trailFrontier AI models produce novel mathematical results through reasoning comparable to a human mathematician's rather than brute-force search
An AI model that generates a verified mathematical result under human direction merits primary discovery credit
Transcript evidence of goal-directed reasoning· for
OpenAI's disproof of the Erdős unit distance conjecture was generated in a single model run without human mathematical intervention
The prompt OpenAI gave its model for the unit distance problem contained no hints toward a counterexample or number-field methods.
OpenAI researchers first examined the model's unit distance proof only after an automated grading pipeline had rated it correct
Published chain-of-thought records of AI mathematical discoveries show goal-directed strategy rather than exhaustive enumeration
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Search at scale and the undisclosed denominator· against
AI labs do not disclose how many failed attempts precede their announced mathematical results
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OpenAI's Navier-Stokes singularity proof was produced by roughly 10,000 autonomous AI agents running for about 88 hours
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Levent Alpöge defined and steered the 2026 Jacobian counterexample search, with Claude Fable 5 generating candidates
The 2026 Jacobian conjecture counterexample could have been obtained from Claude Fable 5 with a single simple prompt
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Akhil Mathew suggested the Jacobian conjecture to Levent Alpöge before the 2026 counterexample was found
Claude Fable 5 generated the polynomial map used as the 2026 Jacobian conjecture counterexample
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A third explanation: breadth and patience· against
AI models' mathematical advantage over human mathematicians comes from encyclopedic knowledge and patience rather than deeper insight
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Current AI systems' mathematical successes come mainly from applying known techniques to neglected problems
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assumed
Reasoning and search are meaningfully distinct modes of problem solving in large language models
assumed
AI language models can find counterexamples to long-standing open mathematical conjectures.
bedrock · value premise
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Frontier AI models produce novel mathematical results through reasoning comparable to a human mathematician's rather than brute-force search
⇄ContestedCredible evidence or argument exists on multiple sides.constitution →
1depended on by
this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →↑supportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →⇄contestedCredible evidence or argument exists on multiple sides.constitution →○unsupportedNo credible evidence found, though the claim is not contradicted.constitution →✕contradictedAvailable evidence weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →verified factopen questionvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →Fig. Detail falls off with distance; every claim is an address.