[Hasz]

Perhaps the eponymous fundamental theorem of algebra is a good place to start.

https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

[thomasahle]

From the same page: "the Fundamental Theorem of Algebra is neither fundamental, nor a theorem of algebra"

[jacobolus]

For more on this theme, see: https://www.math.nyu.edu/faculty/edwardsd/carnegie.pdf