OpenAI publishes 722 math manuscripts grouped into 372 families
OpenAI's public math repository contains 722 manuscripts organized into 372 families of related papers, which may include companion arguments, consequences, or alternative proofs. The README says the vast majority were produced using an unreleased internal model; results are at different stages of verification, many but not all are formalized in Lean, and some unformalized work could have issues. It reports an evaluation of approximately 4,000 problems and average compute equivalent to roughly three hours of ChatGPT Pro thinking per result.
The record ends here. Everything below this line is invented.
What if one theorem had several proofs, but a single family label hid who wrote them?
Part one
The Family Count
At the proof room's opening bell, Nara clipped a blue thread between two theorem cards and watched the result map group them. Four manuscripts, one result family: a main proof, a consequence, and two alternate routes through the same claim.
Her younger sister Sol had submitted a fifth proof overnight. The institute's fellowship panel would use Nara's mathematical review at noon; if Sol's work was marked a duplicate, it could vanish from the portfolio that got her into the room.
The result concerned a network of mirrored tiles. Each edge either flipped the arrow on a traveling bead or left it alone. In a closed loop, Sol's proof said, the flips had to come in even pairs for the bead to return facing the same way.
Nara believed the family label meant the proof paths were interchangeable. She pulled one machine manuscript beside Sol's. Its diagram began at a different tile, but its last line matched.
"Same result," Nara said, and the blue thread tightened around the cards. A result family could contain multiple proofs of one claim. On the wall, four grey paths met at one theorem. Sol's blue path reached the same knot by a route the archive could not flatten.
What’s real
- OpenAI reported 722 manuscripts across 372 result families.
- Families may group companion arguments and alternative proofs.
- Many, but not all, manuscripts have Lean formalizations.
What’s invented
- Nara, Sol, and the archive are fictional.
- The mirrored-tile parity theorem is invented for the story.
- The fellowship metric and archive's blue thread are invented.
Part two: Two Paths, One Family
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Filed under technology, mathematics, ai research, proofs.