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ShowingImportancePrizesTopicWang–Zahl method
The method of Hong Wang and Joshua Zahl proving the Kakeya set conjecture in three dimensions (2025), combining induction on scales with structure theory of tube configurations. Claims about the proof's ingredients, validity, or its extension to higher dimensions and related problems belong here; general Kakeya conjecture claims that do not turn on this method do not.
Any counterexample to the three-dimensional Kakeya conjecture must be a grainy set.
SupportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Kakeya conjectureHarmonic analysisimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Extending the Wang–Zahl method to Kakeya in dimensions four and higher faces primarily technical rather than fundamental obstacles.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Kakeya conjectureHarmonic analysisimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The proof of the three-dimensional Kakeya conjecture is a once-in-a-century mathematical result.
SupportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →evaluativeA judgment of worth or quality against some standard: good, fair, effective.constitution →Kakeya conjectureHarmonic analysisimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
A small-volume union of tubes in R^3 whose points lie in tubes pointing in three quantitatively different directions clusters into rectangular slabs (grains) at an intermediate scale.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Harmonic analysisKakeya conjectureimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The mathematical community accepts the Wang–Zahl proof of the three-dimensional Kakeya conjecture as correct.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Kakeya conjectureMathematicsHarmonic analysisimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Hong Wang and Joshua Zahl posted an arXiv preprint in February 2025 claiming a proof of the three-dimensional Kakeya set conjecture.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Kakeya conjectureHarmonic analysisimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
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