Three Dutch mathematicians published a constructive proof of this theorem that used a Coq formalization but no rational numbers, believing them to be irrelevant.
Three Dutch mathematicians published a constructive proof of this theorem that used a Coq formalization but no rational numbers, believing them to be irrelevant. That proof built off of one by Hellmuth Kneser and his son Manfred, which used a version of the Durand-Kerner method. A topological proof uses the so-called "growth lemma" to show that if this theorem did not hold, there would have to be a homotopy between two curves with different winding numbers without crossing zero, a contradiction. A proof of this using Galois theory shows that the complex numbers cannot have a finite extension field, and perhaps the most famous proof uses Liouville's theorem to show that if this theorem did not hold, then one over a polynomial would be constant. For 10 points, name this theorem first proven by Gauss that states that a polynomial of order n has exactly n complex roots.
Three Dutch mathematicians published a constructive proof of this theorem that used a Coq formalization but no rational numbers, believing them to be irrelevant.
{Fundamental Theorem of Algebra} (prompt on “FTA”)