Grokability in five inequalities
TLDR
Grok collaborated on five new mathematical inequalities, including improved Gaussian perimeter bounds and sharper moment comparisons.
Key contributions
- Improved lower bound on maximal Gaussian perimeter of convex sets.
- Sharper L2-L1 moment comparison inequalities on the Hamming cube.
- Strengthened autoconvolution inequality.
- Optimal balanced Szarek's inequality.
Why it matters
This paper demonstrates Grok's capability in making novel mathematical discoveries, verified by human authors. It highlights the potential of AI in advancing pure mathematics, opening new avenues for research and collaboration.
Original Abstract
In this note, we report five mathematical discoveries made in collaboration with Grok, all of which have been subsequently verified by the authors. These include an improved lower bound on the maximal Gaussian perimeter of convex sets in $\mathbb{R}^n$, sharper $L_2$-$L_1$ 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 $\{1,\dots,n\}$, and an optimal balanced Szarek's inequality.
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