Fundamental Theorem of Algebra - Numberphile

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Catch David on the Numberphile podcast: • A Proof in the Drawer ...
Part one on odd polynomials: • Odd Equations - Number...
More links & stuff in full description below ↓↓↓
A nice extra bit about complex numbers: • Complex Numbers are Aw...
Professor David Eisenbud is an algebraic geometer (and director of the Mathematical Sciences Research Institute at Berkeley)
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Videos by Brady Haran
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8 июл 2014

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Комментарии : 1,2 тыс.

@numberphile 5 лет назад

Catch David on the Numberphile podcast: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9y1BGvnTyQA.html

@FourthDerivative 7 лет назад

"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

@tim60312 3 года назад

Which video is this from?

@ragnkja 2 года назад

@@tim60312 “1 is not prime”, I think.

@photonicpizza1466 2 года назад

@@tim60312 "1 is not prime" like the other person said, the quote is referring to the fundamental theorem of arithmetic

@PC_Simo 10 дней назад

Maybe Pythagoras’ Theorem also deserves a pompous name. 🤔

@fuckmyego 9 лет назад

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

@ditzfough 5 лет назад

Omg!! Funny

@jacderida 9 лет назад

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

@dnddmdb642 2 года назад

There's a few different videos with this professor and he seems to be the king of understatement, lol.

@SquirrelASMR 2 года назад

@@dnddmdb642 hahah "most prime numbers are odd"

@SilverArro 8 лет назад

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

@njabulomahlalela2912 8 лет назад

me too lol

@benjaminlehman3221 8 лет назад

His voice is too relaxing for me. If I listened to is lecture I might get very tired and fall asleep.

@Alexagrigorieff 7 лет назад

I've actually had a professor in university with extremely soporific voice (means it puts you to sleep).

@savonliquide7677 7 лет назад

he's not soporific at all, when you listen to him!

@savonliquide7677 7 лет назад

he's very confident and clear, it's a chance for youg student, they can understand the proof of such an important theoreme. Congratulation to him!

@wouldntyaliktono 9 лет назад

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

@rudnickulous 9 лет назад

wouldntyaliktono Bob Ross

@TheMilwaukeeProtocol 8 лет назад

+wouldntyaliktono Don't joke about it going belly up, because everything else is going that way. :-( Case in point: the only type of education with job openings anymore in my country is Special Education. ...But if you weren't joking, then disregard my request.

@AcornFox 7 лет назад

Rhett Rudnicki The Joy of Mathematics

@cameronspalding9792 6 лет назад

I agree

@dansanger5340 9 лет назад

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.

@ALeafOnTheWind42 7 лет назад

It's because to be technical with the proof, you're using algebraic topology, which is something not generally taught in undergrad (at least in my experience). It is a great proof, though

@becomepostal 5 лет назад

Dan Sanger it’s more an explanation than a proof.

@marquez2390 5 лет назад

It wasn't a proof though it was more of a visual concept.

@SilverLining1 5 лет назад

@@ALeafOnTheWind42 You need to use algebraic topology? I don't believe this. Can't you just use limits and the intermediate value theorem?

@ALeafOnTheWind42 5 лет назад

@@SilverLining1 You don't necessarily need algebraic topology because there are other proofs that don't use it (if I recall correctly, as it's been years since I watched this video, the actual proof they were getting at in this video does require algebraic topology). That said, no, you can't use the IVT for the simple reason that some polynomials with real coefficients only have complex roots. As a simple example, take f(x) = x^2 + 1. We can't use the IVT to find a root because for all real values of x, f(x) is positive. The solutions in this case are, of course i and -i, so we need to go to the complex plane in order to get the solutions, and the IVT simply doesn't exist in the complex plane. There are generalizations of the IVT to other metric spaces, but that's already getting into point-set topology at the very least.

@MadaxeMunkeee 10 лет назад

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.

@Brien831 3 года назад

@@welid9772 yea I have seen the Gauss proof and it is a lot. My linear algebra professor scared us first semester students with it back then. This is not even a summary of the gauss proof. I dont believe for a second op has seen the actual gauss proof.

@MrAksupriatna 3 года назад

@@welid9772 Where is the proof? Is it available in this channel?

