A short ODE proof of the Fundamental Theorem of Algebra
Ramona Anton, Mihalache, Nicolae, François Vigneron · arXiv (Cornell University) · 2023
We propose a short proof of the Fundamental Theorem of Algebra based on the ODE that describes the Newton flow and the fact that the value $|P(z)|$ is a Lyapunov function. It clarifies an idea that goes back to Cauchy.