Section: New Results

A formal proof of the irrationality of $\zeta \left(3\right)$

We have obtained a formal proof, machine-checked by the Coq proof assistant, of the irrationality of the constant $\zeta \left(3\right)$, under the single assumption of the asymptotic behavior of the least common multiple of the first $n$ natural numbers. The core of this formal proof is based on (untrusted) computer-algebra calculations performed outside the proof assistant with the Algolib Maple library. Then, we verify formally and a posteriori the desired properties of the objects computed by Maple and complete the proof of irrationality.