@urmi-e-azar1776 2 года назад

@@Brien831 If I'm not mistaken, this is Gauss' fundamental idea. To make this precise without using algebraic topology is absolutely bound to be morbidly technical. Indeed, a somewhat equivalent of Intermediate Value Theorem for the plane would be Brower's fixed point theorem - which is a fairly involved result from algebraic topology. If you could refer me to an English translation of Gauss' PhD thesis, by the way, I would be grateful.

@lazzerbear 10 лет назад

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

@1998wiwi 6 лет назад

The difference between learning by choice and learning by necessity

@SkillUpMobileGaming 5 лет назад

They make math *SCARY* not boring. Not all teachers (some are really great!) but a whole lot of teachers do this. This is because of shitty teachers, plain and simple. Everything I learn at school from my teachers I can learn so much better elsewhere. Even math tutors are better at teaching than actual teachers nowadays.

@christianrodriguez823 5 лет назад

The art of mathematics is lost through school, mainly due to standardized testing and a lack of knowledgeable teachers. My favorite book is A Mathematician’s Lament by Paul Lockhart, he discusses what is wrong with the math education system and how students should really be exposed to mathematics so it’s not boring.

@tommydashed4205 5 лет назад

Because some math is boring. You have to know the boring bits to understand the mindblowing ones.

@bwatspro 5 лет назад

Because they think calculating like machines is equal to doing math. And using computer, degrades understanding of math, when in fact, its quite the opposite.

@HowToBasic 10 лет назад

X = Egg

@lilpump2183 8 лет назад

y÷x+7 (7-7×3+4-x) x=2 y=6

@nestorv7627 7 лет назад

HowToBasic nurd

@sphinx1659 7 лет назад

HowToBasic 😂😂😂

@SkywardPvP 7 лет назад

HowToBasic wow didnt expect you here.

@dwither6594 7 лет назад

HowToBasic wtf why are you here 0_0

@EternalBooda 8 лет назад

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

@Clint945 8 лет назад

+EternalBooda There are far worse ways to procrastinate. At least this way you're learning something interesting.

@Aruthicon 8 лет назад

For me, I just take my machete, my grappling hook, etc, and I go on an adventure to Wikipedia.

@ChessNetwork 10 лет назад

Glad to not be the only one. 8:27

@52bicycles 10 лет назад

Jerry watches Numberphile. All these years of looking for some form of validation... finally my search comes to a close.

@tigervision7 10 лет назад

Jerry! :D glad youre a fellow numberphile :)

@junka22 10 лет назад

love your videos man

@devagarwal1591 6 лет назад

Am I solving a chess puzzle or a math problem. Confused!

@RachelsSweetie 6 лет назад

ChessNetwork, I love the way you walk through your thinking about a chess game, just like Prof Eisenbud took us through this theorem.

@NuisanceMan 8 лет назад

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.

@JohnnyDoeDoeDoe 8 лет назад

Haha, love this

@Patalenski 8 лет назад

Well, Chuck Norris can jump it over! :-)

@davecrupel2817 8 лет назад

lololololol

@kleinfaf 8 лет назад

yeah... they come around, but they never come close to

@TosiakiS 7 лет назад

No it does reach it, because the function is continuous.

@DudeGlenn 8 лет назад

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

@NuisanceMan 8 лет назад

+Glenn Beeson (BeesonatotX) Actually, I wish they would change either the paper or the markers to something more compatible with my spine.

@666Tomato666 10 лет назад

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

@emlmm88 4 года назад

666Tomato666 It's certainly trivial if you're allowed Liouville's theorem from analysis.

@AkshaySinghJamwal 8 лет назад

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

@pwhqngl0evzeg7z37 4 года назад

@Vasbrasileiro Haha! I came to see if anyone else noticed!

@michaelwoodhams7866 3 года назад

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.

@rlamacraft 10 лет назад

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…

@jacoboribilik3253 6 лет назад

yes I know, the lenght of the video is some power of Pi

@element4element4 7 лет назад

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.

@hanniffydinn6019 7 лет назад

element4element4 truth is numbers are higher dimensional objects, so true maths is algebraic geometry. That is everything is geometry in higher dimensions. Because reality is actually 11 dimensions. The number line and 2d plane is a gross simplification of reality.

