Improved bound for the Erdős minimum-overlap problem
AlphaEvolve nudged the best known bound for Erdős's minimum-overlap constant, the first improvement since 2016, and sharpened several autocorrelation inequalities.
- Model
- AlphaEvolve (Gemini-based)
- Field
- Mathematics
- Date
- 2025-05-14
- Problem posed
- 1955 · open 70 yrs
Sources
Original work
Announcement
Independent commentary
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 and known objections
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.
The open problem
316064
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History of this entry
- CorrectedRecorded the MathDB record for this result as a registration.
- AddedEntered the registry graded Independently checked and Search scaffold.
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Community discussion
Graded independently checked for verification and search scaffold for autonomy. What these mean.
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-overlapBibTeX
@misc{whataifound-googledeepmind-2025-overlap,
title = {Improved bound for the Erdős minimum-overlap problem},
author = {{whataifound.org}},
year = {2025},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Google DeepMind. Verification: Independently checked. Autonomy: Search scaffold.},
url = {https://whataifound.org/finding/2025-05-alphaevolve-minimum-overlap}
}