Grokability in five inequalities
2026-05-06 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors worked with Grok to find five new mathematical results, each of which they later confirmed themselves. Their discoveries improve our understanding of shapes in high-dimensional space, provide better comparisons of certain mathematical measurements on binary cubes, enhance an inequality related to self-convolution, offer tighter bounds on special subsets of numbers called g-Sidon sets, and optimize a known inequality called Szarek's inequality. These findings contribute to various areas in mathematical analysis and combinatorics.
Gaussian perimeterconvex setsHamming cubemoment inequalitiesautoconvolutiong-Sidon setsasymptotic boundsSzarek's inequalitycombinatoricsmathematical inequalities
Authors
Paata Ivanisvili, Xinyuan Xie
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.