Functions and Analysis

    

A Brief Expository Note on the Transcendence of the Number e

Authors: Amin Bagheri

The number e, which is Euler’s number, has an important role in the fields of analysis, differential equations, and number theory. In 1873, Charles Hermite proved the transcendence of e , which was a fundamental achievement in the theory of transcendental numbers. In this note, we focus on the historical and mathematical context surrounding Hermite's original proof, followed by an outline of a modern, elegant, and straightforward approach proving e’s transcendence. This paper intends to present a clear, succinct, and self-explanatory assembly ideal for undergraduate students or early career researchers and shifts focus from severe technical overgeneralization to clarity of explanation and conceptual understanding.

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[v1] 2025-10-26 22:48:15

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