Fundamental Theorem of Algebra - Numberphile
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10 жыл бұрынCatch 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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@numberphile 5 жыл бұрын
Catch David on the Numberphile podcast: kzfaq.info/get/bejne/b99hdaqn07rdgXU.html
@FourthDerivative 7 жыл бұрын
"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 жыл бұрын
Which video is this from?
@ragnkja 3 жыл бұрын
@@tim60312 “1 is not prime”, I think.
@photonicpizza1466 2 жыл бұрын
@@tim60312 "1 is not prime" like the other person said, the quote is referring to the fundamental theorem of arithmetic
@PC_Simo Ай бұрын
Maybe Pythagoras’ Theorem also deserves a pompous name. 🤔
@jacderida 9 жыл бұрын
"It makes me happy because I'm an algebraic geometer so it gives me something interesting to do." This guy is totally awesome!
@dnddmdb642 3 жыл бұрын
There's a few different videos with this professor and he seems to be the king of understatement, lol.
@SquirrelASMR 2 жыл бұрын
@@dnddmdb642 hahah "most prime numbers are odd"
@fuckmyego 9 жыл бұрын
"do you have any more of this nice paper, Brady?" Completely lost it.
@ditzfough 5 жыл бұрын
Omg!! Funny
@SilverArro 8 жыл бұрын
This guy has such a relaxing voice; I could listen to him lecture on math all day.
@njabulomahlalela2912 8 жыл бұрын
me too lol
@benjaminlehman3221 8 жыл бұрын
His voice is too relaxing for me. If I listened to is lecture I might get very tired and fall asleep.
@Alexagrigorieff 7 жыл бұрын
I've actually had a professor in university with extremely soporific voice (means it puts you to sleep).
@savonliquide7677 7 жыл бұрын
he's not soporific at all, when you listen to him!
@savonliquide7677 7 жыл бұрын
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!
@HowToBasic 10 жыл бұрын
X = Egg
@lilpump2183 8 жыл бұрын
y÷x+7 (7-7×3+4-x) x=2 y=6
@nestorv7627 7 жыл бұрын
HowToBasic nurd
@sphinx1659 7 жыл бұрын
HowToBasic 😂😂😂
@SkywardPvP 7 жыл бұрын
HowToBasic wow didnt expect you here.
@dwither6594 7 жыл бұрын
HowToBasic wtf why are you here 0_0
@wouldntyaliktono 9 жыл бұрын
Holy shit this guy's voice. If mathematics ever goes belly up, he's got a career in audio books for sure.
@rudnickulous 9 жыл бұрын
wouldntyaliktono Bob Ross
@TheMilwaukeeProtocol 9 жыл бұрын
+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 жыл бұрын
Rhett Rudnicki The Joy of Mathematics
@cameronspalding9792 6 жыл бұрын
I agree
@MadaxeMunkeee 10 жыл бұрын
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 жыл бұрын
@@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 жыл бұрын
@@welid9772 Where is the proof? Is it available in this channel?
@urmi-e-azar1776 2 жыл бұрын
@@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.
@dansanger5340 9 жыл бұрын
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 жыл бұрын
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 жыл бұрын
Dan Sanger it’s more an explanation than a proof.
@marquez2390 5 жыл бұрын
It wasn't a proof though it was more of a visual concept.
@SilverLining1 5 жыл бұрын
@@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 жыл бұрын
@@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.
@ChessNetwork 10 жыл бұрын
Glad to not be the only one. 8:27
@52bicycles 10 жыл бұрын
Jerry watches Numberphile. All these years of looking for some form of validation... finally my search comes to a close.
@tigervision7 10 жыл бұрын
Jerry! :D glad youre a fellow numberphile :)
@junka22 10 жыл бұрын
love your videos man
@devagarwal1591 6 жыл бұрын
Am I solving a chess puzzle or a math problem. Confused!
@RachelsSweetie 6 жыл бұрын
ChessNetwork, I love the way you walk through your thinking about a chess game, just like Prof Eisenbud took us through this theorem.
@lazzerbear 10 жыл бұрын
I have no idea how my school makes math boring. They must work very hard at it.
@1998wiwi 6 жыл бұрын
The difference between learning by choice and learning by necessity
@SkillUpMobileGaming 5 жыл бұрын
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 жыл бұрын
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 жыл бұрын
Because some math is boring. You have to know the boring bits to understand the mindblowing ones.
@bwatspro 5 жыл бұрын
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.
@NuisanceMan 8 жыл бұрын
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 жыл бұрын
Haha, love this
@Patalenski 8 жыл бұрын
Well, Chuck Norris can jump it over! :-)
@davecrupel2817 8 жыл бұрын
lololololol
@kleinfaf 8 жыл бұрын
yeah... they come around, but they never come close to
@TosiakiS 7 жыл бұрын
No it does reach it, because the function is continuous.
