Grok's mathematical discoveries span five inequalities
A recent research note highlights five mathematical breakthroughs achieved through collaboration with the AI system Grok, all of which have been confirmed by human researchers. These discoveries encompass a refined lower limit on the maximal Gaussian perimeter of convex sets in ℝⁿ, enhanced L₂–L₁ moment comparison inequalities on the Hamming cube {−1,1}ⁿ, a fortified autoconvolution inequality, better asymptotic limits on the largest g-Sidon sets in {1,…,n}, and an optimal balanced Szarek's inequality. The findings are accessible on arXiv (ID 2605.05193) and are currently under peer review. This partnership illustrates Grok's capability to produce innovative mathematical insights that adhere to strict verification criteria.
Key facts
- Five mathematical discoveries were made in collaboration with Grok.
- All discoveries have been subsequently verified by the authors.
- Includes an improved lower bound on maximal Gaussian perimeter of convex sets in ℝⁿ.
- Sharper L₂–L₁ moment comparison inequalities on the Hamming cube {−1,1}ⁿ.
- A strengthened autoconvolution inequality.
- Improved asymptotic bounds on the size of the largest g-Sidon sets in {1,…,n}.
- An optimal balanced Szarek's inequality.
- The paper is available on arXiv under ID 2605.05193.
Entities
Institutions
- arXiv