Fixed Points

  • Published on Sep 28, 2016
  • My video on Sesame Studios:
    The Curiosity Box by Vsauce:
    My twitter:
    My instagram:
    Moon Museum:
    Brouwer’s fixed point theorem:
    Excellent interactive wolfram demo of Brouwer:
    Online graphing calculator used was:
    fixed points more generally:
    Babylonian method:
    Iterated equation solver you can use to run the Babylonian method:
    aleph fixed point:
    My video on counting past infinity:
    map projections:
    Pacific antipode image:
    “four” is the cosmic number:
    Standupmaths video about how four has four letters. So bummed I only found this AFTER I made this vid, check it out!!

    protocol_7’s comment:
    Other topology pages:
    wiki images:
    Globe is from Ballerby & Co. Globemakers
    music from
    Any VFX that actually look cool are by -- I did the rest the best I could :)
  • Science & TechnologyScience & Technology

Comments • 25 080

  • That guy under the staircase

    Why is he trying to hide it by saying it's his initials? Everyone knows its a penis.

  • Piyush Kumar
    Piyush Kumar 4 hours ago

    let's try it with hindi numbers. .
    pandrah (15)
    saat (7)
    char (4)
    char (4)
    ..ok wtf

  • Kevin Liang
    Kevin Liang 11 hours ago

    Thank you for making

  • Enlightning Airieon
    Enlightning Airieon 13 hours ago

    The video is on Fixed points..

    *spends the first two minutes of the video talking about how there is a dick on the moon*

  • Riley Banks
    Riley Banks 13 hours ago

    Look I drew squidward

  • mohammed hikmat
    mohammed hikmat 19 hours ago

    22-4-4-4=10???!??!?! // THIS IS WRONG 5:01

  • Don'tPlayOverwatch
    Don'tPlayOverwatch 22 hours ago +1

    lawl iz a pennis

  • Minh Nguyen
    Minh Nguyen Day ago

    The initial penis thing is genius

  • Thiago Uchida
    Thiago Uchida Day ago +1

    Gotta love how that thumbnail perfectly fits with the loading circle

  • Maddox Robinson
    Maddox Robinson Day ago


  • Great Warships
    Great Warships 2 days ago

    Fixed point? Isn't the earth moving?

  • Krunschy
    Krunschy 2 days ago

    If you can't appreciate the concept of continuity after these examples you probably won't do that ever.

  • nicholas flamegun
    nicholas flamegun 2 days ago

    The most colossally infinite entity in this universe is just how boring this guy is.

    THINGS AND STUFF4 2 days ago

    How come all of vsauces videos from like years ago have more top comments that were posted in the past 3 months than any other point in time

  • DamianZocker
    DamianZocker 2 days ago

    12:15 hey tahts pretty god :)

  • Trevor The Trilby
    Trevor The Trilby 3 days ago

    The most celestial shit post by humanity

  • Black Rose
    Black Rose 3 days ago

    Fellas, if there’s a dick on the moon, that means lookin at the moon is gay now

  • Josh Windle
    Josh Windle 3 days ago


  • Joseph Holland Pontes

    TheXvid Realized they could make money with Vsauce1 and then Bought it just for red, come on man season 3 is is out there and now people have to pay 💰 is becoming obvious the next one will be kurzgesagt and so on until we are all left with Jake Paul 😡

  • Berke Hitay
    Berke Hitay 4 days ago

    13:08 Arrested Development! :)

  • Jonah Fath
    Jonah Fath 4 days ago


  • Delphi Riddle
    Delphi Riddle 5 days ago

    14:36 Puns out of control 🤣🤣🤣

  • LavaDagger
    LavaDagger 5 days ago


  • andose88
    andose88 5 days ago

    Does anyone know the name of the music that starts playing at 12:36?

  • Karsten T
    Karsten T 5 days ago

    All this talk of infinities. There is just one, simple answer to this. Infinity is a process.

  • Daniel Kim
    Daniel Kim 6 days ago


  • FluffyLilEspurr
    FluffyLilEspurr 6 days ago +1

    let's see

    26 twenty six
    9 nine
    4 four- welp.

  • FluffyLilEspurr
    FluffyLilEspurr 6 days ago +1

    2:11 flat-earthers be warned

  • Adrian Ulbrich
    Adrian Ulbrich 6 days ago

    The thing with the four even works in german! I Just checked.

  • ChaoticMouseMan Plays

    What Four-mula do you use to meke sure your videos? Lolol the four puns are amazing

  • Danny C D
    Danny C D 7 days ago

    he blinked 4 times

  • רפאל כהן
    רפאל כהן 7 days ago

    Wow!!! The thing with the four work perfectly the same in hebrew too!!!
    Zero - אפס
    One - אחד
    Two - שנים
    Three - שלוש
    *Four - ארבע*
    Five - חמש
    Six - שש
    Seven - שבע
    Eight - שמונה
    Nine - תשע
    Ten - עשר
    And so on

  • Rubber Duckey Overlord

    those puns were realy FOUR-ced

  • Akhlaq
    Akhlaq 8 days ago +1

    1:59 Dick pic on moon..

