Irrationality of Catalan's constant at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Irrationality of Catalan's constant

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	primes, fractions, patience	Levels:	1
Category:	Number theory	Lean version:	YES! ✔
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Irrationality of Catalan’s constant. Proves that Catalan's constant $G=\sum_{j\ge0}(-1)^j/(2j+1)^2$ is irrational.

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LEVEL 1 Catalan's constant is irrational

released 2026-09-24 | 1 theorem · 4 lemmas · 12 proofs · 14,861 words | PLAY LEVEL 1 » (pdf)

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

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