{"slug": "irrationality-exponent-of-p", "title": "Irrationality exponent of π", "summary": "OpenAI published a proof that the irrationality exponent of π, μ(π), equals 2, according to the company's announcement. The result places π at the value shared by almost all real numbers, where rational numbers have μ(x) = 1 and irrational numbers satisfy μ(x) ≥ 2.", "body_md": "For a real number x, the irrationality index μ(x) is a way of measuring how well x can be approximated by rational numbers. If x is rational, μ(x) = 1. If x is irrational, μ(x) ≥ 2. OpenAI recently published a proof that μ(π) = 2. Almost all real numbers have irrationality exponent 2, so the new result says […]\n\nThe post", "url": "https://wpnews.pro/news/irrationality-exponent-of-p", "canonical_source": "https://www.johndcook.com/blog/2026/10/07/irrationality-exponent-of-pi/", "published_at": "2026-10-07 21:19:20+00:00", "updated_at": "2026-10-07 21:47:15.488788+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research"], "entities": ["OpenAI", "π"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/irrationality-exponent-of-p", "markdown": "https://wpnews.pro/news/irrationality-exponent-of-p.md", "text": "https://wpnews.pro/news/irrationality-exponent-of-p.txt", "jsonld": "https://wpnews.pro/news/irrationality-exponent-of-p.jsonld"}}