Irrationality of Catalan’s constant

Proves that Catalan's constant G=\sum_{j\ge0}(-1)^j/(2j+1)^2 is irrational. (Lean)

Manuscript

Catalan's constant is irrational

September 24, 2026 · source · cite as \cite{OAI:Catalans-constant-is-irrational-September-24-2026}

We prove that Catalan's constant G=\sum_{j\geq0}(-1)^j/(2j+1)^2 is irrational.

Result 005 · Number theory. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.