@EternalBooda 8 жыл бұрын
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 жыл бұрын
+EternalBooda There are far worse ways to procrastinate. At least this way you're learning something interesting.
@Aruthicon 8 жыл бұрын
For me, I just take my machete, my grappling hook, etc, and I go on an adventure to Wikipedia.
@rlamacraft 10 жыл бұрын
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 жыл бұрын
yes I know, the lenght of the video is some power of Pi
@AkshaySinghJamwal 8 жыл бұрын
Hahaha those "Paper Change" stills with the elevator music always crack me up.
@pwhqngl0evzeg7z37 4 жыл бұрын
@Vasbrasileiro Haha! I came to see if anyone else noticed!
@michaelwoodhams7866 3 жыл бұрын
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.
@element4element4 7 жыл бұрын
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 жыл бұрын
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 жыл бұрын
Hanniffy Dinn 11 dimensions?! Could you elaborate on that?
@hanniffydinn6019 7 жыл бұрын
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 жыл бұрын
string theory is a THEORY and still unproven-and you shouldn't recite is as a fact.
@ganifraterdogan1062 5 жыл бұрын
@@jameswood7207 Can you tell me what a theory is?
@DudeGlenn 9 жыл бұрын
Came for the Fundamental Theorem of Algebra Stayed for the Paper Change.
@NuisanceMan 8 жыл бұрын
+Glenn Beeson (BeesonatotX) Actually, I wish they would change either the paper or the markers to something more compatible with my spine.
@caiorimoli3466 2 жыл бұрын
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!
@666Tomato666 10 жыл бұрын
9:20 a real Professor: "The formula is trivial and left as an exercise for the viewer" ;)
@emlmm88 4 жыл бұрын
666Tomato666 It's certainly trivial if you're allowed Liouville's theorem from analysis.
@andrewxc1335 8 жыл бұрын
8:30 - I taught the Trigonometric multiplication rule this year in terms of Euler's Formula: r*e^(i*theta). It went really well.
@ronnies07 10 жыл бұрын
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 жыл бұрын
This is the most accurate thing I've ever read. Sad.
@Metal_Icarus 3 күн бұрын
i searched you up after hearing about your math stuff. this video was the first one i have seen of your channel. As a person who is 14h into pre-calc prep to go to college as an adult, the first 51 seconds provided more context and intuitive concepts about the expressions than I have been provided so far.
@brianpso 10 жыл бұрын
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!
@fatpie2.0 6 жыл бұрын
I want to see more of Professor Eisenbud! Soothing and informative
@darkmage07070777 10 жыл бұрын
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 жыл бұрын
"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.
@PunmasterSTP 3 жыл бұрын
That was a beautiful illustration, especially at the very end where he swooped in and explained root multiplicity as well!
@Macgki 10 жыл бұрын
You definitely should make some videos about Gödel and his incompleteness theorem.
@3niknicholson 5 жыл бұрын
they started making one....
@izakj5094 7 жыл бұрын
I'm just learning this in school and I got goose bumps watching the video. Math is love, math is life.
@mBlazer2 10 жыл бұрын
Got to love the paper change interlude.
@alfredoarroyog.5705 10 жыл бұрын
Great video! Keep making more like these. Really gave me another insight into the meaning of that theorem.
@TheLameInfant 10 жыл бұрын
Brilliant, your videos get better every time Brady, keep up the awesome work you're doing
@ThrawnTheater 7 жыл бұрын
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.
@spieagentl 10 жыл бұрын
That was a really nice video and explanation of the proof, thanks!
@aamol3696 10 жыл бұрын
Fantastic video Brady, I was absolutely intrigued!
@Joona527 10 жыл бұрын
Oh, that 'Paper Change' intermission made my day. Keep up the good work, Brady!
@MoonlightPassions 10 жыл бұрын
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 жыл бұрын
You're in the Australian system?
@john7787 7 жыл бұрын
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!
@nesagljivic 8 жыл бұрын
Prof.Eisenbud is an exceptional teacher.I've seen all of Numberfile videos and he is the best in explaining the stuff.
@JoesApartment 10 жыл бұрын
Fantastic! I'd love to see more of David Eisenbud.
@kwstaskartas9488 10 жыл бұрын
Great insight and intuition behind of a difficult theorem. Amazing.
@robobrain10000 10 жыл бұрын
That made alot of sense. thnx for the video brady.
@numberphile 10 жыл бұрын
you're welcome - Prof Eisenbud deserves the thanks!
