The Million Dollar Problem that Went Unsolved for a Century - The Poincaré Conjecture

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  • เผยแพร่เมื่อ 19 ม.ค. 2025

ความคิดเห็น • 113

  • @mlguy8376
    @mlguy8376 4 ปีที่แล้ว +113

    I have a PhD in Theoretical physics and I enjoy your videos. Not sure what you are doing or planning on doing with your career but you have a great way of explaining things. I will be following for sure.

    • @evalsoftserver
      @evalsoftserver 3 ปีที่แล้ว +1

      Robert , Have you ever heard of Phase Field theory?

    • @jaw0449
      @jaw0449 2 ปีที่แล้ว +4

      I’m getting my PhD in theoretical physics and I agree with this. There’s a desperate need for those who can explain concepts well

    • @Hermetics
      @Hermetics 10 หลายเดือนก่อน

      Phd = Pure Heart Divided ymonkeys ;)

  • @chriswest8613
    @chriswest8613 4 ปีที่แล้ว +63

    This channel deserves so many more views and subscribers! Great content!

  • @dylanparker130
    @dylanparker130 4 ปีที่แล้ว +42

    "I'll leave that one for you to figure out for yourself"
    You have wildly over-estimated me, sir!

    • @ativjoshi1049
      @ativjoshi1049 4 ปีที่แล้ว +6

      Video version of "left as an exercise for the reader".

    • @Lufernaal
      @Lufernaal 4 ปีที่แล้ว +6

      It's all around the tourus, as is "the outside", then you also can't do anything to change it to the other shapes, because the line will go around the insides of the tourus and come out to the same place it was before.

    • @dylanparker130
      @dylanparker130 4 ปีที่แล้ว +1

      @@Lufernaal thank you!

    • @roman111117
      @roman111117 3 ปีที่แล้ว

      @@Lufernaal couldn't the same be said if you put it "inside" the hole?

    • @l1mbo69
      @l1mbo69 3 ปีที่แล้ว +1

      @@roman111117 they're both equivalent, I think

  • @xavierg733
    @xavierg733 3 ปีที่แล้ว +9

    I am currently a high school senior taking taking AP Calc BC. I plan on being a math major and it’s videos like yours that motivate me every day

  • @catcatcatcatcatcatcatcatcatca
    @catcatcatcatcatcatcatcatcatca 4 ปีที่แล้ว +24

    There is something deeply beautiful in topology, where the shapes defining feature is not as much the area shaping the hole, or any such property that can be expressed as positively being and thus causing the hole to appear. That all can be abstracted away, morphed and scaled, but the hole itself and crucially only the hole survives as defining feature that gives raise to unique characteristics. A negative being, lack of being, is what defines the object or objects that fall under the category.
    The fact that we humans feel often so keen and connected to something we project as being and notice the lack off, or absence, and that it makes deep and complex sense mathematically, is to me beautiful. After all that is required to even notice a hole: you project something that is not there, and give particular meaning to the lack of it. Else it would be a tunnel; maybe set of low ceiling, walls and floor. There is no definite need to notify the absence or mark it with meaning: all things lack almost everything. Yet we gravitate towards negations and not only give them meaning but define and assign meaning to whole things based on what negations they include.

    • @austin2150
      @austin2150 2 ปีที่แล้ว +1

      What a beautiful comment

    • @Mr0rris0
      @Mr0rris0 ปีที่แล้ว

      You make me sick
      Where do you hide your red sashes Ringo
      Detestable thuggie strawdog pontoon

    • @lyrimetacurl0
      @lyrimetacurl0 ปีที่แล้ว

      I just realised why odd dimensional shapes have Euler characteristic 2 and even dimensional shapes have Euler characteristic 0. Because each shape also has 1 of itself and 1 null set (negative 1 dimensional thing). This makes all Euler characteristics 0 (without holes).

  • @jinjunliu2401
    @jinjunliu2401 4 ปีที่แล้ว +4

    The quality of your videos are amazing man!

  • @richardslater677
    @richardslater677 3 ปีที่แล้ว +3

    Just sen this channel. That was excellent. That was by miles the best explanation of a very difficult topic that I have ever seen. Excellent delivery too. I don’t understand the maths involved in topology but now I at least understand what the Poincaré conjecture was all about. Brilliant thanks.

  • @mr22guy
    @mr22guy 3 ปีที่แล้ว +4

    To shut yourself away and focus on something until you solve it, that's dedication.

  • @5wplush243
    @5wplush243 4 ปีที่แล้ว +4

    Excellent vid!
    Beautifully well done explanations and top-notch quality!