7 лет назад

Hanniffy Dinn 11 dimensions?! Could you elaborate on that?

@hanniffydinn6019 7 лет назад

Viktor Rucký it's all clear from string theory which needs 11 dimensions and describes reality. Search for documentaries on string theory and quantum physics.

@jameswood7207 7 лет назад

string theory is a THEORY and still unproven-and you shouldn't recite is as a fact.

@ganifraterdogan1062 5 лет назад

@@jameswood7207 Can you tell me what a theory is?

@caiorimoli3466 2 года назад

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!

@Macgki 10 лет назад

You definitely should make some videos about Gödel and his incompleteness theorem.

@3niknicholson 4 года назад

they started making one....

@ronnies07 10 лет назад

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.

@SeanBenson23 3 года назад

This is the most accurate thing I've ever read. Sad.

@darkmage07070777 10 лет назад

13:40 - The moment where the lightbulb went off for me and I could see how this all was supposed to work. Excellent video, as usual!

@walt4670 2 года назад

"Somehow this circle shrinks down slowly in some very uneven way" this made me think of Ricci Flow... but I don't know enough to say exactly why or how that applies to this as this theorem is on a complex plane and RF is a partial differential equation.

@Cleisthenes2 3 месяца назад

'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.'

@andrewxc1335 8 лет назад

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

@robobrain10000 10 лет назад

That made alot of sense. thnx for the video brady.

@numberphile 10 лет назад

you're welcome - Prof Eisenbud deserves the thanks!

@steveoti6434 8 лет назад

True .

@cassandrakarshner4157 8 лет назад

+Numberphile for dndndnnmmmjuiuhhbhjjjhbbjjjjj

@TrojanVirus 7 лет назад

at around 4:40 he says that f(x)=x^2, right, so since a function is what you do to a variable. Right? Then, why did he get the function of i, when it is f(x) so it should be function of any number on the x axis, not the y, and i is on the y axis, so i do not understand this.

@Egovip635 7 лет назад

the name of the variable for the function can be any random symbol. so f(x)=f(a)=f(b)... The x is just used twice with different meaning.

@izakj5094 7 лет назад

I'm just learning this in school and I got goose bumps watching the video. Math is love, math is life.

@fatpie2.0 6 лет назад

I want to see more of Professor Eisenbud! Soothing and informative

@landonkryger 10 лет назад

I hope we can see a video about quaternions sometime. They're like super complex numbers.

@JayTemple 5 лет назад

I just saw a link to one in a sidebar. You got your wish!

@justinsankar1164 4 года назад

@@newkid9807 ?

@mBlazer2 10 лет назад

Got to love the paper change interlude.

@MoonlightPassions 10 лет назад

Really enjoyed this, currently studying mathematical methods at school so I feel I could actually understand how this theorem works to a degree. You guys seriously make maths fun :)

@adenpower249 5 лет назад

You're in the Australian system?

@brianpso 10 лет назад

I just loved the little things you did in this video, like the "paper change" part, or the part where the professor was joking about how to spell right. The whole video was greatly informative as always, but these little parts caught up my attention. Thanks Brady!

@PunmasterSTP 3 года назад

That was a beautiful illustration, especially at the very end where he swooped in and explained root multiplicity as well!

@TommiHimberg 10 лет назад

The beauty of mathematics - fundamental theorem of algebra. Excellent video!

10 лет назад

Et ole sattunut saman luokan tilastotieteen peruskurssia verkosta löytämään? Pääsääntöisestihän ne tylsyyteen tappavia hyvin lyhyellä altistuksella...

@TheSentientCloud 10 лет назад

Beauty of mathematics is certainly seen in fractals.

@TommiHimberg 10 лет назад

Hmm, Tero Kankaanperä en ole niin katsellut, että osaisin suoraan suositella, mutta Courserassa on kyllä paljon matskua ja myös tilastotieteen kursseja, mutta ne voi olla aika kuivasti tehtyjä.

@Felipe-sw8wp 8 лет назад

"That's right except for you're saying that I could find them. I'm gonna show you they exist, I'm not gonna find them for you" lol

@aamol3696 10 лет назад

Fantastic video Brady, I was absolutely intrigued!

