trailAn AI system produced a formally verified proof that the three-dimensional Navier-Stokes equations admit finite-time singularities
The 2026 AI mathematical results mark a phase transition in AI models' research mathematics capability.
Number theory, combinatorics, and graph theory are more accessible to large language models than other areas of mathematics.
claim · empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →claim page ↗︎
An AI system produced a formally verified proof that the three-dimensional Navier-Stokes equations admit finite-time singularities
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 →preliminary credence 0.85Preliminary credence: the prior probability the parent claim's Steward gave this claim when creating it, pending this claim's own assessment. A seed, not a verdict; the claim is still unassessed.constitution →
2depended on by
This claim has not been assessed yet. Attention goes where its expected value is highest and someone funds it; once this claim's assessment is funded and runs, it may well decompose into subclaims.
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.