arXiv:2609.04176math.GM
Catalan's constant is irrational
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Abstract
Whether the constant $$G=\sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}=\frac1{1^2}-\frac1{3^2}+\frac1{5^2}-\frac1{7^2}+\cdots$$ introduced by Catalan in the nineteen century is irrational, is a long-standing open problem. In this paper we prove the irrationality of $G$ via using suitable weights.
Catalan's constant is irrational!!! That is a big one. Exciting times to be alive. Regrettably I can't understand the proof at this point. There was a (flawed) proof submitted a month back: https://arxiv.org/abs/2609.04176 I wonder if it gave part of the inspiration.
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