  • Road Yogi
    Road Yogi 9 days ago

    1:55 Trololololol~ Lolololol. XD

  • Yeet It’s Claire
    Yeet It’s Claire 9 days ago

    7:27 sliding into your dm’s like

  • Never Snows
    Never Snows 9 days ago

    1:58 humans are amazing.....

  • Caolan Wulf
    Caolan Wulf 10 days ago +2

    Hey... That's pretty good!

  • Jimmy David
    Jimmy David 11 days ago

    What about "half twenty" (10 letters), "half twenty six" (13 letters) or "half three dozens" (15 letters)?... Just different yet valid ways of saying the same numbers, aren't they?.

  • Charles Nelson
    Charles Nelson 11 days ago


  • Brandon Conway
    Brandon Conway 12 days ago

    I was the 5812804th viewer

  • Aditya Kumar Nagar
    Aditya Kumar Nagar 13 days ago

    Hmmm, I tried this idempotent method in Hindi, each time result was a cycle of one and two.. One= ek (2 characters)
    Two= do (1 character)

  • Someoneawesome123 Plays

    Andy Warhol didn’t know he was putting a @#$&% on the moon?

  • Hoe Boe
    Hoe Boe 14 days ago

    Maybe I'm missing something - but the checkerboard at 3:30 doesn't seem impossible... what if you shrink it down to the same size as just one square, rotate it upside down, then move it to the top left corner (call that square A1), then move it diagonally towards the opposite corner (E5) and stop JUST as the tiny version of A1 is outside of the large A1?

    • Hoe Boe
      Hoe Boe 7 days ago

      Okay, I just drew this up and tried it and if you do it like I said, it's absolutely possible to get them all outside their original square while using the 5x5 grid... or any odd number grid for that matter - it doesn't even have to be square

  • divljacina1
    divljacina1 14 days ago


  • PearuArmasJ
    PearuArmasJ 14 days ago

    How the fuck are initials, a signature art?!!

  • JodieWho
    JodieWho 15 days ago

    haha he blinks 4 times at the end

  • Justin Hakata
    Justin Hakata 16 days ago

    You sinisterly motherbitchs

  • Emily Dupl
    Emily Dupl 16 days ago

    Ok so he said if you choose a two digit number and add the two together and subtract it from the original number until you get a one digit number you will get five but when I did it I got 8 🤨
    -(2+3) = -5
    I know I’m probably an idiot but can you please explain how I am supposed to get to nine?

  • Bard Bakerson
    Bard Bakerson 16 days ago +1

    13:08 Lol nice

  • Boldizsár Fiser
    Boldizsár Fiser 17 days ago

    Are you HowToBasic?

  • Manu louassier
    Manu louassier 17 days ago

    I tried in French but it doesn't works.
    But by multiplying by 2 the number of letters, it always ends by six because six contains 6/2 letters.

  • Why is Gamora
    Why is Gamora 17 days ago


  • Syntaxxed
    Syntaxxed 18 days ago

    Thank you michael, for always making quality videos.

  • 00Geeky00 00Goggles00
    00Geeky00 00Goggles00 18 days ago

    Wait so... Andy Warhol was just like, "lol, I wanna put a tiny dick on the moon" and then it happened??? Dream big kids, one day you too, can put a drawing of a dick on the moon.

  • Logan Coen
    Logan Coen 18 days ago

    Pedantry: the no-slip condition held in fluid dynamics demands that some of the coffee stick to the stirring utensil and then shear off elsewhere. Cutting happens, so the theorem does not apply.

    • WarioGiant
      WarioGiant 10 days ago

      Logan Coen not pedantry, just mathematics

  • eric shaw
    eric shaw 19 days ago

    Going from his good old classic stuff to this is like literally a different michael

  • Filip Novotrik
    Filip Novotrik 19 days ago +1

    In English it's cool, but I'm Czech and I've tried it in Czech counting and you always end up with three...

  • Starlit *
    Starlit * 20 days ago


  • Hilbert Hoppyclaps
    Hilbert Hoppyclaps 21 day ago +2

    Micheal, you could’ve hit your ankle on that scooter. Be careful

  • Hilbert Hoppyclaps
    Hilbert Hoppyclaps 21 day ago

    Micheal, you could’ve hit your ankle on that scooter. Be careful

  • N3mad
    N3mad 22 days ago

    dammit i wanted to be the first one to draw a penis on the moon.