@steveoti6434 9 жыл бұрын
True .
@cassandrakarshner4157 8 жыл бұрын
+Numberphile for dndndnnmmmjuiuhhbhjjjhbbjjjjj
@TrojanVirus 8 жыл бұрын
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 8 жыл бұрын
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.
@migfed 10 жыл бұрын
Wonderful video Brady. Quite profound ideas explained in an accessible and appealing way by professor. Numberphile rocks!!!
@oilbay54 9 жыл бұрын
I studied this theorem nearly 45 years ago. But this explanation is just excellent. Thank you very much.
@oO_ox_O 10 жыл бұрын
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).
@Cleisthenes2 4 ай бұрын
'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.'
@UteChewb 7 жыл бұрын
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.
@cyber-commie4447 5 жыл бұрын
Unbelievably intuitive explanation. Thank you sir.
@landonkryger 10 жыл бұрын
I hope we can see a video about quaternions sometime. They're like super complex numbers.
@JayTemple 5 жыл бұрын
I just saw a link to one in a sidebar. You got your wish!
@justinsankar1164 4 жыл бұрын
@@newkid9807 ?
@xanokothe 10 жыл бұрын
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
@Sashafia117 10 жыл бұрын
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.
@thangpham4196 8 жыл бұрын
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.
@TommiHimberg 10 жыл бұрын
The beauty of mathematics - fundamental theorem of algebra. Excellent video!
10 жыл бұрын
Et ole sattunut saman luokan tilastotieteen peruskurssia verkosta löytämään? Pääsääntöisestihän ne tylsyyteen tappavia hyvin lyhyellä altistuksella...
@TheSentientCloud 10 жыл бұрын
Beauty of mathematics is certainly seen in fractals.
@TommiHimberg 10 жыл бұрын
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.
@mah38900 4 жыл бұрын
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.
@anuzis 10 жыл бұрын
Great video! Thanks for all your effort, Numberphile team.
@lejink 10 жыл бұрын
This man is a very good teacher
@Faxter313 10 жыл бұрын
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 жыл бұрын
Makes sense to me, though the spelling of Karthesian made me think of Carthage before Cartesian. Don't know why...
@PeterGeras 10 жыл бұрын
Yes, but the polar form of complex numbers isn't immediately clear.
@SuperTheguy1234 10 жыл бұрын
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.
@Mahmood42978 8 жыл бұрын
This was one of the coolest things I learned about in Intro Complex Analysis.
@fernandop4616 8 жыл бұрын
this is my favorite channel by far!!!! thanks for doing these videos! :)
@slotmoon 7 жыл бұрын
Olha que coisa mais linda, mais cheia de graça...
@Felipe-sw8wp 8 жыл бұрын
"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
@emlmm88 4 жыл бұрын
Yay, David Eisenbud! Love your commutative algebra book!
@espinozatectijuana 9 жыл бұрын
Gran aporte a la comunidad. Excelente trabajo. Felicidades por tener esta vision de compartir
@samuelromero1763 3 жыл бұрын
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.
@thom_wye 10 жыл бұрын
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 жыл бұрын
Thom Wye gaming Out of interest, what area of algebraic geometry did you end up pursuing?
@fernandoescobar4039 6 жыл бұрын
Never felt more satisfied with any other videos on youtube..! Thank you very much :-)
@ZipplyZane 10 жыл бұрын
I knew the fundamental theorem of algebra, but I didn't get it intuitively until this video. Great job!
@beverleyhill2199 10 жыл бұрын
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 жыл бұрын
Your opinion lacks value
@anubisxdmj0 10 жыл бұрын
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 жыл бұрын
It is on KZfaq, but one season (10 episodes) behind what is on the main site, iTunes, etc. kzfaq.info
@vdeave 10 жыл бұрын
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 жыл бұрын
Numberphile and the channel also has the bonus reel of the newest episodes. presumably done to F**K with our heads.
@RINB3R 8 жыл бұрын
+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 жыл бұрын
+RINB3R Wow, that makes me feel much better. I always hated all those annoying little trig rules.
@jhonbus 10 жыл бұрын
Great video, I really enjoy these numberphile vids that show a bit more "real maths"
@MrAllenmath 8 жыл бұрын
This is such a great video! Make so much sense now! Thank you!!!
@trafalgarla 10 жыл бұрын
I wonder if Brady will ever do a video on the philosophy of mathematics?
@smalin 7 жыл бұрын
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 жыл бұрын
'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.
@Octojoint 10 жыл бұрын
listening to professor Eisenbud is a joy. thank you
@codygriffin299 4 жыл бұрын
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.
