The fundamental dream of algebra | Abstract Algebra Math Foundations 216 | NJ Wildberger

This video reveals the unfortunate truth about the "Fundamental Theorem of Algebra": namely that it is not actually correct. This is meant to be a core result in undergrad mathematics, but curiously undergrads don't see much in the way of proof. Why? Because none of the many current arguments are actually convincing once one stops and looks carefully at them.

Modern mathematics students: prepare for some disruption to your thinking! Modern mathematicians: is it not time to admit the harsh reality? This entire topic is intimately connected with what I consider the fundamental problem in mathematics, which I discuss in the Famous Math Problems 19 lectures. And so we need some seriously new thinking.

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Here are the Insights into Mathematics Playlists:

[gutzimmumdo]

"The fundamental dream of algebra" gotta love this guys humor

[westgatekeeper]

Maybe we could use the idea of Planck's constant to refine numbers. Introduce larger and larger randomness to the positions after decimal, until it becomes completely random at ~34 position after decimal.

[abdonecbishop]

Let 0 < y ≤ ~0 and restrict ~0 to the interval ½ ≥ ~0 > 0 and isolate the contradiction ~0 = 0