The answer, statement by statement
What the answer is made of
Restated check after check
1The load-bearing part of this answer. The longest unbroken run on this Topic stands at 2 checks.
Settled
OpenAI announced that an internal reasoning model disproved the Erdős unit-distance conjecture in planar discrete geometry, by constructing configurations with asymptotically m…
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Entered the record recently
4First stated within the last 3 checks — the least tested part of this answer.
New
Anthropic's model disproved the Jacobian conjecture and advanced the Riemann hypothesis range.
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Reports that Anthropic models advanced the Riemann hypothesis bounds and found an explicit counterexample disproving the Jacobian conjecture.
- DeepSeek
- Grok
Makes no mention of Anthropic's Jacobian or Riemann claims.
- Gemini
- OpenAI
New
The current evidence supports a qualified yes: AI has solved some previously open mathematical problems and has materially advanced others, but the strongest claims sti…
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This is one of the clearest public examples of AI contributing a genuine new result on a recognized open problem.
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it was a real research problem, not a benchmark;
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Dropped 5 statements the models stopped making · 17 one-off phrasings left out +
Stated in more than one earlier check, absent from this one. Nothing here was retracted — the models simply stopped saying it. 9 of the 18 checks listed no statements at all and count as gaps, not as absences.
Dropped
Which specific AI system or company solved or reported the Erdős unit distance problem and other open problems
last Aug 11, 2026
OpenAI announced an internal model produced a construction disproving the Erdős unit-distance conjecture
- OpenAI
- Grok
Google DeepMind's AlphaProof Nexus framework solved open Erdős problems
- Gemini
Dropped
AI has materially advanced several previously unsolved mathematical problems
last Aug 01, 2026
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AlphaProof and AlphaGeometry 2 solved 4 of 6 problems at the 2024 IMO
last Aug 01, 2026
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disproved a longstanding conjecture in discrete geometry
last Aug 05, 2026
Dropped
found new constructions for the cap-set problem
last Aug 05, 2026
Read the full answer Check 18 of 19 · 2026-08-26 · 4 models +
What the models said then
stableThe response was streamlined with minor rephrasing and formatting adjustments, but the core conclusions, specific examples (e.g., Erdős unit-distance conjecture disproof, Lean formal verification), and qualifications remain the same.
As of August 2026, there is credible evidence that AI has materially advanced previously unsolved mathematics, and in a few cases appears to have solved specific open problems. The strongest evidence comes from primary announcements with formal artifacts, external mathematician review, and machine-checkable proofs.openaiopenaiopenai
What the evidence currently supports
1) A real open problem was apparently disproved by AI
The clearest case is OpenAI’s announcement that an internal reasoning model produced a counterexample to the Erdős unit-distance conjecture (a long-open discrete-geometry problem). OpenAI says the result was checked by external mathematicians and accompanied by a human-written companion paper.openai If that result holds up in the normal mathematical sense, it is genuine evidence that AI can do more than solve toy problems.
2) AI systems have produced formally verified proofs of open problems
There are also reports of AI systems working with Lean or similar theorem provers to generate machine-checkable proofs of previously open Erdős-style problems and related conjectures.openaiopenai This matters because formal verification reduces the risk of hidden reasoning errors.
3) AI has materially advanced several open problems without fully solving them
Even where the final theorem is not a complete resolution, AI has produced:
- new constructions
- improved bounds
- counterexamples to conjectures
- new algorithmic parameters
- and in some cases research-level proof contributions.openaiopenai
That kind of progress is mathematically meaningful, even if it is not a full solution.
What is most important to keep in mind
The evidence is strongest in areas where results can be checked automatically or where one counterexample settles the issue, such as combinatorics, discrete geometry, graph theory, and some algebraic or optimization problems.openaiopenai
It is not evidence that AI has solved the hardest remaining prize problems, such as the Riemann hypothesis or Navier–Stokes. Those remain open, and current successes do not show that AI can reliably handle arbitrary deep mathematical research end to end.
Best current bottom line
The current state of evidence is:
- Yes: AI has materially advanced previously unsolved mathematical problems, in some cases substantially.
- Probably yes, in a few cases: AI has actually solved or refuted specific open problems, with the OpenAI unit-distance result being the most prominent example.openai
- No, not yet: there is no solid evidence that AI can reliably solve major open mathematics across the board.
If you want, I can next turn this into a short table of the strongest examples and what kind of evidence supports each one.
Where this comes from 50 sources in this check · 366 dated across the record · 33 new +
Best available sources
Show 45 more sources
Sources that left the record (316)
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.
Anthropic's model disproved the Jacobian conjecture and advanced the Riemann hypothesis range.
Reports that Anthropic models advanced the Riemann hypothesis bounds and found an explicit counterexample disproving the Jacobian conjecture.
- DeepSeek
- Grok
Makes no mention of Anthropic's Jacobian or Riemann claims.
- Gemini
- OpenAI
| Model | Jul 25 | Jul 27 | Jul 29 | Jul 30 | Jul 31 | Aug 01 | Aug 02 | Aug 03 | Aug 04 | Aug 05 | Aug 06 | Aug 07 | Aug 08 | Aug 09 | Aug 10 | Aug 11 | Aug 19 | Aug 26 |
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| OpenAI | ||||||||||||||||||
| Gemini | — | |||||||||||||||||
| Grok | — | — | — | |||||||||||||||
| DeepSeek | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — | — |
The record behind this page 18 checks kept in full · no material change yet +
The record
Unchanged through 17 checks, 31 days.No material change since the first check on Jul 25, 2026. 18 checks kept in full, 366 sources dated.
How this answer held up
84/100 agreement at this checkThe same question, re-asked 18 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.