@Joona527 10 лет назад

Oh, that 'Paper Change' intermission made my day. Keep up the good work, Brady!

@ThrawnTheater 7 лет назад

I've watched many Numberphile videos, and this is the first time that I've seen him. There should be a play list for all of Eisenbud's videos btw.

@lejink 10 лет назад

This man is a very good teacher

@nesagljivic 8 лет назад

Prof.Eisenbud is an exceptional teacher.I've seen all of Numberfile videos and he is the best in explaining the stuff.

@TheLameInfant 10 лет назад

Brilliant, your videos get better every time Brady, keep up the awesome work you're doing

@oilbay54 9 лет назад

I studied this theorem nearly 45 years ago. But this explanation is just excellent. Thank you very much.

@spieagentl 10 лет назад

That was a really nice video and explanation of the proof, thanks!

@JoesApartment 10 лет назад

Fantastic! I'd love to see more of David Eisenbud.

@alfredoarroyog.5705 10 лет назад

Great video! Keep making more like these. Really gave me another insight into the meaning of that theorem.

@cyber-commie4447 5 лет назад

Unbelievably intuitive explanation. Thank you sir.

@kwstaskartas9488 10 лет назад

Great insight and intuition behind of a difficult theorem. Amazing.

@ricardgavalda6135 2 года назад

The "aha!" moment promised in 13:10 comes at 13:40 and it is really "AHA!!". Fabulous! Thanks!

@john7787 7 лет назад

This was really awesome and very intuitive! It's a shame my school didn't teach me this! And the n-root part is also a nice bonus! Thanks Brady!

@oO_ox_O 10 лет назад

Really great explanation, one of my favorite Numberphile videos now! Maybe someone could make an interactive tool that also shows it the way he described it (with the circles) for an arbitrary polynomial (of positive degree). BTW, how many fundamental theorems were covered yet? I certainly remember arithmetic one being even covered several times, maybe you could do a playlist of it Numberphile (on the other hand with so many videos it would take quite some work).

@emlmm88 4 года назад

Yay, David Eisenbud! Love your commutative algebra book!

@Mahmood42978 8 лет назад

This was one of the coolest things I learned about in Intro Complex Analysis.

@thangpham4196 8 лет назад

I love your channel so much, maths look much easier than I was taught so far. I'm turning to love math instead of being scary.

@mah38900 4 года назад

My college algebra teacher really hammered this home to us. I don't think I could ever forget it. In fact this guy reminds me a lot of that teacher, even looks like him.

@UteChewb 7 лет назад

Polynomials and the complex plane bring back warm memories of learning this stuff. Funnily it didn't seem so much fun at the time, but it was mind expanding. Thanks for the video.

@anubisxdmj0 10 лет назад

Why don't you guys put the Hello Internet podcast onto youtube? Mainly because I usually just put a bunch of videos into my watch later playlist and let it play while I do work. Yes I'm saying going to another website to listen to a podcast is too much work.

@numberphile 10 лет назад

It is on RU-vid, but one season (10 episodes) behind what is on the main site, iTunes, etc. ru-vid.com

@vdeave 10 лет назад

On the Hello Internet subject, the guy in the video says he didn't remember his trig identities, and he works in maths...how useful would learning a language be?

@battleforevermore 10 лет назад

Numberphile and the channel also has the bonus reel of the newest episodes. presumably done to F**K with our heads.

@RINB3R 8 лет назад

+vdeave you'd be impressed by how many mathematicians don't know the trig rules, simply because exponentials are much easier to use and trig functions are very VERY closely related to exponentials.

@NuisanceMan 8 лет назад

+RINB3R Wow, that makes me feel much better. I always hated all those annoying little trig rules.

@slotmoon 7 лет назад

Olha que coisa mais linda, mais cheia de graça...

@tannerpittman 10 лет назад

"Paper change" was brilliant. Loved it.

@migfed 10 лет назад

Wonderful video Brady. Quite profound ideas explained in an accessible and appealing way by professor. Numberphile rocks!!!

@Faxter313 10 лет назад

9:10 It's actually also really easy to multiply complex numbers mathmatically, by transferring them from karthesian to polar form first. (I learned math in German and I have no idea if those words make any sense to English speakers). By doing that you acutally see why you can multiply the lengths and add the arguments: |z1| * e^(î*theta1) * |z2| * e1(i*theta2)

@nychold 10 лет назад

Makes sense to me, though the spelling of Karthesian made me think of Carthage before Cartesian. Don't know why...

