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What the answer is made of
Entered the record recently
3First stated within the last 3 checks — the least tested part of this answer.
New
A notable open conjecture in discrete geometry was disproved
1/4
New
AI has reached elite competition-level mathematical reasoning
1/4
New
Formal-proof systems are producing machine-checked research outputs
1/4
Read the full answer Check 5 of 19 · 2026-07-31 · 3 models +
What the models said then
stableThe new consensus reformulates the points and incorporates formal Lean-checked proofs and recent IMO milestones, but the core conclusion—that AI has made material advances and disproved at least one major conjecture without broadly solving frontier math—remains the same.
The current evidence shows that AI has materially advanced several previously unsolved or research-level mathematical problems, and in a few cases has settled prominent long-standing conjectures, but it has not broadly automated frontier mathematics or solved the major open Millennium Prize problems.
What is strongest today
1) A notable open conjecture in discrete geometry was disproved
OpenAI announced that a general-purpose reasoning model produced a proof refuting a long-standing conjecture about the planar unit-distance problem, a question posed by Paul Erdős in 1946.openai The result was supported by a formal manuscript, external mathematician review, and later discussion in the Erdős Problems database, which records the conjecture as disproved.openaiopenai This is currently one of the clearest public examples of AI producing a genuinely new result that settles a prominent open mathematical claim.
2) AI has reached elite competition-level mathematical reasoning
DeepMind reported that its systems achieved IMO silver-medal performance in 2024 and gold-medal performance in 2025.openaiopenai That is not the same as solving an open research problem, but it is strong evidence that AI can now generate sophisticated proofs and solve very hard novel problems in a constrained setting.
3) AI has found new constructions, bounds, and proof ideas in active research
There is solid evidence that AI systems have materially advanced mathematics by:
- discovering improved constructions in combinatorics and geometry via FunSearch and related systems,openai
- finding improved matrix-multiplication algorithms via AlphaTensor,deepmind
- helping humans complete proofs of open or long-standing problems, including research work on Erdős problems and other topics.deepminddeepmind
4) Formal-proof systems are producing machine-checked research outputs
Recent preprints and challenge benchmarks show AI systems generating Lean-checked proofs for research-level problems, sometimes with no or limited human intervention.deepminddeepmind This matters because formal verification sharply reduces the risk of hidden errors.
What this does not show
The evidence does not show that AI has solved the major canonical open problems such as the Riemann hypothesis, P vs NP, Navier–Stokes, Hodge, Yang–Mills mass gap, or Birch–Swinnerton-Dyer. The current record is better described as:
- one or more prominent conjectures settled or disproved,
- many smaller but still research-level advances, and
- rapidly improving assistance for human mathematicians,
rather than full autonomous mathematical discovery at the level of the deepest unsolved problems.
Bottom line
AI has clearly moved beyond toy examples and olympiad-style benchmarks. The strongest current evidence is that it has disproved at least one major open conjecture and materially advanced several others, especially when combined with formal verification or human checking.openaiopenaideepmind But it is still early: the most important open problems in mathematics remain unsolved.
Where this comes from 46 sources in this check · 140 dated across the record · 30 new +
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Every position, model by model Direction Shift 0/100 · Stable +
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A notable open conjecture in discrete geometry was disproved
Supported by
- Grok
- Gemini
- OpenAI
AI has reached elite competition-level mathematical reasoning
Supported by
- Grok
- Gemini
- OpenAI
Formal-proof systems are producing machine-checked research outputs
Supported by
- Grok
- Gemini
- OpenAI
| Model | Jul 25 | Jul 27 | Jul 29 | Jul 30 | Jul 31 |
|---|---|---|---|---|---|
| OpenAI | |||||
| Gemini | |||||
| Grok | — |
The record behind this page 5 checks kept in full · no material change yet +
The record
Unchanged through 4 checks, 6 days.No material change since the first check on Jul 25, 2026. 5 checks kept in full, 140 sources dated.
How this answer held up
64/100 agreement at this checkThe same question, re-asked 5 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.