# On Gauss's first proof of the fundamental theorem of algebra

## TL;DR

This paper revisits Gauss's first proof of the fundamental theorem of algebra, identifies a gap, and provides an elementary method to fill that gap, clarifying historical and mathematical understanding.

## Contribution

It offers an elementary approach to complete Gauss's original proof, addressing a long-standing gap in the historical record.

## Key findings

- Successfully filled the gap in Gauss's proof
- Provided a clearer understanding of Gauss's original method
- Enhanced the historical accuracy of the proof's analysis

## Abstract

Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof.