x.com/sir_lemmings/status/2096007022353555850
1 correction found
gpt-6 astra just solved the hadwiger-nelson problem: the chromatic number of the plane is 7!
This problem has not been solved. As of September 2026, the Hadwiger–Nelson problem remains open, and the chromatic number of the plane is only known to be 5, 6, or 7—not proven to be 7.
Full reasoning
Current mathematical references contradict the post's claim that the Hadwiger–Nelson problem has been solved with answer 7.
- Wolfram MathWorld (updated September 2, 2026) says the Hadwiger–Nelson problem is an unsolved problem. It states that after de Grey's 2018 result, "the existence of this graph established that the chromatic number of the Euclidean plane is 5, 6, or 7," and further that "No unit-distance graph realized in the Euclidean plane with chromatic number greater than 5 is currently known."
- A very recent August 2026 arXiv paper by Jan Kristian Haugland is still working on constructing 5-chromatic unit-distance graphs in the plane. Its abstract discusses new 5-chromatic examples, which is consistent with the problem still being open rather than solved at 7.
- An up-to-date problem tracker reviewed on July 31, 2026 likewise lists the Hadwiger–Nelson problem as Open and gives the current unrestricted value as 5, 6, or 7.
So the statement that GPT-6 Astra "just solved" the problem and established that "the chromatic number of the plane is 7" is incorrect: the exact value is not currently known.
3 sources
- Hadwiger-Nelson Problem -- from Wolfram MathWorld
Last Updated: Wed Sep 2 2026 ... The existence of this graph established that the chromatic number of the Euclidean plane is 5, 6, or 7. ... No unit-distance graph realized in the Euclidean plane with chromatic number greater than 5 is currently known.
- A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane
Submitted on 5 Aug 2026 ... Abstract: With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years ... we ... obtain a ... 5-chromatic unit distance graph on 2131 vertices.
- [#P52] Hadwiger-Nelson problem · TheoremDB
State Open ... Reviewed 2026-07-31 ... Strongest checked result: De Grey proves the lower bound 5 ... the classical hexagonal construction gives the upper bound 7. The current unrestricted value is 5, 6, or 7.