[UPDATE] Mathematicians Say OpenAI's Astra Proofs Recycle Their Work

A week ago OpenAI said its research-stage system Astra had cracked ten mathematics and theoretical computer science problems that had gone unsolved for years, a claim we reported at the time. Now several of the mathematicians whose fields were touched say the proofs lean on their own earlier work without crediting it.

The sharpest complaint comes from Steven Miller, a mathematician at Yeshiva University, who says Astra's sphere-packing result reuses the central argument from a 2016 paper of his and does not cite it. He does not treat it as an honest oversight. As Scientific American reported, Miller argues the work amounts to plagiarism of his research. Francesco Fournier-Facio, a mathematician at Cambridge, points to a second result on non-sofic groups and says its key step stitches together ideas from papers published in 2016 and 2019, again without attribution.

A question of process, not just credit

The dispute is partly about attribution and partly about how the results reached the public. OpenAI cited the Leiden Declaration on responsible disclosure to explain why it went public, then published the proofs in a company blog post rather than through peer review, which is close to the practice that declaration warns against. Reviewers are the people who would normally catch a missing citation before a result is announced to the world.

OpenAI's original framing has also softened. Its first statement said the problems had seen no progress on the main result for at least a decade. The company has since edited that language to be more accurate, an acknowledgment that some of the ground was not as untouched as the announcement implied.

None of this proves the underlying mathematics is wrong. Formal proof checkers can confirm that a chain of logic holds while saying nothing about whether it is original, and that is the gap the mathematicians are pointing at. A machine can assemble a valid argument out of published ideas and present it as new, because it has no sense of who did the work first.

The episode lands on a familiar question. Solving a hard problem and understanding a field are not the same thing, a distinction we looked at separately. This is the second time in under a year that OpenAI has claimed a mathematical advance outside peer review and drawn objections from the researchers involved. For a discipline that runs on citation, that is the part worth watching.