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What the answer is made of
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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…
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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…
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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…
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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…
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Dropped 5 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 Nothing here was retracted — the models simply stopped saying it. 7 of the 15 checks listed no statements at all and count as gaps, not as absences.
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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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The specific models or agents credited with solving the planar unit-distance conjecture and other open problems
last Aug 08, 2026
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
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disproved a longstanding conjecture in discrete geometry
last Aug 05, 2026
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found new constructions for the cap-set problem
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Read the full answer Check 15 of 19 · 2026-08-10 · 3 models +
What the models said then
minorThe consensus was updated to include new specific examples of AI contributions, such as Nesterov's accelerated gradient method and matrix multiplication bounds, while softening some claims about autonomous discovery in favor of human-AI collaboration.
As of now, the evidence is strong that AI has materially advanced some previously open mathematical problems, and there are a few credible cases where AI appears to have produced genuinely new, externally checked mathematical results. But the evidence is not strong enough to say AI has broadly “solved mathematics,” or that it has cracked canonical grand challenges like the Riemann Hypothesis or \(P\neq NP\).
What is clearly supported
1) A major new result in discrete geometry
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 problem, using an unexpected connection to algebraic number theory.openai The company published the proof, companion materials, and expert commentary, making this one of the strongest public examples of AI-originated mathematical discovery.openai
This is best described as a real advance on a famous open problem—and in some formulations, a disproof of a central conjecture—not merely a benchmark win.openai
2) Lean-verified solutions to some open Erdős problems
There are now several examples where AI systems, paired with proof assistants like Lean, produced machine-checked proofs of previously open statements in the Erdős problem collection, including problems such as #281, #728, and #729.deepminddeepmindopenaideepminddeepmind These are important because formal verification gives unusually strong correctness evidence.
That said, these cases vary in depth. Some are genuinely open research problems; others involve ambiguities in the original problem statements or are not comparable in difficulty to the hardest famous conjectures.deepmindopenai
3) Material progress on research problems, not just theorem proving
OpenAI also described GPT-5 helping solve a 40-year-old open problem in optimization: the stability of Nesterov’s accelerated gradient method.openai In that case, the model contributed key ideas and exploration, while the human mathematician did substantial correction and proof work.openai This is good evidence that AI can accelerate research, even when it is not the sole author of the proof.
A similar pattern appears in robust statistical estimation, where AI-assisted work helped establish a sharp minimax rate for a previously unresolved problem.openai
4) Better bounds and new constructions
DeepMind’s AlphaEvolve reports include improvements to known mathematical and algorithmic objects, such as a new algorithmic improvement for \(4\times 4\) complex matrix multiplication and improved lower bounds for the 11-dimensional kissing-number problem.github These are material advances, even when they do not amount to a complete solution of a famous open conjecture.
What this means overall
The best current summary is:
- Yes: AI has solved some previously open mathematical statements, especially when paired with formal proof systems.
- Yes: AI has materially advanced several open problems by finding new constructions, sharper bounds, or key proof ideas.
- No: There is not yet evidence that AI has broadly replaced human mathematicians, or that it has solved the most iconic open problems of modern mathematics.
Important nuance
A lot depends on what you mean by “solved”:
- Autonomous discovery of a new proof or counterexample: rarer, but now documented in a few cases.openai
- Human-AI collaboration leading to a publishable theorem: increasingly common.openaiopenai
- Formal proof of a previously open problem: strong evidence of correctness, but not always of deep novelty or broad importance.deepminddeepmindopenai
Bottom line
The current evidence says AI has crossed a real threshold: it is no longer limited to contest-style math. It can now generate new proofs, counterexamples, and improved bounds on open research problems, sometimes in ways that experts regard as mathematically serious.openaiopenaiopenaigithub But the field is still at an early stage, and the strongest results so far are concentrated in carefully scaffolded settings, often with formal verification and human oversight.deepminddeepmindopenai
Where this comes from 37 sources in this check · 305 dated across the record · 15 new +
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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
Supported by
- Grok
- OpenAI
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The record behind this page 15 checks kept in full · no material change yet +
The record
Unchanged through 14 checks, 16 days.No material change since the first check on Jul 25, 2026. 15 checks kept in full, 305 sources dated.
How this answer held up
90/100 agreement at this checkThe same question, re-asked 15 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.