Grokability in five inequalities
For mathematicians, these are incremental improvements on known inequalities and bounds, with no broad impact beyond the specific problems.
The authors report five mathematical discoveries made in collaboration with Grok, including improved bounds on Gaussian perimeter, moment comparisons, autoconvolution, Sidon sets, and Szarek's inequality, all verified by the authors.
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.