  • @MadScientyst
    @MadScientyst 2 ปีที่แล้ว

    By far the BEST exposition I've yet seen on The P.C., Topology & Ricci Flow!
    I've 2 Math Degrees & was able to follow quite easily & enjoyably...LOL
    U deserve more views & subscribers my young, versatle friend!
    Keep up the excellent work indeed...

  • @The-KP
    @The-KP ปีที่แล้ว

    One of the best, clearest videos on any topic, let alone maths or topology. So nice I watched it twice!

  • @TheCanon66
    @TheCanon66 2 ปีที่แล้ว

    I am surprised this doesn't have more views. Great video!

  • @marklama6435
    @marklama6435 4 ปีที่แล้ว +4

    This is great! Thank you for giving me at least an intuitive notion of what Ricci flow is!

  • @back2d_lobby
    @back2d_lobby ปีที่แล้ว

    The best video I’ve seen on this abstruse proof, well done. You are talented at this!

  • @reverend11-dmeow89
    @reverend11-dmeow89 3 หลายเดือนก่อน

    "...and VIOLA!"
    It is "VOILA!", actually.
    what is funny is the part where I have been typing it as "VIOLA!" for ages, awaiting someone anywhere to speak it this way.
    Thank You!
    PS. Thanks for this with YOULER!
    I was let go as an Apprentice at a recording studio here in Seattle, the one by the Neptune theatre in the 'U' district, where Heart recorded their first release, for speaking it as NEWMAN for the NOYMAN microphones.
    🍕

  • @143TYAGI
    @143TYAGI 4 ปีที่แล้ว +2

    Excellent job buddy. I love the way you explained. The no. of views on your videos shows that very few viewers are interested in such specialized topics. I wish more people get motivated to take up advanced mathematics.

    • @tim40gabby25
      @tim40gabby25 ปีที่แล้ว

      I disagree with your conclusion. The number of viewers is primarily determined by the algorithmic shuffling of these videos, not the number who would enjoy if such videos were presented in their intray, as happened to me. Just saying.

  • @Simson616
    @Simson616 4 ปีที่แล้ว +10

    That's the first time I've been told, why he rejected the price. Up until now I liked to believe that he valued math so much higher than anything else that he could simply not see the necessity of having a million dollars...

  • @balqaasem
    @balqaasem 4 หลายเดือนก่อน

    This channel is so underrated ❤

  • @RahulKumar-cl6xq
    @RahulKumar-cl6xq 3 ปีที่แล้ว

    well i am a biology student and came here just out of curiosity and i was awestruck by the way you explained it .. SUBSCRIBED

  • @mediamannaman
    @mediamannaman 2 ปีที่แล้ว

    I never made it past high school Trig, and I am able to follow along with you. You are an excellent communicator.

  • @prasoongupta12
    @prasoongupta12 4 ปีที่แล้ว +8

    Can I request a video on P vs Np particularly if P = NP with a fairly practical algorithm to solve NP problem in practical times?

  • @nyckhusan2634
    @nyckhusan2634 ปีที่แล้ว +3

    In 2010 Gregory Perelman proved that we live in 4-D Universe ( X^2+Y^2+Z^2+t^2=1). Now he is working on the problem of " Holes ". Possibly, will prove how this Universe was born.

    • @uncmac
      @uncmac 6 หลายเดือนก่อน +1

      He quit math

  • @SanjaySingh-oh7hv
    @SanjaySingh-oh7hv ปีที่แล้ว

    Let me echo what others have said. This video is so very excellent for explaining and making accessible a complex and difficult and abstract topic. The creator and host of this video is a gifted teacher and orator. So glad I found this video. Adding it to my playlist for future reference!

  • @Laxxas
    @Laxxas 4 ปีที่แล้ว +11

    Great to see more videos, keep it up!

  • @cara-seyun
    @cara-seyun 2 ปีที่แล้ว +1

    The third path on the torus is where you draw it on top and encircling the hole, right?

  • @kishorechhetri4018
    @kishorechhetri4018 4 ปีที่แล้ว +1

    Brilliant content with smooth explanation ! Please keep it up.

  • @AbhishekTiwari-nw5sq
    @AbhishekTiwari-nw5sq 4 ปีที่แล้ว +5

    3:00 what's the tune name, btw liked the video 👍, make one on yang miller's and reimann too

  • @yogeshshahi
    @yogeshshahi 3 ปีที่แล้ว

    Brilliant mann just keep going TH-cam takes some time to reach you to the people who actually loves it... Don't stop keep going ❤️

  • @shreyasjv4877
    @shreyasjv4877 4 ปีที่แล้ว

    This was really well done! Kudos to you man!

