Littlewood's proof of the fundamental theorem of algebra: a simpler version

TL;DR

This paper offers a simplified, elementary proof of the fundamental theorem of algebra inspired by Littlewood's approach, avoiding complex functions and emphasizing constructive methods.

Contribution

It provides a more accessible and elementary version of Littlewood's proof, eliminating the need for circular functions and making the proof more constructive.

Findings

Elementary proof of the fundamental theorem of algebra

Avoids circular functions used in traditional proofs

Emphasizes constructive and accessible arguments

Abstract

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary and constructive arguments.