The answer, statement by statement
What the answer is made of
Entered the record recently
5First stated within the last 3 checks — the least tested part of this answer.
New
Which specific AI system or company solved or reported the Erdős unit distance problem and other open problems
0/8
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
New
Lean-checked proofs of open problems: systems combining LLMs with formal proof assistants have produced machine-verified proofs of some open Erdős problems and related conjectu…
1/8
New
OpenAI announced in May 2026 that an internal model produced a construction violating the conjectured near-linear growth of unit distances among (n) planar points, yielding a low…
1/8
New
OpenAI reported that an internal reasoning model found a new family of point configurations that disproves a long-standing conjectural picture around the Erdős unit-distance pr…
0/8
New
The current evidence is that AI has materially advanced several previously open mathematical problems, and in a few cases may have solved them in a credible, externally che…
1/8
Dropped 4 statements the models stopped making · 15 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 Nothing here was retracted — the models simply stopped saying it. 8 of the 16 checks listed no statements at all and count as gaps, not as absences.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
Dropped
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 16 of 19 · 2026-08-11 · 3 models +
What the models said then
stableThe consensus answers are substantively very similar, both concluding that AI has made material advances on research-level math and solved some open problems (like Erdős-related and geometry problems) but has not broadly solved mathematics or major millennial problems. The differences are purely structural and wording-based.
The current evidence is yes, but narrowly and with important caveats: AI has materially advanced several previously open mathematical problems, and in a small number of cases it has produced results that appear to resolve long-standing open conjectures, especially in discrete geometry and some algebra/combinatorics settings.openaiopenaiopenai
What the evidence is strongest for
1) A major discrete-geometry breakthrough
The clearest recent case is OpenAI’s reported AI-generated counterexample to a long-standing conjecture in the planar unit-distance problem, a conjecture associated with Erdős.openaiopenai OpenAI published a detailed write-up and supporting materials, and the result was publicly discussed by outside mathematicians.openaiopenai This is strong evidence that AI can now produce genuinely novel mathematical constructions, not just contest-style solutions.
2) Formal-proof-search systems solving open problems in restricted domains
There is also evidence from systems that combine search with proof assistants like Lean. A recent arXiv report describes an AI-driven formal proof-search system that resolved 9 of 353 Erdős problems in its evaluation set and 44 of 492 OEIS conjectures, with Lean verification.openai Because Lean mechanically checks the proof, this is stronger evidence than an unverified natural-language argument.openai
3) Additional open-problem advances in algebra and combinatorics
Another recent preprint reports open problems in commutative algebra being resolved by an automated system, again with subsequent checking and some formalization.openai There are also examples where AI supplied the key idea and humans finished the proof, which still counts as a material advance even if not a fully autonomous solution.openaideepmind
What this does not yet show
This evidence does not mean AI has solved mathematics broadly or defeated major canonical problems such as the Riemann Hypothesis, P vs NP, Navier–Stokes existence/smoothness, or the remaining Millennium Prize Problems. The best-documented successes are concentrated in areas where:
- the problems are highly structured,
- search is feasible,
- formal verification is available,
- and the result can be checked mechanically or by expert review.openaiarxiv
A careful summary
The most accurate current summary is:
AI has crossed from benchmark performance into research-level mathematics. It has materially advanced many open problems and appears to have resolved a small number of previously open conjectures, but it is not yet a general-purpose autonomous mathematician.
Important caveat
There is also a substantial amount of overclaiming in this area. Some public “AI solutions” later turned out to be rediscoveries of known results, partial results, or proofs with gaps, which is why formal verification and independent checking matter so much.arxiv
If you want, I can next turn this into a short table of the strongest documented cases, with each result, status, and source.
Where this comes from 36 sources in this check · 320 dated across the record · 15 new +
Best available sources
Show 31 more sources
Sources that left the record (284)
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.
Which specific AI system or company solved or reported the Erdős unit distance problem and other open problems
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
| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| OpenAI | ||||||||||||||||
| Gemini | — | |||||||||||||||
| Grok | — | — | — |
The record behind this page 16 checks kept in full · no material change yet +
The record
Unchanged through 15 checks, 17 days.No material change since the first check on Jul 25, 2026. 16 checks kept in full, 320 sources dated.
How this answer held up
22/100 agreement at this checkThe same question, re-asked 16 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.