  • @PierreFT
    @PierreFT 4 ปีที่แล้ว +6

    Your animations are so beautiful ! What softwares do you use to make them ?

    • @kinertia4238
      @kinertia4238  4 ปีที่แล้ว +3

      Normally Adobe After Effects, but there's a couple of 3D effects in this video which I used C4D to make.

  • @Protopara
    @Protopara ปีที่แล้ว

    Rad! Best explanation on TH-cam bar-none.

  • @maypiatt3766
    @maypiatt3766 4 ปีที่แล้ว +4

    inb4 10k subs for the people who are coming from 1 mil! This channel is going places fs

  • @Lufernaal
    @Lufernaal 4 ปีที่แล้ว +3

    The other way is all around the tourus in a horizontal line. The first shape is a square, right? The second is a "ring" that circles the tourus like a ring circles a finger in a sort of vertical way and it can move around horizontally. The third is a straight line going all around the tourus, in a sort of horizontal way, and connecting it around it. You can then go around vertically, reaching the inside of the tourus. You can never make that line become the other two shapes.

  • @cycklist
    @cycklist 4 ปีที่แล้ว

    Wonderful visuals. What a superb video.

  • @zhess4096
    @zhess4096 6 หลายเดือนก่อน

    11:18 - Is it a spiralling looping line across the torus? Turns it into a slinky

  • @bazboy24
    @bazboy24 2 ปีที่แล้ว

    You are a very gifted teacher indeed

  • @TheArkadyuti
    @TheArkadyuti 4 ปีที่แล้ว +2

    Awesome video, but little bit more info on Perelman solution would have been great 🙏
    One of the finest and apt explanation on the problem statement BTW.

  • @ישראליעקובוביץ
    @ישראליעקובוביץ 2 ปีที่แล้ว

    my guess for the 3rd unique type of loop on the surfuse of a turso is a circle around the girth of the shape.

  • @stanislavmatusevschi6142
    @stanislavmatusevschi6142 3 ปีที่แล้ว

    Great piece of work, nice job

  • @MG-wj5bn
    @MG-wj5bn 3 ปีที่แล้ว

    What’s the third way to draw the line around the thing???? I’m going insane I can’t figure it out

  • @HadiM-rb7yo
    @HadiM-rb7yo 4 ปีที่แล้ว +2

    Your videos are amazing 👍👍

  • @calvinjackson8110
    @calvinjackson8110 3 ปีที่แล้ว

    I still did not get why the man rejected the prize? What was his reason?

  • @prasoongupta12
    @prasoongupta12 4 ปีที่แล้ว +1

    Bhai bhai!
    People like you make indians proud!

  • @jabunapg1387
    @jabunapg1387 3 ปีที่แล้ว

    Great explanation

  • @Leo-if5tn
    @Leo-if5tn 3 ปีที่แล้ว +1

    Great video

  • @satyajitsaha29ss
    @satyajitsaha29ss 2 ปีที่แล้ว

    I am a student in this subject and my research interest is in low dimension topology. You made it good but one thing I want to say that if you were bit slow it would be better..

  • @lebusiness2847
    @lebusiness2847 4 ปีที่แล้ว +1

    Hey, i love the content of your videos! You deserve much more attention. Only thing that makes it sometimes hard to unterstand and fallow is your accent. I know that is hard to change. I am from Germany so my accent isnt perfect neither. You can use an app called Elsa Speak to exercise your accent, it uses AI and is very good. I know this may sound stupid to you because you are probably a native speaker but it could help grow your channel a lot.

    • @kinertia4238
      @kinertia4238  4 ปีที่แล้ว +1

      Thanks for the tips! This is not my normal accent, it's one that I'm putting on by popular demand. Hopefully as I get more used to speaking in a more Americanized accent (I'm also getting a new mic, so the entirety of the audio will eventually improve) the issue gets sorted. Meanwhile I've put subtitles on the video.

  • @MarkSummersCAD
    @MarkSummersCAD 4 ปีที่แล้ว +1

    Very nice job my friend...

  • @williamzame3708
    @williamzame3708 ปีที่แล้ว

    Smale came *before* Stallings, not after - but their work was independent of each other.

  • @analogico3615
    @analogico3615 2 ปีที่แล้ว

    Oh my god you explained it so well, thank you!

  • @itsRAWRtime007
    @itsRAWRtime007 8 หลายเดือนก่อน

    great analogy

  • @netomdam
    @netomdam 3 ปีที่แล้ว

    I really like your videos, keep it up

  • @marcocecchi9853
    @marcocecchi9853 4 ปีที่แล้ว

    Is a manifold the set of points
    (x,y) €R^n*R such that y=f(x) with f being differentiable and with a non zero jacobian?
    Great job btw, keep it up!

