Fundamental Theorem of Algebra

Theorem
Every non-constant polynomial with coefficients in $\C$ has a root in $\C$.

Historical note

 * 1746: A proof of this theorem was published 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.


 * 1799: The first correct proof of this was given by Gauss, and hence is also known as the D'Alembert-Gauss Theorem.


 * 1814: The first full and rigorous proof in the field of complex numbers was published by Jean-Robert Argand.