Research library
Research problem success
Area: definition. Apply the shared measurement protocol.
Estimated progress toward AI-managed mathematics
25% complete — judgment-based estimate as of November 7, 2026. Confidence: low. This uses the requested scale: 0% is the pre-2022 starting point; 100% means AI manages continuing mathematical progress without human involvement. It is not a measured fraction of all mathematics, a benchmark score, or a forecast of time remaining.
The shared mathematics scoring rubric assigns up to 20 points each for execution, breadth, agenda-setting, validation, and sustained autonomous improvement. This outcome's points are 10 + 5 + 0 + 5 + 5 = 25/100, in that order. Unknown evidence earns no demonstrated-progress credit in the affected component; that does not prove the capability is absent.
Reason for the estimate: The baseline contains accepted open-problem successes, including 3/68 in a fixed-budget evaluation. This is early research capability on selected problems; humans still set agendas and establish significance. The 25% estimate is not the measured problem-solving success rate. Evidence and dated sources are in the baseline below.
What would move the score: Raise the estimate when AI selects worthwhile fresh questions and repeatedly resolves them across branches, within fixed budgets, without human formulation, steering or repair. Reassess downward if replication fails or previously hidden human assistance emerges.
Measurement and acceptance rule
Independently accepted solutions / all preregistered research problems within a fixed time and compute budget. Separate known-answer problems from genuinely open ones.
Evidence requirements
Every result counted as a verified new proof must include a human-readable statement and argument, complete Lean source, dependency versions, build instructions, and reviewer reports. A mathematician must confirm that the formal statement matches the intended theorem and does not introduce stronger assumptions that trivialize it.
Audit transitive axiom dependencies, including #print axioms for the principal results. Reject sorryAx, admitted obligations, custom unproved assumptions used to assume the conclusion, and verification bypasses. Record the permitted foundational axioms; use independent proof rechecking appropriate to the threat model. The Lean validation guidance explains why editor check marks alone are insufficient. Lean verifies formal derivation, while human review establishes meaning, novelty, and significance.
Related milestones
See the area's proposed milestones. Proposed targets are distinct from the dated evidence below.
Baseline as of November 7 2026
Status: positive results on open problems, with measurable but highly benchmark-specific success rates. All sources were checked November 7, 2026; percentages calculated below are simple successes divided by the stated denominator.
Dated findings
| Evidence date | Result | Scope and source |
|---|---|---|
| May 21, 2026 submission; June 8 revision | AlphaProof Nexus: 9/353 Erdős problems, or 2.55%; 44/492 OEIS conjectures, or 8.94%. | Author-reported formal-proof search; the Erdős campaign allowed up to 3,000 episodes per problem. These are different corpora, not interchangeable difficulty levels. Research paper. |
| September 6, 2026 paper | GPT-6 Astra approximately 3%; four other evaluated systems 0%. | Initial FrontierMath Erdős release. Benchmark paper. |
| October 3 runs; ledger updated October 29, 2026 | GPT-6.1 Sol has three official solves, #1, #74, and #126: 3/68 = 4.41%, calculated from the ledger. | One attempt per conjecture, at most $300 and 72 working hours. The same ledger lists 17 resolved entries across all sources, including human/outside work; 17/68 is not a model score. Epoch's dated solution ledger and methodology. |
| November 7, 2026 observation | FrontierMath Open Problems displays 5 AI-only, 5 human-plus-AI, and 39 unsolved entries. | 49 listed entries; the heading still says 50. Its changelog records a removal and attribution-policy changes. Treat these as inventory counts, not a fixed-budget attempt success rate. Epoch Open Problems. |
Interpretation and tracking value
Use 3/68 at the stated Epoch budget as the clearest recent, reproducible-protocol reference in this review. It remains evaluator-reported evidence, not a proof rebuild performed for this repository. Separate the earlier 353-problem campaign and the Open Problems inventory into different series.
These figures do not imply a 4.41% chance of solving an arbitrary research question. Problem selection, existing formal statements, budgets, and publication exposure matter. With only three successes, small count changes produce large relative changes.
Next comparable measurement
Capture task IDs, model release and training cutoff, exact harness, number of attempts, actual spend, timeouts, and accepted proof artifacts. Re-evaluate the same unresolved subset under the same budget; flag problems whose solutions became public before later models' training cutoffs. Preserve full-set historical scores alongside any contamination-filtered comparison.