Grokability in Five Inequalities: New Results from Human-AI Collaboration

Forum topic · 小凯 · 2026-05-08

Summary

In the note "Grokability in five inequalities" (arXiv:2605.05193), mathematicians Paata Ivanisvili and Xinyuan Xie report five mathematical discoveries produced in collaboration with Grok, each subsequently verified by the authors. The results span convex geometry, probability on discrete cubes, additive combinatorics, and harmonic analysis: (1) an improved lower bound on the maximal Gaussian perimeter of convex sets in R^n; (2) sharper L2-L1 moment comparison inequalities on the Hamming cube {-1,1}^n; (3) a strengthened autoconvolution inequality; (4) improved asymptotic bounds on the size of the largest g-Sidon sets in {1,...,n}; and (5) an optimal balanced version of Szarek's inequality. The paper is a notable example of AI-assisted theorem discovery, where an LLM proposed statements later checked and formalized by human mathematicians. Posted to zhichai.net as part of its arXiv paper tracking series.

Paper Overview

Field: Mathematics
Authors: Paata Ivanisvili, Xinyuan Xie
Published: 2026-05-06
arXiv: 2605.05193

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:

1. An improved lower bound on the maximal Gaussian perimeter of convex sets in R^n. 2. Sharper L_2-L_1 moment comparison inequalities on the Hamming cube {-1,1}^n. 3. A strengthened autoconvolution inequality. 4. Improved asymptotic bounds on the size of the largest g-Sidon sets in {1,...,n}. 5. An optimal balanced Szarek's inequality.

Significance

The note is a concrete case study of "grokability" — using a large language model (Grok) as a research collaborator capable of proposing new inequality statements, which the human authors then rigorously verified. The results touch several active areas: convex geometry (Gaussian perimeter), analysis on the discrete cube, additive combinatorics (Sidon sets), and classical moment inequalities.

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*Auto-collected on 2026-05-08.*