The Four-Color Theorem Gets a Rare New Proof
20 days ago
- The four-color theorem, proven a century after being posed, remains controversial due to reliance on computer proofs.
- Kempe's 1879 proof contained an error, but his color-swapping method (Kempe chains) remains foundational.
- Appel and Haken's 1976 computer proof required checking 1,482 configurations and faced skepticism about computational reliability.
- A 1997 proof simplified the process to 633 configurations and gained acceptance with improved computing.
- A 2026 proof by Thorup, Thomassen, and colleagues uses 8,202 configurations but enables parallel reduction for faster coloring.
- This new proof achieves n(log n) coloring steps, improving on the prior n² method, and reveals structural insights into planar graphs.
- The work opens avenues for coloring theorems on other surfaces like tori, though a computer-free proof remains elusive.