Poincare Conjecture and Ricci Flow | A Million Dollar Problem in Topology 229,757 viewsJun 24, 2020

Poincare Conjecture and Ricci Flow | A Million Dollar Problem in Topology 229,757 viewsJun 24, 2020 7.6K DISLIKE SHARE DOWNLOAD CLIP SAVE Aleph 0 128K subscribers How do we use Riemannian Geometry and Surgery Theory to crack a million-dollar problem in topology? Ricci flow, that's how. In this video, we tackle the only Millennium Prize Problem that's been solved so far, and find the deep mathematics uncovered in the process. --- Official Problem Statement: https://www.claymath.org/millennium-p... --- Follow me! Twitter: https://twitter.com/00aleph00 Instagram: https://www.instagram.com/00aleph00 __ Music Info: Documentary - AShamaluevMusic. Music Link: https://www.ashamaluevmusic.com Intro: (0:00) Poincare Conjecture: (0:45) Riemannian Geometry: (2:31) Ricci Flow: (4:17) Surgery Theory: (7:10) Proof of Poincare Conjecture: (7:26) 461 Comments rongmaw lin Add a comment... Pollux Pollux 1 year ago As an engineer, I can tell you with cerainty that it's true for small angles. 633 Starship X Starship X 1 year ago Man your effort is appreciated. I hope your channel grows. 409 Aleph 0 Owen McKinley Owen McKinley 1 year ago I do wonder what Perelman is up to these days. Again, supremely good content! I've seen a lot of the Poincaré videos on YouTube; your effort exceeds them all! Great presentation 👍👍 202 Aleph 0 Clutch Man Clutch Man 1 year ago The effort on these videos is insane. You should have more subs. 118 Aleph 0 tony banks tony banks 1 year ago Disclaimer: there are easier ways to make a million dollars 899 Sam Hawke Sam Hawke 1 year ago Holy shit. I didn’t think I’d ever see a video that explains a millennium problem this well, let alone problem + solution 🤯 My new favorite math channel for sure 👏 50 Edwin Edwin 1 year ago This video is awesome tip for the animation: you can add a sort of "smoothing" when combining two objects. Of course with low level access to the renderer it's easy, but even in programs like blender they have metaballs and stuff which will make the spheres combining looks smooth. 10 DC Blunt DC Blunt 1 year ago (edited) 0:20 “By the end of this video you’ll understand exactly what it is” - how dare you overestimate me, sir 313 Marco Aurélio Nascimento Marco Aurélio Nascimento 1 year ago This was the best video explaining the poincaré conjecture that I've found, awesome!! Of course I'll have to watch it some more 3 times to get a better grasp of the math, but I got the chills in the end nevertheless. Pretty elegant proof, that surgery thing is a great insight, never heard of it before. 14 Aleph 0 Nianyi Wang Nianyi Wang 1 year ago The question is: WHO CARES? Well, Poincares. 779 Mr Hanky Mr Hanky 1 year ago THANK YOU. Geez it’s impossible to get someone to give a straightforward answer about what this even is lol 72 Aleph 0 Igneus Beats Igneus Beats 1 year ago (edited) im a clueless of math stuff, but i like them.. its somehow inspiring...it pushes me to think on boundaries of human mind and its working principles.. math is a human creation, boundaries of math are the form of pure human mind; everything we create, problems or solutions, everything we find in searching for answers is just an reflection of our mind field.. and we all can go there and search, its just that someone who doesnt know math LANGUAGE practically cannot do it in the same way someone who knows can, but intuitively its very possible.. boundaries of our language are boundaries of our world 7 Jonathan Jonathan 1 year ago Great video and great channel! You illustrate the idea of Perelman‘s proof very nicely. What you don’t mention, however, is where the real „hard work“ in his proof had to be done: namely to control the geometry of the evolving necks in such a way that one knows that after surgery the next singularity will occur only after a controlled amount of time. This is necessary in order to guaranty that only finitely many surgeries happen before extinction. By the way, the regions near the surgery look much more like very long tubes and not like cones, but I admit that this is really hard to illustrate. 6 Bogdan Girdea Bogdan Girdea 1 year ago (edited) Brilliantly simple explanation. The video does it all, at least for us with less expertise in the field. I could not imagine those shapes in this context without the video. Indeed an images is worth 1000 words... 17 Aleph 0 magicmulder magicmulder 1 year ago Thanks man, that was a great explanation, though I would’ve loved more details on the surgery part. 5 Rafael Calsaverini Rafael Calsaverini 1 year ago That's a great explanation of a surreal complex topic. I'm amazed. I guess the comparisons with 3b1b are warranted. 