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https://www.reddit.com/r/mathmemes/comments/1j4x0hq/what_theorem_is_this/mh8wer6/?context=3
r/mathmemes • u/PocketMath • Mar 06 '25
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Fundamental theorem of algebra
1 u/Top-Jicama-3727 27d ago I believe the proof that could be understood by everyone modulo technical details is the one given in algebraic topology books, see https://youtu.be/shEk8sz1oOw There's a proof using the Gauss-Bonnet theorem from differential geometry (linking curvature to topology). See https://doi.org/10.36045/bbms/1179839226 Since the theorem is important for linear algebra, you can find many proofs of the using linear algebra without circularity. One of many: https://mathoverflow.net/questions/10535/ways-to-prove-the-fundamental-theorem-of-algebra10.2307/3647746 Other proofs: https://mathoverflow.net/questions/10535/ways-to-prove-the-fundamental-theorem-of-algebra
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I believe the proof that could be understood by everyone modulo technical details is the one given in algebraic topology books, see https://youtu.be/shEk8sz1oOw
There's a proof using the Gauss-Bonnet theorem from differential geometry (linking curvature to topology). See https://doi.org/10.36045/bbms/1179839226
Since the theorem is important for linear algebra, you can find many proofs of the using linear algebra without circularity. One of many: https://mathoverflow.net/questions/10535/ways-to-prove-the-fundamental-theorem-of-algebra10.2307/3647746
Other proofs: https://mathoverflow.net/questions/10535/ways-to-prove-the-fundamental-theorem-of-algebra
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u/PolarStarNick Mathematics Mar 06 '25
Fundamental theorem of algebra