# A Formal Proof of the Irrationality of zeta(3)

arXiv: https://arxiv.org/abs/1912.06611 · HTML: https://mlsanity.com/paper/1912.06611/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Towards a Bridge Layer Between Bibliographic and Formalized Mathematical Knowledge](https://mlsanity.com/paper/2606.11430/) (2026)

## Abstract (arXiv)

This paper presents a complete formal verification of a proof that the evaluation of the Riemann zeta function at 3 is irrational, using the Coq proof assistant. This result was first presented by Ap'ery in 1978, and the proof we have formalized essentially follows the path of his original presentation. The crux of this proof is to establish that some sequences satisfy a common recurrence. We formally prove this result by an a posteriori verification of calculations performed by computer algebra algorithms in a Maple session. The rest of the proof combines arithmetical ingredients and asymptotic analysis, which we conduct by extending the Mathematical Components libraries.