# Irrationality exponent of π

> Source: <https://www.johndcook.com/blog/2026/10/07/irrationality-exponent-of-pi/>
> Published: 2026-10-07 21:19:20+00:00

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 […]

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