Hales: a proof of the Kepler conjecture

What changed

A long-standing sphere-packing conjecture received a published proof.

Scientific scope

Hales's exact 2005 article and cited proof resources; Ferguson thesis components and later Flyspeck separate.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is Hales’s exact 2005 Annals paper and associated proof package. Kepler’s conjecture, Fejes Tóth’s reductions, Samuel Ferguson’s separately authored thesis components, later Flyspeck formal verification and higher-dimensional sphere packing remain separate.

Contributors

• Thomas C. Hales · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Annals of Mathematics, A proof of the Kepler conjecture
• Hales, A proof of the Kepler conjecture full paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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