erdős #508 · Hadwiger-Nelson problem
What is the chromatic number of the plane? That is, what is the smallest number of colours required to colour such that no two points of the same colour are distance apart?
unreviewedOpen. Worked here; no verified result yet.
geometry · open · formalized (Lean) · 0 attempts
use this data
vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsEvidence
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
The exact value is **not known**. This is the **Hadwiger–Nelson problem**: determine the chromatic number of the unit-distance graph on (\mathbb{R}^2).
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗Formal proof
AMS 52 · open (literature)
theorem HadwigerNelsonProblem :
χ(ℝ²) = answer(sorry)formal-conjectures/508.lean ↗Connections1
Hadwiger-Nelson problem · reference
Check it yourself
One command re-derives this record's receipts on your machine.
vela reproduce examples/erdos-problems