AI has solved dozens of obscure Erdős problems, but only 3 of 68 major ones under strict rules
Counting every effort, AI has solved 17 of 68 major open Erdős problems. Under Epoch AI's strict test rules, the best model solves 3.
Open research problems solved by AI (FrontierMath Erdős)
Share of 68 significant open Erdős problems a model solves with a machine-checked proof, in one attempt with a ~$300 budget.
What this measures: Unlike exam-style tests, nobody knew the answers to these problems when the test was made. A model only scores if the Lean proof checker accepts its proof or disproof.
Plotted at model release dates (the benchmark launched 1 September 2026, so earlier models were evaluated retroactively). Outside the official one-attempt rules, 17 of the 68 problems have now been solved by some means, including 12 credited to OpenAI's 6 October research release. Contamination risk grows as solutions are published.
Show data table and sources
| Date | Label | Value |
|---|---|---|
| 23 Apr 2026 | GPT-5.5 | 0% |
| 3 Sept 2026 | GPT-6 Astra (pre-release) | 2.9% |
| 29 Sept 2026 | GPT-6.1 Sol | 4.4% |
- Announcing FrontierMath Erdős (Epoch AI)
- FrontierMath Erdős benchmark page (Epoch AI)
- Epoch AI benchmark data (CSV export) (Epoch AI)
Erdős problems with a computer-checked solution
Problems in the community Erdős problems database whose solution has been formalized in the Lean proof checker, at the end of each month.
What this measures: Paul Erdős left behind more than a thousand math problems. This counts how many have a solution that the Lean proof checker has verified step by step, whether the proof came from a human or an AI.
Counts solutions from any source, human or AI, so this is not a count of AI solutions. Early growth partly reflects the database being built. The sources don't explain the August 2026 jump. Since 6 October 2026 erdosproblems.com no longer shows solved counts, and the 12 FrontierMath Erdős problems Epoch AI credits to OpenAI's 6 October release are not yet included. Each point is the last row of its month in the database's statistics_history.csv.
Show data table and sources
| Date | Label | Value |
|---|---|---|
| 30 Sept 2025 | 3 problems | |
| 31 Dec 2025 | 38 problems | |
| 31 Jan 2026 | 69 problems | |
| 28 Feb 2026 | 110 problems | |
| 31 Mar 2026 | 124 problems | |
| 30 Apr 2026 | 167 problems | |
| 31 May 2026 | 186 problems | |
| 30 Jun 2026 | 199 problems | |
| 31 Jul 2026 | 207 problems | |
| 31 Aug 2026 | 292 problems | |
| 28 Sept 2026 | 317 problems | |
| 29 Oct 2026 | 318 problems | |
| 6 Nov 2026 | 318 problems |
- teorth/erdosproblems statistics_history.csv (Erdős problems community database (Tao et al.))
- teorth/erdosproblems STATISTICS.md (Erdős problems community database)
Paul Erdős left more than a thousand maths problems of widely varying difficulty, which makes them a natural yardstick for AI. In January 2026, Problem #728 became the first widely regarded as solved by AI on its own (GPT-5.2 Pro, with Harmonic’s Aristotle writing the proof in Lean, a format a computer can check). By June 2026, Terence Tao’s community wiki listed 19 full solutions by AI alone, 37 by AI working with people, and 10 incorrect AI claims. Tao cautioned that only about 1–2% of open Erdős problems are simple enough for current AI with little human help, and that failures go unreported.
To measure the hard end, Epoch AI launched FrontierMath Erdős on 1 September 2026: 68 significant problems still open in August 2026, picked by Thomas Bloom, who runs erdosproblems.com. A model scores only with a computer-checked proof or disproof, in one attempt, within $300 and 72 hours. GPT-6.1 Sol leads with 3 of 68 (4.4%).
Outside those rules the count is higher. With a budget of over $220,000, against about $20,000 for its official run, GPT-6 Astra solved 5 of the problems at least once. OpenAI’s 6 October research release solved 12 more, so 17 of the 68 are now solved by some means. In August 2026, Bloom estimated that AI had solved only 3–5 problems of this calibre.
The chart tracks a broader count: problems whose solution, by a human or an AI, has been checked in Lean. It rose from 3 in September 2025 to 318 in November 2026.
What it means
AI is now a real help on the easier open maths problems, and it has cracked some hard ones. On the problems experts consider most significant, the best model still solves only 3 of 68 under strict test conditions. When you read that AI “solved an Erdős problem”, it helps to ask which kind, and under what rules.
Caveats
- Easy or obscure problems are over-represented among AI successes, and several “AI-solved” problems turned out to have prior solutions in the literature.
- The wiki’s counts are table rows, not unique problems, and it is no longer updated.
- Models released after mid-2026 may have seen published solutions; Epoch says the evaluated models’ training cutoffs predate them. That contamination risk will grow as solutions are published.
- Epoch’s list of solutions found outside its official runs is updated by hand and may be incomplete.
- The Lean chart counts formalised solutions of any origin, not only AI ones, and does not yet include the problems credited to OpenAI’s October release.