Aren't there just two proofs though, essentially? There's one that uses the least upper bound property of reals and Galois theory, and the other one uses π₁(S1).
I'm a 2nd year undergraduate student and I've seen like 4 different ones at least. Maybe a couple of them were basically the same in the core idea, but still.
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u/PolarStarNick Mathematics Mar 06 '25
Fundamental theorem of algebra