togethercomputer/EinsteinArena-new-SOTA

togethercomputer/EinsteinArena-new-SOTA

Description: New state-of-the-art bounds for open problems

Language: Jupyter Notebook

Stars: 119

Forks: 13

Open issues: 1

Created: 2026-03-04T21:31:08Z

Pushed: 2026-04-12T18:23:07Z

Default branch: main

Fork: no

Archived: no

README:

EinsteinArena state-of-the-art results

New state-of-the-art results on open math problems, purely obtained by AI agents. All results are available at Einstein Arena leaderboard.

Problems (Last update: April 1, 2026)

| Problem | Objective | Our Result | Previous Best | Improvement | |---------|-----------|-----------|---------------|-------------| | [Erdős' Minimum Overlap](erdos-minimum-overlap/) | minimize | 0.380871 | 0.380876 | −0.000005 | | [First Autocorrelation Inequality](first-autocorrelation/) | minimize | 1.50286286 | 1.50286290 | −0.00000004 | | [Flat Polynomials (degree 69)](flat-polynomials/) | minimize | 1.280932\* | 1.340925 | −0.059993 | | [Edges vs Triangles](edges-vs-triangles/) | maximize | −0.712256 | −0.712494 | +0.000238 | | [Tammes Problem (n = 50)](tammes-problem/) | maximize | 0.5134721 | 0.5134719 | +0.0000002 | | [Hexagon Packing in a Hexagon (n = 12)](hexagon-packing/) | minimize | 3.9416523 | 3.9419123 | −0.0002600 | | [Heilbronn Problem for Convex Regions (n = 14)](heilbronn-convex/) | maximize | 0.0278355805 | 0.0278355715 | +0.0000000091 | | [Circles in a Rectangle (n = 21)](circles-rectangle/) | maximize | 2.3658323759 | 2.3658321334 | +0.0000002425 | | [Second Autocorrelation Inequality](second-autocorrelation/) | maximize | 0.961206\* | 0.962580† | — | | [Third Autocorrelation Inequality](third-autocorrelation/) | minimize | 1.454555\* | 1.455643 | −0.001088 | | [Min Distance Ratio (2D, n=16)](min-distance-ratio-2d/) | minimize | 12.889230 | 12.889266 | −0.000036 | | [Uncertainty Inequality](uncertainty-inequality/) | minimize | 0.31885\* | 0.3102†† | − | | [Prime Number Theorem](prime-number-theorem/) | maximize | 0.994179\* | 0.921292 | +0.072887 |

\*After the release of Einstein Arena, a collaborative platform for AI agents, on March 19, 2026, better solutions were found for these problems. Our results here predate the arena launch. For the most up-to-date numbers, see the Einstein Arena leaderboard.

†ImprovEvolve (arXiv:2602.10233) reports 0.96258, but the solution is not publicly available. The previous publicly available best is 0.961021 from AlphaEvolve's repo.

††Unpublished arxiv paper (Cohn-de Laat-Goncalves, 2025) reports 0.3102, but the previous publicly availble best is 0.32159 from AlphaEvolve's repo.

Each folder contains:

• README.md — Problem statement, results comparison, and references
• solutions/ — Solution data
• analysis.ipynb — Verification and visualization