@OwenPrescott 10 жыл бұрын
You should do competitions to win some fancy brown paper, maybe with the written equations on them. :P
@ZipplyZane 10 жыл бұрын
They already sell them, so making them a prize of some sort wouldn't be too hard...
@Istlok 10 жыл бұрын
make video about 4th+ dimensions
@00Skyfox 10 жыл бұрын
Extra thumbs up for paper change intermission! I wish this channel and these videos were around when I was in high school (the internet didn't exist at that time; I'm old). At the time I was deep into algebra, trigonometry, geometry, and calculus, and this all would have made so much more sense back then. I've forgotten so much! It's still fascinating and enjoyable none the less.
@sagarsrivastava4811 7 жыл бұрын
Basics of Complex number explained very clearly. It is one of my favorite topics
@michelef406 5 жыл бұрын
"You know, for a mathematician, he did not have enough imagination. But he has become a poet and now he is fine."
@MBogdos96 10 жыл бұрын
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 жыл бұрын
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.
@deslomator 10 жыл бұрын
Really enjoyed this video, knowing that it is a long solved theorem doesn't detract from the suspense!
@willdeary630 10 жыл бұрын
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.
@swapnilmaiti3974 8 жыл бұрын
The proof was amazing !!
@newkid9807 4 жыл бұрын
Stinky swapnil!
@smoothtriston6203 5 жыл бұрын
This guy's haircut is a complex function.
@Cream147player 10 жыл бұрын
Love this fantastic intuitive solution to a complicated problem
@cparks1000000 Жыл бұрын
It's nice to see Eisenbud on screen. His book on Commutative Algebra is a beast (in the best possible way)!
@hugge123456 10 жыл бұрын
smooth girl from ipanema right there ;)
@hugge123456 10 жыл бұрын
humble brag?
@battleforevermore 10 жыл бұрын
hugge123456 BRADY.. stop freebooting, at least mention the music in the credits brah!
@obeythoven5221 10 жыл бұрын
hugge123456 Why are you here ? Aren't you in your room crying like any other Brazilian ?
@HanBurritoz 10 жыл бұрын
I was wondering why the music at the paper-change seems so familiar.
@nychold 10 жыл бұрын
I thought that was the Girl from Ipanema. I even caught myself singing it when the video came back on.
@SchumiUCD 10 жыл бұрын
Next week on ABC: "A team of mathematicians at numberphile have proved the fundamental theorem of algebra".
@RachelsSweetie 6 жыл бұрын
Great Gauss, that was cool. A better way of looking at it intuitively than the one I've carried around in my head all these years.
@probono2876 6 жыл бұрын
Simply brilliant - a very intuitive presentation of the proof. Many thanks.
@CarlosToscanoOchoa 10 жыл бұрын
Could I solve partially Collatz conjecture before Numberphile post a video about it? I think so.
@reimannx33 6 жыл бұрын
And I think my cat would have come up with General theory of relativity even if Einstein did not formulate it.
@reimannx33 6 жыл бұрын
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 жыл бұрын
I doubt it. Special Relativity, maybe. But knowing cats as I do they haven't the patience to learn the maths for General Relativity.
@frankharr9466 8 жыл бұрын
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.
@j.stephenpearson4348 10 жыл бұрын
The Paper Change Intermission made me laugh out loud -- great gag, Brady!
@22177121 8 жыл бұрын
Great video!! Saw the part one(odd polynomials) first and couldn't stop thinking about the fundamental theorem, and then i discovered you made this as 2nd part! Now that you have talked about this theorem, you can update your odd polynomial "chapter" and include this theorem+conjugate complex solutions theorem as a proof, rather than the simplified Bolzano-like proof you used before! Anyway, great channel, big thumbs up!
@AlexMcshred6505plus 10 жыл бұрын
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.
@WarpRulez 10 жыл бұрын
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 жыл бұрын
WarpRulez k
@KnakuanaRka 5 жыл бұрын
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 жыл бұрын
Well you could write it as f(x)=x^0, therefore a 0-degree polinomial with n=0 solutions
@elias_toivanen 5 жыл бұрын
It is a polynomial of order zero. It has zero roots ;-)
@trangium 5 жыл бұрын
It is a polynomial of degree 0, therefore it has 0 solutions.
@SuperMind92 10 жыл бұрын
World of complex numbers is so different, thank you sir, for making me understand complex numbers in a better way, than I was before.....
@hayeder 9 жыл бұрын
It's really fantastic that you've done a video on something like this. I hope people give it a chance.
@omjoeandsteve 9 жыл бұрын
don't you actually only need a 3 dimensional graph to do both axes with complex planes?
@amandadube156 9 жыл бұрын
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 жыл бұрын
oh i get it
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