qedbot

Erdős·erdos:659

Erdős Problem 659

problem formal record: solved source: proved (Lean) F0 no formal statement

No formal proof attached. Any claim here rests on a write-up or a report.

Fidelity F0: Absent. No formal statement is attached to the result.

geometry, distances·Source

AI activity

How grades work
Aletheia

2 Feb 2026

Full solution

full A3 V1 F0
Reasoning and sources

Autonomy

AI standalone, with comparable literature existing

Details

literature: 🟡 Sheffer and Lund (2014); 🟢 Grayzel (2026)

literature found on: 2 Feb, 2026; 14 Jan, 2026

similar?: Yes

Gemini 3

13 Jan 2026·with Benjamin Grayzel

Full solution

full A1 V1 F0
Reasoning and sources

Autonomy

AI collaborating with humans

Gemini Deep Research

13 Jan 2026·supporting task

Partial results, upgradeable to full solution, found

partial A1 V1 F0
Reasoning and sources

Autonomy

Secondary contribution: literature search

Aristotle

14 Jan 2026·supporting task

Gemini and Grayzel (2026)

full A1 V1 F0
Reasoning and sources

Autonomy

Secondary contribution: formalization

Details

proof to formalize: Gemini and Grayzel (2026)

F0 no formal statement. Absent. No formal statement is attached to the result.

Follow and discuss

All discussion

Discussion and bounties for this problem load here.

Something wrong or missing here? Request a correction or add a claim, with its sources.

Formal material

Formal statements · 1
Cited proofs · 0

No proof artifact cited by the formal record.

Recorded elsewhere

Compare the registries
  • vibemathed — Erdős Problem #659

    checked·machine-led·their labels: lean-verified, ai-discovered

Also known as · 3
  • https://www.erdosproblems.com/659
  • https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/659.lean
  • FormalConjectures/ErdosProblems/659.lean

Cite this record

qed.bot, “Erdős Problem 659”, https://qed.bot/s/erdos-659, as of 30 Sep 2026.

This record as plain text, with each claim, its grades and its sources.