Erdős Problem #173
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The colouring `c` contains a monochromatic triangle congruent to `T`. Since `T'` is arbitrary, relabellings and reflections of `T` are allowed. Rescaling is not.
In any \(2\)-colouring of \(\mathbb{R}^2\), for all but at most one triangle \(T\) (up to congruence), there is a monochromatic congruent copy of \(T\). The colouring is arbitrary. No measurability is assumed. `≅` compares vertices with the same label, so the conclusion allows a relabelling `σ`.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/173.Prizenone
Topicsgeometry, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/173
Attempts
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