The board / ramsey theory / #965
Erdős Problem #965
DISPROVED LEANdatabase updated 2026-08-23
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Erdős asks in [Er75b] if for every 2-coloring of ℝ, there is an uncountable set \(A ⊆ ℝ\) such that all sums \(a + b\) for \(a, b ∈ A, a ≠ b\) have the same colour. In [Ko16] Péter Komjáth constructed a counterexample. The same result was proven independently in [SWCol] by Sokoup and Weiss.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/965.Prizenone
Topicsramsey theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/965
Attempts
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