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What the answer is made of
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2Still in the answer, stated differently by different models. Open a row to read each position and who holds it.
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AI has assisted in solving the Jacobian conjecture, a major open problem in algebraic geometry
1/2
AI assisted in solving the Jacobian conjecture
- Gemini
The strongest evidence is the unit-distance conjecture, not the Jacobian conjecture
- OpenAI
Split
AI has solved multiple additional specific conjectures beyond the unit-distance and Erdős #728 cases
1/2
AI has solved several other specific conjectures like the Dinitz-Garg-Goemans and primitive set conjectures
- Gemini
Other results are more modest and less central
- Grok
Read the full answer Check 2 of 19 · 2026-07-27 · 3 models +
What the models said then
stableThe core conclusion remains that AI has solved or materially advanced some open mathematical problems but has not achieved broad general breakthroughs. Differences are in wording and emphasis, not in substantive claims.
Yes—there is now credible live evidence that AI has materially advanced mathematics and, in a few cases, appears to have solved previously open research problems. The strongest evidence is still selective and often hybrid (AI + human verification), but it is no longer limited to olympiad-style benchmarks.
Short answer
AI has clearly crossed three thresholds:
- Elite contest performance on problems like the IMO, showing strong mathematical reasoning.openaiarxiv
- Research-level contributions, including novel proofs and counterexamples on problems that were previously open.arxivarxiverdosproblems
- Machine-checked correctness in some cases, especially where Lean formalization is available.arxiverdosproblems
What it has not yet demonstrated is reliable, fully autonomous resolution of the hardest famous open problems, such as the Millennium Prize problems.
The strongest current evidence
1) A long-standing discrete-geometry conjecture was disproved
OpenAI reported that an internal reasoning model produced a proof/disproof of a central Erdős unit-distance conjecture in discrete geometry.arxiv This was an 80-year-old problem, and the result was externally checked by mathematicians; a companion paper then gave a human-readable account and sharpened the quantitative bound.arxivarxiv
Why this matters:
- it is not just solving a benchmark;
- it overturns a genuine open conjecture;
- and it appears to have been driven by AI-generated ideas rather than simple retrieval.arxivarxiv
This is the clearest current example of AI making a real research-level breakthrough.
2) Lean-verified solutions to open Erdős problems
There are also reports of AI systems generating proofs for open problems in the Erdős collection, with some formalized in Lean.arxiv One example is Erdős Problem #728, where a paper describes an AI-generated proof that was formalized and checked in Lean.arxiv
This is important because formal verification gives strong correctness evidence. The caveat is that some of these problems are less mathematically central than the unit-distance conjecture, so they are better described as genuine but modest open-problem resolutions.arxiv
3) Additional research-level progress in commutative algebra and related areas
Recent preprints describe AI systems generating and verifying solutions to several open problems in commutative algebra and related fields, including at least one result formalized in Lean 4.arxivarxiv These are credible signs that AI can now contribute to actual research, not just classroom or contest mathematics.
4) Broader large-scale formal proof search
A separate line of work reports formal-proof agents solving multiple open Erdős problems and many OEIS conjectures in batch mode.arxiv This suggests growing capability, but the headline counts should be interpreted cautiously because:
- “open” covers problems of very different difficulty,
- some may be low-hanging or ambiguously stated,
- and formal correctness does not automatically imply major mathematical significance.arxiv
Important caveats
- Human checking still matters. In the strongest cases, mathematicians reviewed, clarified, or re-expressed the arguments.arxivarxiv
- Not all “open” problems are equally important. Some database-listed problems are obscure or lightly stated rather than deep frontier questions.arxivarxiv
- Contest success is not the same as research success. IMO-level performance is impressive, but it is a different category from resolving an open conjecture.openaiarxiv
- No evidence yet of a general theorem-solving machine. The successes are real but uneven, and they do not show that AI can consistently solve arbitrary hard mathematics.
Bottom line
The current evidence supports this conclusion:
AI has materially advanced mathematics and has likely solved a small number of previously open research problems, including at least one major open conjecture in discrete geometry.arxivarxiv
But these successes remain selective, heavily verified, and not yet broadly general.
If you want, I can also give you a chronological timeline of the best-documented cases or a table separating contest results from genuine research breakthroughs.
Where this comes from 30 sources in this check · 58 dated across the record · 23 new +
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Sources that left the record (28)
A source dropping out is part of the record too: it carried an earlier version of this answer and is not part of the current one. The models re-run their own web search on every check, so single links come and go. The 8 most recently dropped are shown here, dated to their last appearance.
Every position, model by model Direction Shift 0/100 · Stable +
Where the models actually split
Each question keeps its own dimensions. Ask one model and you get one of these positions with no sign that the others exist.
AI has assisted in solving the Jacobian conjecture, a major open problem in algebraic geometry
AI assisted in solving the Jacobian conjecture
- Gemini
The strongest evidence is the unit-distance conjecture, not the Jacobian conjecture
- OpenAI
AI has solved multiple additional specific conjectures beyond the unit-distance and Erdős #728 cases
AI has solved several other specific conjectures like the Dinitz-Garg-Goemans and primitive set conjectures
- Gemini
Other results are more modest and less central
- Grok
| Model | Jul 25 | Jul 27 |
|---|---|---|
| OpenAI | ||
| Gemini | ||
| Grok |
The record behind this page 2 checks kept in full · no material change yet +
The record
Unchanged through 1 check, 2 days.No material change since the first check on Jul 25, 2026. 2 checks kept in full, 58 sources dated.
How this answer held up
37/100 agreement at this checkThe same question, re-asked 2 times. The score moves between a small set of grading levels, so read the steps as levels, not as measurements.
No check in this window was graded a material change. The steps in the curve are wording-level differences between two answers that say the same thing.