Improved bound for the Erdős minimum-overlap problem
Improved bound for the Erdős minimum-overlap problem is graded independently checked on whataifound.org, with the AI's role graded search scaffold.
AlphaEvolve nudged the best known bound for Erdős's minimum-overlap constant, the first improvement since 2016, and sharpened several autocorrelation inequalities.
- Verification
- Independently checked
- Autonomy
- Search scaffold
- Lab
- Google DeepMind
- Model
- AlphaEvolve (Gemini-based)
- Field
- Mathematics
- Date
- 2025-05-14
- Problem posed
- 1955 · open 70 yrs
What was found
As part of a sweep across open problems in mathematical analysis, AlphaEvolve improved the upper bound on the Erdős minimum-overlap constant from about 0.380927 to about 0.380924, the first movement since 2016, and improved constants in autocorrelation inequalities. The gains are numerically small but exceed long-standing records, and the constructions are explicit and checkable.
Novelty check
The minimum-overlap constant and the autocorrelation inequalities have well-tracked records. AlphaEvolve's values were compared against the standing bounds and confirmed to improve them.
Caveats
The improvements are marginal in magnitude, and both were improved again by other automated systems in 2026. As with the other AlphaEvolve results, a human-designed evaluator and search loop did the selecting.
Sources
Community discussion
How this is graded
whataifound.org grades every entry on two axes: verification (how solid the result is, from a machine-checked proof down to refuted) and autonomy (how much the AI did versus its human collaborators). This finding is independently checked and search scaffold. Full definitions are in the methodology.
Cite this entry
whataifound.org (2025). Improved bound for the Erdős minimum-overlap problem. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2025-05-alphaevolve-minimum-overlap