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AI findings from OpenAI

Every finding in the registry credited to OpenAI, with what each one claims and how solid the evidence is.

By verification grade

11 of 28 carry an independent check. Open the review queue.

Open longest before falling

  1. 177 yrPrime gaps at most 186, conditional on three unproved Lean axiomsposed 1849 · GPT-6 Astra
  2. 167 yrQuasi-Riemann hypothesis: no zeros of zeta or any Dirichlet L-function with real part above 7/8posed 1859 · Unreleased internal OpenAI model, not named in the release
  3. 99 yrArtin's primitive root conjecture: infinitely many primes for every admissible baseposed 1927 · Unreleased internal OpenAI model, not named in the release
  4. 96 yrLean disproof of Krempa's matrix form of the Koethe conjectureposed 1930 · GPT-6 Astra (pre-release)

From the 17 of 28 entries recording a posed year. Add a missing one.

All findings in the registry, sortable by column.
DateFindingLabModelVerificationAutonomyField
2026-10-26 A subexponential counting algorithm for fixed-width CNF, refuting the Exponential Time Hypothesis OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led computer-science
2026-10-26 Sogge's local smoothing conjecture claimed in every dimension, with Bochner–Riesz and Kakeya as consequences OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 719 manuscripts in 372 result families from an unreleased OpenAI model OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Quasi-Riemann hypothesis: no zeros of zeta or any Dirichlet L-function with real part above 7/8 OpenAI Unreleased internal OpenAI model, not named in the release Claimed Collaborative mathematics
2026-10-06 Kakeya maximal conjecture in three dimensions and the Kakeya set conjecture in four OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Counterexample to the Borel conjecture in dimension four OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Artin's primitive root conjecture: infinitely many primes for every admissible base OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Modularity of every elliptic curve over every imaginary quadratic field OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Negative answer to the hyperinvariant subspace problem on Hilbert space OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Massive continuum limit of the two-dimensional O(3) model OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Proof of Barnette's conjecture on Hamiltonian cycles in cubic bipartite planar graphs OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Shelah's eventual categoricity conjecture for abstract elementary classes OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led mathematics
2026-10-06 Matrix multiplication exponent bounded by 9/4 OpenAI Unreleased internal OpenAI model, not named in the release Formally verified AI-led computer-science
2026-10-06 Integer multiplication below n log n, against the Schönhage–Strassen optimality conjecture OpenAI Unreleased internal OpenAI model, not named in the release Claimed AI-led computer-science
2026-09-08 Finite-time blowup for Navier-Stokes with smooth forcing, Clay alternatives C and D OpenAI Unnamed OpenAI model described as more capable than GPT-6 Astra for the proof; GPT-6 Astra through Codex for the Lean formalization Claimed AI-led mathematics
2026-09-08 Finite-time blowup for the unforced Euler equations from smooth compactly supported data OpenAI Unnamed OpenAI model described as more capable than GPT-6 Astra for the proof; GPT-6 Astra through Codex for the Lean formalization Claimed AI-led mathematics
2026-09-05 Disproof of the Ibragimov-Iosifescu conjecture for phi-mixing sequences OpenAI / Epoch AI GPT-6 Astra (pre-release) Claimed AI-led mathematics
2026-09-03 Lean disproof of Krempa's matrix form of the Koethe conjecture OpenAI / Epoch AI GPT-6 Astra (pre-release) Formally verified Autonomous mathematics
2026-09-03 Erdos-Sos conjecture proved in Lean, in a form marginally weaker than the classical statement OpenAI / Epoch AI GPT-6 Astra (pre-release) Formally verified Autonomous mathematics
2026-09-03 Counterexample to Smale's mean value conjecture at K = 1 OpenAI / Epoch AI GPT-6 Astra (pre-release) Formally verified Autonomous mathematics
2026-09-02 Prime gaps at most 186, conditional on three unproved Lean axioms OpenAI GPT-6 Astra Claimed AI-led mathematics
2026-08-01 Ten results in mathematics and theoretical computer science with Lean certificates OpenAI Astra Formally verified AI-led mathematics
2026-07-10 Cycle double cover conjecture proved for all bridgeless multigraphs OpenAI GPT-5.6 Sol Ultra Formally verified AI-led mathematics
2026-05-20 Disproof of the Erdős unit-distance conjecture OpenAI GPT-5 series reasoning model Independently checked AI-led mathematics
2026-01-13 Erdős problem #728 resolved and formalized in Lean OpenAI / Harmonic GPT-5.2 Pro + Aristotle Formally verified Autonomous mathematics
2025-11-20 Early science acceleration experiments with GPT-5 OpenAI GPT-5 Peer reviewed AI-assisted computer-science
2025-10-19 GPT-5 "solved 10 Erdős problems": it located existing solutions OpenAI GPT-5 Already known Retrieval mathematics
2025-08-01 Improved step-size bound in smooth convex optimization OpenAI GPT-5 Pro Already known AI-assisted mathematics

← The whole registry