  • @jimmycricket7385
    @jimmycricket7385 3 ปีที่แล้ว

    My one year old can make a spherical shape out of a doughnut shape. No problem.

  • @rickyardo2944
    @rickyardo2944 3 ปีที่แล้ว

    Did you make a massive error? [look at the frames between 1:39 and 1:50]

  • @mr.tinman8149
    @mr.tinman8149 2 ปีที่แล้ว

    Math truly has no limits

  • @mathisfunbybikisharma2579
    @mathisfunbybikisharma2579 3 ปีที่แล้ว

    Great content .. What are u doing brother ???

  • @priyathammanoharkoka4300
    @priyathammanoharkoka4300 3 ปีที่แล้ว

    Where do you go to college

  • @omargaber3122
    @omargaber3122 4 ปีที่แล้ว +1

    You are so genius💖

  • @nachiketakumar9645
    @nachiketakumar9645 3 ปีที่แล้ว

    Please bhaiya, make a playlist on topology and string theory... Please please please accept my request 🙏🙏🙏🙏

  • @pimthephysicsguy1056
    @pimthephysicsguy1056 4 ปีที่แล้ว +1

    Wonderful!

  • @MrController12345
    @MrController12345 4 ปีที่แล้ว

    great work....

  • @gekkkoincroe
    @gekkkoincroe 2 ปีที่แล้ว

    Thank you

  • @Misteribel
    @Misteribel 6 หลายเดือนก่อน

    The million dollar price has been used to finance the Poincaré Chair for young, promising mathematicians.

  • @ViralKiller
    @ViralKiller 2 ปีที่แล้ว

    Still waiting on a video to explain this properly...let's see how yours fares....it's really not that complex, just needs to be explained visually

  • @avinashsparrow2911
    @avinashsparrow2911 3 ปีที่แล้ว

    Best EXPLAINed
    man

  • @shaunmodipane1
    @shaunmodipane1 4 ปีที่แล้ว

    I see you were interested in the poincaré conjecture

  • @jake_runs_the_world
    @jake_runs_the_world 3 ปีที่แล้ว

    Really good

  • @ManishKumar-ix5jj
    @ManishKumar-ix5jj 3 ปีที่แล้ว

    Waooo keep it going 🙌

  • @ramsundaram2696
    @ramsundaram2696 4 ปีที่แล้ว +1

    And here I thought topology was the same as topography

  • @ctai010
    @ctai010 2 ปีที่แล้ว

    Your explanation is very good but background music is very distracting

  • @thetaomega7816
    @thetaomega7816 4 ปีที่แล้ว +1

    cool channel

  • @zachansen8293
    @zachansen8293 2 ปีที่แล้ว

    13:50 - So they did what most mathematicians do when they do when they can't solve something: Make a prize for someone else to do it.

  • @nongon5283
    @nongon5283 ปีที่แล้ว

    бля я извиняюсь, но меня прорвало, как же сложно объяснить кому то , что 3d сфера это двумерный объект... это походу просто за гранью интеллекта

  • @rajeshrajgaya287
    @rajeshrajgaya287 2 ปีที่แล้ว

    You are doing anything original or just cut copy and paste

  • @shubhamvishwakarma3629
    @shubhamvishwakarma3629 3 ปีที่แล้ว

    Great content, but mediocre minds will never catch it .That's why few subscribers and less views.

  • @mhduhastmich13
    @mhduhastmich13 3 ปีที่แล้ว

    CUT CUT CUT CUT CUT

  • @sabhachu
    @sabhachu 2 ปีที่แล้ว

    👍

  • @hamiltonianpathondodecahed5236
    @hamiltonianpathondodecahed5236 4 ปีที่แล้ว

    cool

  • @Tadesan
    @Tadesan 2 ปีที่แล้ว

    "Vanilla circle"
    Fetish language. Interesting.

  • @jakublizon6375
    @jakublizon6375 ปีที่แล้ว

    Ohhhhh, so Trump was just doing topology! 8:23

  • @larsjoensson3322
    @larsjoensson3322 2 ปีที่แล้ว

    Hamilton lost!, Perelann won! Why cannot Hamilton relise his loss?

  • @klauswolfer5207
    @klauswolfer5207 3 ปีที่แล้ว

    Speak s l o w e r , t h a n k s

  • @nsfeliz7825
    @nsfeliz7825 3 ปีที่แล้ว

    dont call me homo😡

  • @johnstfleur3987
    @johnstfleur3987 2 ปีที่แล้ว

    A PERFECT WOMAN.