The fractional chromatic number of the plane is at least 4 · HackerPapers discussions

The fractional chromatic number of the plane is at least 4 — mentioned by skinner_

Mon, 01 Jun 2026 15:09:08 GMT

> You just know nothing about math and are happy to parrot bullshit AI salesmen are selling you. Not the parent poster here. I do know things about math. I wrote a few papers related to the unit distance problem (https://arxiv.org/abs/2311.10069, https://arxiv.org/abs/2406.15317) and spent quite some time trying to solve it. I had no chance of coming up with the proof that the spicy autocomplete came up with. Dumb benchmark, sure.

Paper and discussion history. A mention is not an endorsement.

The fractional chromatic number of the plane is at least 4 — mentioned by skinner_

Mon, 23 Dec 2024 02:57:36 GMT

Sure, these are standard problems, I’ve said so myself. My point is that my productivity is multiplied by ChatGPT, even if it can only solve standard problems. This is because, although I work on highly non-standard problems (see https://arxiv.org/abs/2311.10069 for an example), I can break them down into smaller, standard components, which ChatGPT can solve in seconds. I never ask ChatGPT "where's the race condition" kind of questions.

Paper and discussion history. A mention is not an endorsement.

The fractional chromatic number of the plane is at least 4 — mentioned by skinner_

Sat, 20 Apr 2024 15:54:42 GMT

Very good question! Yes, the final value is somewhere in there. I expect that it's the lowest point, meaning Croft's Tortoise is optimal. Since then we have an unpublished new 0.241 upper bound with the same proof but wider computer search. We don't know what Erdős had in mind when picking 1/4, but we know something that seems to make the 1/4 value special. Many of the earlier attempts to prove Erdős's conjecture were based on a notion called fractional chromatic number. The numbers went down like this: 0.2857, 0.2813, 0.2763, 0.2565, 0.2518, 0.2506. We now have a new preprint that reaches…

Paper and discussion history. A mention is not an endorsement.