One of the most famous proofs of the Fundamental Theorem of Algebra involves Liouville's theorom stating that a bounded entire function in constant.

Who first came up to the idea of deriving FToA from Liouville's theorem? Was it Liouville himself?

I would be also grateful for information about when this proof was found.

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    $\begingroup$ And who proved Liouville's theorem? :) $\endgroup$ – Carsten S Mar 7 '14 at 8:42

At the bottom of page 124 of Jesper Lützen's "Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics", it is stated that Liouville was in fact the first person to use this approach to proving the Fundamental Theorem of Algebra. The date given for Liouville's theorem is 1844, but Liouville's formulation was given in the context of elliptic function theory. Lützen notes that after Cauchy saw Liouville's presentation, he quickly obtained the now-current form of Liouville's theorem and claimed priority for the result. Liouville gave his proof of the Fundamental Theorem of Algebra as a short unpublished note, based on his version of Liouville's theorem, and this sketch is given on page 544 of Lützen's book.


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