Erdős Problem #198

AlphaProof found a new proof of a problem that was already solved (2025).

Problem
Erdős problem #198 (additive combinatorics, sidon sets, arithmetic progressions); current status: disproved (Lean)
Credit
AlphaProof · AI building on known literature
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2025 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PRIOR
ARTPer Tao's AI-contributions wiki

The problem

If A⊂NA\subset \mathbb{N} is a Sidon set then must the complement of AA contain an infinite arithmetic progression?

Statement quoted from erdosproblems.com/198, maintained by Thomas Bloom. Original source: [ErGr79][ErGr80]. Current status there: disproved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Outcome Literature
2025 AI building on known literature AlphaProof 🟢 New proof found 🟢 Baumgartner (1975)

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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