Fundamental Theorem of Algebra/Historical Note
Historical Note on Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra was first conjectured by Albert Girard, who published about it in $1629$, recognising the existence of imaginary roots.
A proof, geometric in nature, of the Fundamental Theorem of Algebra was published in $1746$ by Jean le Rond d'Alembert. It was for some time called D'Alembert's Theorem.
However, it was later discovered that D'Alembert's proof was incorrect.
The first correct proof was published by Carl Friedrich Gauss in his doctoral dissertation in $\text {1799}$:
- Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree)
in which he gave the Fundamental Theorem of Algebra its name.
During the course of his career, he gave a total of four proofs of this theorem.
The first full and rigorous proof in the field of complex numbers was published in $1814$ by Jean-Robert Argand.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Introduction
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.25$: Gauss ($\text {1777}$ – $\text {1855}$)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): fundamental theorem of algebra
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fundamental theorem of algebra