@PeterGeras 10 лет назад

Yes, but the polar form of complex numbers isn't immediately clear.

@SuperTheguy1234 10 лет назад

what you said is exactly what we learn in america (at least for me). the only difference is that we spell it Cartesian, not karthesian, but that is only one word.

@samuelromero1763 3 года назад

I remember being in algebra 2 and just not getting how or why we could draw this imaginary axis and have this new set of numbers. But now I see it as an axiom. Mathematicians didn’t need to justify the creation of imaginary numbers, just let them exist. And by letting them exist you end up being able to solve many problems that you couldn’t before. As a high school student this idea seemed so foreign to me; that you could just make up something and if it solved your problems or made something make for sense then just let it be and accept it.

@ianmichael5768 4 месяца назад

This is seriously underrated. Calming and profound.

@xanokothe 10 лет назад

I found this video awesome! I worked with numerical methods in college, where I transformed algorithms into programs. Some methods I did not understand how do they work, but seem to use the same rules

@trafalgarla 10 лет назад

I wonder if Brady will ever do a video on the philosophy of mathematics?

@thom_wye 10 лет назад

possibly a future algebraic geometer watching right now! algebraic geometry ftw! :D LOL, loved the paper change :D and the proof is fantastic!

@emlmm88 4 года назад

Thom Wye gaming Out of interest, what area of algebraic geometry did you end up pursuing?

@fernandop4616 8 лет назад

this is my favorite channel by far!!!! thanks for doing these videos! :)

@EtzEchad 2 года назад

I never saw this explained better. Thanks!

@michelef406 5 лет назад

"You know, for a mathematician, he did not have enough imagination. But he has become a poet and now he is fine."

@beverleyhill2199 10 лет назад

do bezout's theorem after this :) you'll have to talk about multiplicity and the projective plane in order to properly state it though. but it's one of the best theorems in mathematics IMO

@newkid9807 4 года назад

Your opinion lacks value

@willdeary630 10 лет назад

I have to hand it to Brady, he really is good at listening to the comments and presenting it in such a way to keep as many people possible happy.

@hobomanchild2504 8 лет назад

If I close my eyes and listen from a distance it's almost like Mr. Burns is giving me a lecture; I love it.

@smoothtriston6203 5 лет назад

This guy's haircut is a complex function.

@SchumiUCD 10 лет назад

Next week on ABC: "A team of mathematicians at numberphile have proved the fundamental theorem of algebra".

@anuzis 10 лет назад

Great video! Thanks for all your effort, Numberphile team.

@Octojoint 10 лет назад

listening to professor Eisenbud is a joy. thank you

@Istlok 10 лет назад

make video about 4th+ dimensions

@hugge123456 10 лет назад

smooth girl from ipanema right there ;)

@hugge123456 10 лет назад

humble brag?

@battleforevermore 10 лет назад

hugge123456 BRADY.. stop freebooting, at least mention the music in the credits brah!

@obeythoven5221 10 лет назад

hugge123456 Why are you here ? Aren't you in your room crying like any other Brazilian ?

@HanBurritoz 10 лет назад

I was wondering why the music at the paper-change seems so familiar.

@nychold 10 лет назад

I thought that was the Girl from Ipanema. I even caught myself singing it when the video came back on.

@cepson 10 лет назад

I would love for someone to do a video investigating the point when The Girl from Ipanema became the go-to song for short interludes.

@sagarsrivastava4811 7 лет назад

Basics of Complex number explained very clearly. It is one of my favorite topics

@smalin 7 лет назад

What happens if 'a' (in the first term, ax^n) is less than one? In that case, it would not make a complete circuit around the origin, and shrinking that path might not involve intersecting the origin. I'm guessing that I'm wrong and the fundamental theorem is right, so what's my mistake?

@michaelwoodhams7866 3 года назад

'a' is just a scaling of the radius of the large circle. 'n' is how many times you go around the circle, which is an integer which is at least 1.

@swapnilmaiti3974 8 лет назад

The proof was amazing !!

