Rebuttal of Kowalenko's paper as concerns the irrationality of Euler's constant

TL;DR

This paper critically challenges Kowalenko's 2010 claims of proving Euler's constant's irrationality and presenting a new rational series for it, defending the current mathematical understanding.

Contribution

It provides a detailed rebuttal to Kowalenko's claims, clarifying the status of Euler's constant and disputing his purported proof and series.

Findings

Kowalenko's proof of irrationality is not accepted by the mathematical community.

The rational series presented by Kowalenko is not new or valid as a proof.

The paper reaffirms the unresolved status of Euler's constant's irrationality.

Abstract

We rebut Kowalenko's claims in 2010 that he proved the irrationality of Euler's constant, and that his rational series for it is new.