GROK 4.20 solved problems humans CAN'T

Quick Overview

Grok 4.20 successfully found an explicit Bellman function for a complex mathematical problem that Professor Paata Ivanisvili and his student N. Alpay had been working on, providing a square root improvement in the logarithmic factor, demonstrating advanced automated theorem discovery capabilities, which contrasts with the lawsuit Elon Musk is facing against OpenAI.

Key Points: Grok 4.20, in an internal beta, found a new Bellman function for a problem involving identifying the pointwise maximal function U(p,q) under two constraints. The explicit formula produced by Grok 4.20 yields a square root improvement in the logarithmic factor for U(p,0) as p approaches 0. The problem relates to previous work in a paper by Ivanisvili and Alpay (arXiv:2502.16045) where they proved U(p,0) >= l(p), with l(p) being the Gaussian isoperimetric profile. The significance of this result is a step toward understanding averages of stochastic analogs of derivatives of Boolean functions, not an immediate world-changing event. The video also references Elon Musk's lawsuit against OpenAI and the general trend of AI models like GPT 5.2 and AlphaEvolve achieving automated theorem discovery. The speaker draws an analogy to a 'cliff' problem to simplify the concept of finding the maximal function U(p,q), illustrating the boundary conditions. Another tweet from Hongyuan Mei confirms doubling down on pushing Grok's mathematical reasoning, citing the successful solution of Erdos problem #728 by AI tools.

Context: The video discusses a significant achievement by the internal beta version of Grok 4.20, an AI model developed by xAI, which solved a complex mathematical problem posed by Professor Paata Ivanisvili and his student N. Alpay. The problem concerns identifying a pointwise maximal function U(p,q) related to the Gaussian isoperimetric profile. The video contrasts this specific success with broader themes in AI progress, including Elon Musk's ongoing legal battle with OpenAI and xAI's stated mission to develop Frontier AI for government use.