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Proof of the Algebraic Independence of π and γ

Year: 2026

Type: preprint

Abstract: This paper establishes a criterion for the algebraic independence of two numbers. Applying this theorem, we prove that π and the Euler–Mascheroni constant γ are algebraically independent. Consequently, it follows that πγ, π/γ, π+γ , and π−γ are all transcendental. Furthermore, we deduce that at least one of the following statements must hold: π and e are algebraically independent, or γ and e are algebraically independent.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23385781

Author: Jin, Qi

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7222147165

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