Mathematicians develop new computer-assisted proof of the four-color theorem

The short version

• Thorup, Thomassen, and four colleagues have developed a new computer proof of the four-color theorem.[Hacker News]
• The demonstration relies on a large unavoidable set containing 8,202 configurations.[Hacker News]
• The method introduces an improved coloring algorithm that requires n(log n) steps for an n-vertex graph.[Hacker News]
• The paper was posted online in March 2026 ahead of an upcoming conference presentation.[Hacker News]

Key facts

• Thorup, Thomassen, and four colleagues produced a new computer proof of the four-color theorem that was posted online in March 2026.[Hacker News]
• The new proof relies on an unavoidable set consisting of 8,202 configurations.[Hacker News]
• The new approach provides an algorithm requiring n(log n) steps to color an n-vertex graph, improving on previous n² methods.[Hacker News]
• The four-color theorem was previously proved using supercomputers in 1976 with 1,482 configurations and simplified in 1997 using 633 configurations.[Hacker News]

Sources

Outlet counts describe coverage, not independent confirmation. Reports may share a wire service or original source.

• The Four-Color Theorem Gets a Rare New ProofHacker News