@newkid9807 4 года назад

Stinky swapnil!

@SuperMind92 10 лет назад

World of complex numbers is so different, thank you sir, for making me understand complex numbers in a better way, than I was before.....

@Sashafia117 10 лет назад

Thank you so much for this video; the Fundamental Theorem of Algebra is something that I've used and learned about, but I had never learned why, what the reasoning was, what the proof of it was. I'm glad to (partially) understand it now, so thanks.

@MBogdos96 10 лет назад

Maybe you should have employed limits to help explain it a bit better, that whole circle story isn't very understandable without the maybe to back it up. Or maybe just like other times, a link on the description to a video with all the math in depth

@attilakiss8585 6 лет назад

It is not about limits, but it is about the property of continuity (or smoothness). Though precise math def of continuity requires limits, for this level it is way enough as he explained, using the "common sense" of continuity or smoothness.

@CarlosToscanoOchoa 10 лет назад

Could I solve partially Collatz conjecture before Numberphile post a video about it? I think so.

@reimannx33 6 лет назад

And I think my cat would have come up with General theory of relativity even if Einstein did not formulate it.

@reimannx33 6 лет назад

Carlos Toscano Ochoa ....and I think my cat would have come up with General theory of relativity even if Einstein would not have formulated it....

@a690ac52ed7 6 лет назад

I doubt it. Special Relativity, maybe. But knowing cats as I do they haven't the patience to learn the maths for General Relativity.

@fernandoescobar4039 6 лет назад

Never felt more satisfied with any other videos on youtube..! Thank you very much :-)

@jhonbus 10 лет назад

Great video, I really enjoy these numberphile vids that show a bit more "real maths"

@OwenPrescott 10 лет назад

You should do competitions to win some fancy brown paper, maybe with the written equations on them. :P

@ZipplyZane 10 лет назад

They already sell them, so making them a prize of some sort wouldn't be too hard...

@frankharr9466 8 лет назад

Oooooooooooh, now I get it. It took me like three or four tries. But I was baking at the time, so I have an excuse.

@cparks1000000 Год назад

It's nice to see Eisenbud on screen. His book on Commutative Algebra is a beast (in the best possible way)!

@deslomator 10 лет назад

Really enjoyed this video, knowing that it is a long solved theorem doesn't detract from the suspense!

@WarpRulez 10 лет назад

Is f(x)=1 not a polynomial? If it is, what are its zeros? If it isn't, how is polynomial defined, then?

@marisolmaciel2184 7 лет назад

WarpRulez k

@KnakuanaRka 5 лет назад

Since its one term would be represented as 1x^0, that is a zeroth-degree polynomial, which by the theorem would have zero solutions, as is proper.

@valeriobertoncello1809 5 лет назад

Well you could write it as f(x)=x^0, therefore a 0-degree polinomial with n=0 solutions

@elias_toivanen 5 лет назад

It is a polynomial of order zero. It has zero roots ;-)

@trangium 5 лет назад

It is a polynomial of degree 0, therefore it has 0 solutions.

@AlexMcshred6505plus 10 лет назад

This is all very well done and all but I'm being somewhat distracted by how much the professor looks like Sean Connery in Indiana Jones and the last crusade.

@ZipplyZane 10 лет назад

I knew the fundamental theorem of algebra, but I didn't get it intuitively until this video. Great job!

@codygriffin299 4 года назад

It’s been years since I first watched this video. And I’ve got to say: it’s still one of your best yet. The only video to really get me to understand why the Fundamental Theorem of Algebra is true.

@omjoeandsteve 9 лет назад

don't you actually only need a 3 dimensional graph to do both axes with complex planes?

@amandadube156 9 лет назад

no, because both x and y need an imaginary number line. hence, why x and y both had their own planes in the demonstration: together, they add up to 4 dimensions.

@omjoeandsteve 9 лет назад

oh i get it

@MozartJunior22 10 лет назад

YES! Some hardcore mathematics, just as I like it.

@mattikauppinen459 10 лет назад

So hardcore and stuff, with only graphical representation, no limits or any actual maths involved. He showed that we have a polynomial (should be "non-constant polynomial") of degree n and it has "at least" 1 (actually its exactly n) complex roots. But no actual maths presented