Sergey Diakov
⬤ Grok 4.20 just pulled off something that's making mathematicians do a double-take. The early beta version of xAI's latest model tackled a brutally difficult problem in probability theory and Boolean systems—the kind of stuff that usually requires expert mathematicians grinding away for months or years. The AI cracked it in about five minutes and delivered a solution that's actually better than anything humans had come up with before.
⬤ The challenge involved finding the sharpest possible lower bounds for random and Boolean systems, a gnarly problem sitting at the intersection of probability theory, harmonic analysis, and extreme mathematical behavior. Grok 4.20 independently cooked up a new Bellman function—a powerful analytical tool mathematicians use to nail down optimal inequalities. This fresh function instantly improved a critical logarithmic factor in the final bound, producing sharper and stronger results than previous approaches.
⬤ Earlier work in this space had only managed weaker bounds that didn't fully capture what these systems could actually do. Grok 4.20's solution hit the theoretical ceiling—it's not just better, it's mathematically optimal. The model resolved a long-standing question about how aggressively certain mathematical quantities can grow under extreme conditions, and it did so with the best possible answer.
⬤ This isn't going to revolutionize your daily life tomorrow, but it's a legit advance in fundamental mathematics. When an AI model can independently generate original research-grade improvements in minutes on problems humans have been chewing on for years, that's a signal worth paying attention to. We're watching AI systems move from calculation tools to actual contributors in theoretical research—the kind of deep scientific work that's traditionally been driven by long, painstaking human inquiry.
Sergey Diakov
