Fundamental Theorem of Algebra - Numberphile

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Professor David Eisenbud is an algebraic geometer (and director of the Mathematical Sciences Research Institute at Berkeley)

NUMBERPHILE

Videos by Brady Haran

[FourthDerivative]

"You can tell it's an important theorem because it has a name. And you can tell it's a *very* important theorem because it has a *pompous* name." -James Grime

[jacderida]

"It makes me happy because I'm an algebraic geometer so it gives me something interesting to do." This guy is totally awesome!

[fuckmyego]

"do you have any more of this nice paper, Brady?" 
Completely lost it.

[SilverArro]

This guy has such a relaxing voice; I could listen to him lecture on math all day.

[wouldntyaliktono]

Holy shit this guy's voice.  If mathematics ever goes belly up, he's got a career in audio books for sure.  

[dansanger]

I'm ashamed to say that I was a math major in college and had never seen that proof before now.  It was quite beautiful.

[MadaxeMunkeee]

That was the most concise, amazing explanation of the Fundamental Theorem of Algebra I've ever seen. I've seen a fair number of proofs of it before, but none of them have been as clear as this one. Thanks for sharing, and wow - mind blown.

[NuisanceMan]

Yes, the circle shrinks down and gets very close to the red c...but it never quite reaches it. And why is that? Because only Moses could cross the red c.

[lazzerbear]

I have no idea how my school makes math boring. They must work very hard at it.

[EternalBooda]

I had a lot of things I needed to get done today. I got the laundry done. The rest of the day was Numberphile.

[michaelwoodhams]

One of my undergraduate maths professors told us of an exam he had once had to sit. It was a single question:
Proove the fundamental theorem of algebra as many ways as you can.

[caiorimoli]

Man, I have PhD in Biophysics and this is the most beautiful approach I've seen to prove a mathematical theorem in my life. It is such a physicist way to see things, playing with scales to get an approximate feeling of what is going on. So much different approach from all the mathematical strict formalism that I've seen from my mathematics professors at the university. The coolest thing, in my opinion, was that the main constraint he used to work with was the polynomial continuity. Because he knew the polynomial is a smooth complex surface/curve, each term of the polynomial is most likely to work at different ranges in the image-plane f(x). This is so beautiful. I've never thought from that perspective, although I've been indirectly working with that all the time. Thank you!

[DudeGlenn]

Came for the Fundamental Theorem of Algebra
Stayed for the Paper Change.

[Tomato]

9:20 a real Professor: "The formula is trivial and left as an exercise for the viewer" ;)

[rlamacraft]

Quite possibly the best Numberphile video ever! Perfect length, really interesting and pushing the boundaries of my knowledge! Couldn't ask for more, other than more like this…

[elementelement]

Interesting proof of the fundamental theorem of algebra. As a physicist using topology a lot in my work, I am always amazed by simple topological proofs of basic mathematical theorems.

[AkshaySinghJamwal]

Hahaha those "Paper Change" stills with the elevator music always crack me up.

[Cleisthenes]

'This is the fundamental theorem of algebra because it's the basic connection between algebra and geometry. Roots are points somewhere, so they're geometric objects, and polynomials are algebraic objects, so this is the connection that makes algebraic geometry work.'

[ronnies]

8:29 - "If you remember your high school trigonometry"

I would if it was offered.
Standardized testing exists here. The results of which determine school funding, staffing levels, and whether the principal gets fired. Many schools are dropping anything that is not explicitly tested for in order to focus on classes that improve their scores. The cursory glance of the ratio of two given sides being equal to the sine/cosine/tangent satisfies the states trig requirement and that's about all we get. We might even spend 10 minutes and calculate an angle. Once.

If I want a proper trig class here I have to enroll in the local community college for something and bomb the placement exam so I can take a remedial.

[andrewxc]

8:30 - I taught the Trigonometric multiplication rule this year in terms of Euler's Formula: r*e^(i*theta). It went really well.