Searching for Apery-Style Miracles [Using, Inter-Alia, the Amazing Almkvist-Zeilberger Algorithm]

TL;DR

This paper automates Apery's irrationality proof method using the Almkvist-Zeilberger algorithm, enabling rapid proofs of irrationality for mathematical constants, though most remain unproven or not famous.

Contribution

It introduces a computational approach to Apery's method, applying the Almkvist-Zeilberger algorithm to automate irrationality proofs of mathematical constants.

Findings

Automated proof of zeta(3) in one second

Generated new irrationality proofs for various constants

Most proofs are not for famous or yet unproven constants

Abstract

Roger Apery's seminal method for proving irrationality is "turned on its head" and taught to computers, enabling a one second redux of the original proof of zeta(3), and many new irrationality proofs of many new constants, alas, none of them is both famous and not-yet-proved-irrational.