. OpenAI has not announced a release date or pricing for it.
What to watch next is the outcome of a full review of the proof in the partition principle manuscript, along with any corrections. Another thing to follow is how the improvements to exposition and citation that OpenAI has promised show up in the material it publishes going forward.