Automatic Discovery of Irrationality Proofs and Irrationality Measures

TL;DR

This paper explores how experimental mathematics and symbolic computation can be used to discover and partially automate proofs of irrationality and measures of irrationality for natural constants, highlighting both successes and the need for human insight.

Contribution

It demonstrates the potential of combining computational tools with human intuition to find and verify irrationality proofs and measures of natural constants.

Findings

Automated methods can suggest irrationality proofs.

Some proofs are fully automatable, others require human input.

The approach advances understanding of irrationality measures.

Abstract

We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but sometimes there is still need for a human touch.