Yesterday in AI: 23 May 2026 — AI Cracks 80-Year Math Proof, Karpathy Joins Anthropic

TL;DR — OpenAI's reasoning model autonomously disproved an 80-year-old Erdős geometry conjecture using algebraic number theory; Andrej Karpathy, OpenAI co-founder, started at Anthropic's pre-training team on May 19; Anthropic shipped self-hosted sandboxes and MCP tunnels that let enterprise agents run entirely inside a customer's own firewall. --- 1️⃣ OpenAI's AI Autonomously Disproves an 80-Year Erdős Geometry Conjecture - What: An internal OpenAI general-purpose reasoning model solved the planar unit distance problem — proving that n points can form n^1+δ unit-distance pairs, shattering the square-grid optimality assumption Paul Erdős made in 1946. - Why it matters: This is the first time an AI has independently solved a prominent open problem at the frontier of a mathematical subfield, with the proof verified by multiple Fields medalists and Princeton combinatorialists. - Key number: δ = 0.014 — the polynomial improvement exponent, later refined by Princeton mathematician Will Sawin after the AI's initial proof. The breakthrough came from an unexpected direction: rather than attacking the geometry directly, the model drew on Golod-Shafarevich theory and infinite class field towers from algebraic number theory — a connection that surprised the discrete geometry community. OpenAI published companion remarks from Noga Alon Princeton and Thomas Bloom, both independently verifying the argument. Fields medalist Tim Gowers called it "a milestone in AI mathematics." The model was not prompted to use number theory; it arrived there through its own reasoning chain. The result is undisputed, and the debate now centers on whether this constitutes genuine mathematical creativity or highly sophisticated pattern-matching operating across disciplinary boundaries. 📎 explainx.aihttps://explainx.ai/blog/openai-planar-unit-distance-erdos-problem-solved-2026 · Dataconomyhttps://dataconomy.com/2026/05/21/openai-model-disproves-erdos-geometry-conjecture/ · Interesting Engineeri