A Note on a Recent Attempt to Prove the Irrationality of $\zeta(5)$

TL;DR

This paper critiques a recent attempted proof of the irrationality of ta(5), identifying the logical errors and clarifying why the proof does not hold, thereby contributing to the ongoing discussion on ta values.

Contribution

It provides a detailed analysis of the fallacies in Shekhar Suman's attempted proof, clarifying common misconceptions and guiding future research on ta(5).

Findings

The proof contains a logical fallacy.

The attempted proof does not establish irrationality.

Clarifies misconceptions about ta(5) proof strategies.

Abstract

Recently Shekhar Suman [arXiv: 2407.07121v6 [math.GM] 3 Aug 2024] made an attempt to prove the irrationality of $\zeta(5)$. But unfortunately the proof is not correct. In this note, we discuss the fallacy in the proof.