# GROK 4.20 solved problems humans CAN'T Source: https://www.youtube.com/watch?v=F_Yly8Ra520 Recap page: https://rapidrecap.app/video/F_Yly8Ra520 Generated: 2026-01-15T06:04:31.316+00:00 --- ## 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. ![Screenshot at 00:15: Paata Ivanisvili's tweet detailing that Grok 4.20 found a new Bellman function, yielding a square root improvement in the logarithmic factor for U\(p,0\), highlighting the specific mathematical breakthrough achieved by the AI.](https://ss.rapidrecap.app/screens/F_Yly8Ra520/00-00-15.jpg) **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. ## Detailed Analysis The presenter begins by detailing a tweet from Paata Ivanisvili, who had early access to the internal beta of Grok 4.20. Grok 4.20 successfully found a new Bellman function for a problem Ivanisvili and his student N. Alpay were working on, which reduces to identifying the pointwise maximal function U(p,q) under two constraints. The AI produced an explicit formula for U(p,q) that yields an improvement in the asymptotic behavior of U(p,0) as p approaches 0, specifically a square root improvement in the logarithmic factor. This result builds upon their prior work proving U(p,0) >= l(p), where l(p) is the Gaussian isoperimetric profile. Ivanisvili notes that while this result does not immediately change the world, it is a crucial step toward understanding stochastic analogs of derivatives of Boolean functions. The presenter then draws a simplified analogy of a person walking near a cliff edge to explain the mathematical problem's constraints. The discussion shifts to related news, including Elon Musk's tweet about losing battles but never losing the war against OpenAI, as the odds of his lawsuit winning increased from 36% to 41% following relevant events. The presenter also shows a tweet from Hongyuan Mei of xAI, confirming they are doubling down on Grok's mathematical reasoning, citing Grok's autonomous solution of Erdos problem #728, which was accepted by Terence Tao. Finally, the presenter shows xAI's announcement of a partnership with the US Department of War (DoW) to deliver Frontier AI, contrasting this with the perceived opacity of OpenAI's internal development, noting that Grok 4.20, Slateflow, and Tidewisp are already being tested. ### Grok 4.20 Mathematical Breakthrough - Found an explicit Bellman function for U(p,q) - Yielded a square root improvement in the logarithmic factor for U(p,0) - Confirmed in a paper by Ivanisvili and Alpay (arXiv:2502.16045) ### AI Theorem Discovery Milestones - Grok 4.20 solved the problem autonomously after 5 minutes - GPT 5.2 and AlphaEvolve are also mentioned as advancing automated theorem discovery ### Erdos Problem #728 Solved - Hongyuan Mei confirmed xAI solved this problem autonomously, which Terence Tao accepted - The result was not replicated in existing literature ### Elon Musk/OpenAI Conflict - Musk tweeted 'I've lost a few battles over the years, but I've never lost a war' after the chance of him winning his lawsuit against OpenAI rose from 36% to 41% ### xAI Government Contract - xAI is working with the US Department of War (DoW) to deliver Frontier AI, emphasizing US-based tokenization and avoiding perceived data silos. ![Screenshot at 00:15: Paata Ivanisvili's tweet detailing that Grok 4.20 found a new Bellman function, yielding a square root improvement in the logarithmic factor for U\(p,0\), highlighting the specific mathematical breakthrough achieved by the AI.](https://ss.rapidrecap.app/screens/F_Yly8Ra520/00-00-15.jpg) ![Screenshot at 01:17: The presenter sketching the cliff analogy to explain the mathematical constraints U\(p,q\) concerning the boundary condition.](https://ss.rapidrecap.app/screens/F_Yly8Ra520/00-01-17.jpg) ![Screenshot at 03:39: The presenter illustrating the speed of AI discovery by showing Grok 4.20 solving a problem in 5 minutes, contrasting with the slow climb of the human mathematician.](https://ss.rapidrecap.app/screens/F_Yly8Ra520/00-03-39.jpg) ![Screenshot at 05:40: A comparison chart showing GPT 5.2, AlphaEvolve, and Grok 4.20 as examples of models capable of automated theorem discovery.](https://ss.rapidrecap.app/screens/F_Yly8Ra520/00-05-40.jpg) ![Screenshot at 11:37: A screenshot of the Kalshi market showing the probability of Elon Musk winning his case against OpenAI rising from 36% to 41% after his tweet.](https://ss.rapidrecap.app/screens/F_Yly8Ra520/00-11-37.jpg)