The answer, statement by statement
What the answer is made of
Restated check after check
2The load-bearing part of this answer. The longest unbroken run on this Topic stands at 1 check.
Settled
found new constructions for the cap-set problem
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Settled
disproved a longstanding conjecture in discrete geometry
1/7
Entered the record recently
3First stated within the last 3 checks — the least tested part of this answer.
New
The specific nature and origin of other major open problem breakthroughs besides the Erdős conjecture.
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Model B claims breakthroughs include the Jacobian conjecture via Levent Alpöge and Anthropic's Claude, and AlphaProof Nexus solving 9 out of 353 open Erdős problems.
- Gemini
Model A and Model C focus on DeepMind's Aletheia/Gemini work, FunSearch, and general theorem-proving benchmarks rather than Model B's specific novel claims.
- Grok
- OpenAI
New
or other theorem provers to generate machine-checkable proofs.
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New
The specific models or agents credited with solving the planar unit-distance conjecture and other open problems
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OpenAI’s public claim involved an internal reasoning model disproving the discrete geometry conjecture
- OpenAI
Anthropic's Claude Fable 5 uncovered a counterexample to the Jacobian conjecture
- Gemini
Dropped 2 statements the models stopped making · 13 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 Nothing here was retracted — the models simply stopped saying it. 6 of the 13 checks listed no statements at all and count as gaps, not as absences.
Dropped
AI has materially advanced several previously unsolved mathematical problems
last Aug 01, 2026
Dropped
AlphaProof and AlphaGeometry 2 solved 4 of 6 problems at the 2024 IMO
last Aug 01, 2026
Read the full answer Check 13 of 19 · 2026-08-08 · 3 models +
What the models said then
minorThe new consensus slightly streamlines the presentation, removes some specific citations (like AlphaEvolve and AlphaProof names) in favor of broader categories, introduces an example regarding nonconvex optimization, but maintains the core conclusion that AI has made real contributions to math without broadly solving frontier problems.
As of now, the evidence is strong that AI has materially advanced some previously unsolved mathematical problems, and in a few cases has produced genuinely new mathematical results that were independently checked or formally verified. It is not yet evidence that AI has broadly or routinely solved the hardest flagship open problems of mathematics.
What the current evidence shows
1) AI has produced real advances on open problems
There are now publicly documented cases where AI systems found:
- new constructions that improve known bounds,
- counterexamples that overturn long-held conjectures, and
- proofs formalized in Lean and checked by a theorem prover kernel.openaideepminddeepmind
A particularly important example is OpenAI’s public claim that one of its models disproved a longstanding conjecture in discrete geometry, specifically related to the planar unit-distance problem.openaiopenai That is a genuine mathematical advance, even though it is not the same as solving every aspect of the underlying broader problem.
2) Formal proof systems matter a lot
Some of the strongest evidence comes from results that were not merely “plausible” but were machine-checked in a formal system such as Lean. For example, AI-assisted work has been reported on Erdős problems, including fully formalized proofs for specific open problems.openaideepmind This matters because it sharply reduces the risk of hidden gaps.
3) AI can materially help human mathematicians
There is also evidence of AI acting as a research collaborator: suggesting proof ideas, helping explore cases, and accelerating work that a human expert then verifies and writes up. OpenAI highlighted an example where GPT-5 helped with a roughly 40-year-old open problem in nonconvex optimization, but the human mathematician still did the verification and final mathematical judgment.deepmind That is strong evidence of material assistance, not necessarily autonomous solving.
4) Systems are improving on benchmark-style research tasks
Google DeepMind and others have shown systems that solve competition-level problems and some research-style open problems, especially in areas with strong automated checking or search structure.deepmind These results demonstrate real capability growth, but benchmark success is not the same as settling a major open theorem.
Best current summary
The most accurate summary is:
AI has already helped solve or materially advance several previously unsolved mathematical problems, especially in combinatorics, geometry, number theory, and optimization, but it has not yet broadly conquered the deepest open problems in mathematics.deepmindopenaideepmind
Important caveat
Some public claims about “solving many open problems” are stronger than what is currently independently established. The most reliable evidence is where there is:
- a clear problem statement,
- a public proof or construction,
- formal verification or expert review, and
- an attributable announcement or paper.openaiopenaideepmind
Bottom line
Yes: AI has crossed the line from toy examples into real mathematical research advances.
No: the current evidence does not show that AI has generally solved the hardest open problems of mathematics.
Where this comes from 40 sources in this check · 281 dated across the record · 19 new +
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Sources that left the record (241)
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 — · Not comparable +
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.
The specific models or agents credited with solving the planar unit-distance conjecture and other open problems
OpenAI’s public claim involved an internal reasoning model disproving the discrete geometry conjecture
- OpenAI
Anthropic's Claude Fable 5 uncovered a counterexample to the Jacobian conjecture
- Gemini
| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| OpenAI | |||||||||||||
| Gemini | |||||||||||||
| Grok | — | — | — |
The record behind this page 13 checks kept in full · no material change yet +
The record
Unchanged through 12 checks, 14 days.No material change since the first check on Jul 25, 2026. 13 checks kept in full, 281 sources dated.
How this answer held up
64/100 agreement at this checkThe same question, re-asked 13 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.