Jan 2025 Email to Math Professors which references article, Rational or Not? This Basic Math Question Took Decades to Answer.
This article is about developments regarding the "ancient question" of whether a number is rational or irrational.
Email gives a key Theorem/Conjecture, assuming which as true leads to new theorems that help answer the "ancient question."
From: Ashish Sirohi
To: Math Professors cited in Article on Rational/Irrational Numbers (& Some Others)
Sent: Jan 2025
Subject: Rational or Not? See “Telescoping Rational-Valued Series …”
Dear Esteemed Professors,
Great and informative article on deciding whether numbers are rational or irrational, https://www.quantamagazine.org/rational-or-not-this-basic-math-question-took-decades-to-answer-20250108/
Given your interest in “broad new method[s]” that address “this ancient question” of a number being irrational/rational (or your interest in related matters the above article mentions via links) please see the note at the end of below paper, which refers to a wide methodology that goes far beyond the method that their paper proposes.
Telescoping, Rational-Valued Series, and Zeta Functions – Transactions Of The American Mathematical Society, Volume 357, Number 8, Pages 3339–3358
The note at the end of the paper reads:
“After we had submitted this paper, R. Askey called our attention to the website of Ashish Sirohi where an understanding of some of the phenomena we investigate is displayed.”
I am Ashish Sirohi and my website they were referring to contains a simple and broad Conjecture regarding which numbers are rational and which are irrational, https://infiniteseriestheorem.org
Hope you will find the simple and broad conjecture at https://infiniteseriestheorem.org about rational/irrational numbers to be of interest. Assuming this conjecture to be true, theorems can be proved from it, one of which shows that Riemann zeta series will all be irrational.
Thanks and regards,
Ashish Sirohi
Related Developments and Links