Hi Dotikers!

xAI Grok 4.20, currently in closed beta, is an AI model designed to assist in the automatic discovery of mathematical theorems. In a concrete example, it solved a stochastic problem modeling an animal moving randomly on cliff-like terrain, proving it never falls despite unpredictable steps.

In just 5 minutes, Grok 4.20 derived a new Bellman function; an equation used in dynamic programming to evaluate optimal decisions in uncertain environments; providing a tighter lower bound on the safety margin than previous human estimates, which relied on intuitive zones away from the edge.

This bound surpasses the best known lower bounds, contributing to better understanding of stochastic averages, derivatives, quadratic variations, and boolean functions.

Mathematician Pata Ivani, a professor at the University of California Irvine (UCI), verified these results, confirming the improvement.

Unlike black-box approaches that produce opaque solutions, Grok's approach generates explicit, inspectable formulas, allowing humans to analyze and extend the discoveries.

This advancement fits into a broader trend, as noted by mathematician Terence Tao: AIs like Grok 4.20 and GPT-5.2 are crossing a threshold by autonomously solving unique and complex mathematical problems.

G.