# Erdős Problem 120

A statement in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: erdos:120
- Collection: Erdős
- Page: https://qed.bot/s/erdos-120
- Formal record: mixed; at its source: open
- Prize: $100
- Machine-checked: no independent check has verified it
- Fidelity F2: The statement corpus cites this proof against its own statement.
- Source: https://www.erdosproblems.com/120

## AI claims

### DeepMind prover agent, 14 Mar 2026

Solution to variant problem (Lean)

- Outcome: partial
- Autonomy A3: Autonomous. The system produced the result without significant human mathematical involvement.
- Evidence V2: Artifact reported. A proof or a constructed object is published, but nobody independent of its authors has rebuilt it.
- Fidelity F2: Declared. The authors record how the formal statement corresponds to the claim — a comparator challenge, an alignment table or written divergences — or a statement corpus cites the proof against its own statement.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

### GPT-5.4 Thinking, 14 Mar 2026

Solution to variant problem found

- Outcome: full (a supporting task)
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V1: Informal. A public write-up exists and has had community scrutiny.
- Fidelity F2: Declared. The authors record how the formal statement corresponds to the claim — a comparator challenge, an alignment table or written divergences — or a statement corpus cites the proof against its own statement.
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

## Checks

- not self-contained, by qed.bot: imports project modules: FormalConjectures.Util.ProblemImports (https://github.com/google-deepmind/formal-conjectures/blob/153d79d6c82c76fe1bee860742af800840c974d9/FormalConjectures/GreensOpenProblems/94.lean#L174)

## Formal statements

- FormalConjectures/ErdosProblems/120.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/120.lean
- FormalConjectures/GreensOpenProblems/94.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/GreensOpenProblems/94.lean

Cite as: qed.bot, "Erdős Problem 120", https://qed.bot/s/erdos-120, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/