  • CrimsonKnight 02
    CrimsonKnight 02 22 days ago

    But isn’t moving the spoon around in the coffee cutting through it therefore it is not a contentious transformation

  • Dranonium
    Dranonium 23 days ago

    "Michael, it's been 6 months. You must release the video about Fixed Points." "I MUST FIND ANOTHER WAY TO SAY FOUR"

  • Almost Brilliant
    Almost Brilliant 23 days ago

    He was, evidently, in so much pain from ripping the four off of his four arm that they had to four-fit filming and cut to a di-four-ent take

  • Julian Wood
    Julian Wood 23 days ago

    C O N F U S I O N

  • Gamikane
    Gamikane 24 days ago

    I tried the trick where you count letters and always end up with 4, and it doesn't work in Finnish. It seems like you either always end up with 5 or end up repeating 8, 9, 8, 9.

  • Sisbro 125
    Sisbro 125 24 days ago

    I picked aleph aleph aleph aleph aleph...... as my number. Since it has infinite alephs, the number of letters never changes so it can’t go to four. I BEAT YOUR SYSTEM

  • Nathan Peroceski
    Nathan Peroceski 25 days ago

    Still can't get over the dick drawing on the moon

  • John Dusenberry
    John Dusenberry 25 days ago

    uhhh.... I started with my birthdate day... 27. Eleven from that. Six from that. Three from that, not four.

  • CringyCookie
    CringyCookie 26 days ago

    I was really scared when you said at the end: Thanks FOUR watching

  • Wolf NZ Outdoors
    Wolf NZ Outdoors 26 days ago

    four/4 seems to work fine in Teutonic language group: four (English), vier (German, Dutch). Not so great in "Romance languages" - French, Italian, Spanish, Portuguese.
    Got to try out some of the number 9 fun on my kids, see how long it takes them to get the pattern...

  • KcayosStudio .
    KcayosStudio . 26 days ago


  • Galuin
    Galuin 26 days ago

    That's cool

  • Some nerd 157
    Some nerd 157 27 days ago

    *space dicc*

  • Larry Larry
    Larry Larry 27 days ago


  • MumChum
    MumChum 28 days ago


  • Infinity Gaming
    Infinity Gaming 28 days ago

    YOOOO did anyone catch him blinking four times at the end? 14:56

  • Carter Smith
    Carter Smith 28 days ago

    Y'all ever read the comments before you watch the video and think TF is going on?

  • Vincent Slater
    Vincent Slater 28 days ago

    16 ÷ 16 = 1

  • Kento Sento
    Kento Sento 28 days ago

    14:56 - Did anybody spot that he blinked four times?? This is not important, by the way! I thought I just wanted you to know.

  • YogSoth
    YogSoth 29 days ago

    Khada Jhin liked this video

  • Arie Copley-Radder
    Arie Copley-Radder 29 days ago

    12:15 nice iDubbbz reference

  • Nathaniel Prawdzik
    Nathaniel Prawdzik 29 days ago

    Four + word play = four play? o.O

    ROHAN TOMLIN 29 days ago

    four hundred
    😮 Did I do it
    No...No i did not😤

  • Miles of Memes
    Miles of Memes 29 days ago

    hawaii is the opposite of africa

  • Pumpkin Burritos
    Pumpkin Burritos 29 days ago

    12:15 hmm

  • ViniGameplay
    ViniGameplay Month ago

    the four thing in portuguese works with five

  • Shota Ghost
    Shota Ghost Month ago

    Lets try this with polish 6 (sześć)
    24 dwadzieścia cztery
    17 siedemnaście
    12 dwanaście
    9 dziewięć
    8 osiem
    5 pięć
    4 cztery
    6 sześć
    Oh... Ok

  • Dragon Cat
    Dragon Cat Month ago

    I am sure that the ending of the video was strongly disliked by chinese watchers. And also the fact that 4 is imminent

  • Rabiul Alam Sarker
    Rabiul Alam Sarker Month ago

    Andy Warhol greatest memer

  • Harper Tucker
    Harper Tucker Month ago

    give humans artistic integrity, and no matter the medium or the place, they will draw dicks.

  • Marie BCFHS
    Marie BCFHS Month ago

    now the moon aliens will know what a human dick looks like XD XD XD

  • Marie BCFHS
    Marie BCFHS Month ago

    the WA dick XD XD XD XD

  • skudzer1985
    skudzer1985 Month ago

    Does the fixed point thing work on something like the universe? Is there an exact opposite side of where we are right now?

  • Thomas Bolton
    Thomas Bolton Month ago

    T h a t s o n t h e m o o n r i g h t n o w

  • B.G. Beats
    B.G. Beats Month ago

    anybody see him blink 4 times at the end?😂

  • George Holloway
    George Holloway Month ago

    The Borsuk Ulum theorem seems fallacious to me, as the idea of swapping the measuring devices my moving them through space implies temporal (or an albeit a-temporal but necessarily incremental) succession. There is nothing to imply that by the "time" we have crossed two points on the original "equal temperature" line where the pressure is the same, that the temperature has not already changed. It seems logically necessary that for one given variable, such a line exists of equal quantities, but it does not follow that on this line there are points of identical values for other variables. Do tell me if I've missed something here!