11 Eric Eric 1 year ago I just found your Channel and i am amazed of the quality of your Content.it's Really extremly interesting And well explained. Keep it up! :) 4 Aleph 0 yellow книга yellow книга 1 year ago This is definitely my favorite channel on youtube. Thank you for your hard work. 4 Airblader Airblader 1 year ago This was a fantastic video, thanks! One thing I was missing, however, is a reasoning for why n=3 was so much more difficult. 11 Sonar Bangla Sonar Bangla 5 months ago SPELLBINDINGLY BEAUTIFUL. Thank you Aleph. If it is possible for Schrodinger's wave function of quantum sates to clump up like Ricci flows, then it might be possible to define how classical objects (planets, suns, black holes etc.) can evolve from quantum states and Hawking's theory of the unitary evolution of the entire universe, maybe correct. 2 atil4 atil4 1 year ago (edited) Best math video I have seen in a very long time! If you keep delivering this quality videos you will have a big success. Totally subscribed! 2 Robert Schlesinger Robert Schlesinger 4 months ago Very interesting, informative and worthwhile video. 4 A A A A 4 months ago Beautiful, absolutely beautiful. Thank you so much. I wish you nothing but the highest orders of success because you’re helping more humans than you could ever imagine with this 1 Elena Yablonskaya Elena Yablonskaya 1 year ago Wow... this channel gives exceptionally well made explanations.. please keep going! 1 Ishan Banerjee Ishan Banerjee 1 year ago Sir your presentation is amazing , you are an inspiration for me and I hope I will be able to learn a lot from your channel . 7 Aleph 0 Richard Liu Richard Liu 4 months ago The visual effects are awesome 🤩It really offers me a invitation into learning Ricci flow 🥳 1 kanishk mehto kanishk mehto 1 year ago your modular work is outstanding . loved it . thanks for quality knowledge. 1 Michael Mansfield Michael Mansfield 1 year ago Fantastic explanation, especially considering I'm not a mathematician yet I understood precisely what you were trying to get across. Thank you that's the first video I've watched on the subject that made it clear. Can you point me to an exact equation for the pointcare that may help explain movements and financial markets that go beyond the rational explanation? Market topology seems to be one of the fields that could do this. There is a group of traders that supposedly used Perelman's algorithm in their AI to achieve tremendous results. Thank you. 1 Artemis M Artemis M 1 year ago Amazing. Lots of effort were put into this, truly a great video; thank you! 1 12jgy 12jgy 1 year ago (edited) That proof is quite the elegant one, if I would say so myself! I had already seen an outline of the proof while I was reading a book about the conjecture, but it still amazes me quite a bit. Another thing related to it that find interesting is Perelman himself, he's quite the interesting character, pretty much refusing both a Fields Medal and the 1 million dollar prize, and that if I remember correctly, he treated on his first paper about it, he presented it as just an afterthought, just a corollary of his proof of the geometrization conjecture (which, admittedly, was a very big result, but c'mon, we are talking here about the Poincaré's conjecture!). Speaking of famous conjectures, I wonder if you could do a video on Fermat's Last Theorem, but not just talking about it, but do something similar to this one, giving a bit of insight and a general overview of how the proof goes, talking about the actual theorem that was proved by Andrew Wiles, the modularity of elliptic curves, or you think that's just way too out of your league? Anyway, great video, looking forward to the next one. 33 Aleph 0 marialiyubman marialiyubman 5 months ago My only question (as an ignoramus) is, what’s so special about a 3D space that makes it so difficult to calculate? 2 LigmaEnigma LigmaEnigma 1 year ago Thank you for the detailed explanation of this amazing conjecture! Watching this made me want to dive more into what these mathematical geniuses were thinking about 2 Aleph 0 Paolo C Paolo C 1 year ago Amazing video and content! What program do you use to make the animations? 1 Richard Palme Richard Palme 1 year ago excellent explanation, thank you so much! 1 Ryan P Ryan P 1 year ago Ricci Flow always sounded like a rapper name to me... 100 Will K Will K 1 year ago Pretty cool, I actually vaguely comprehended that - thanks for the great explanation and visualization. 1 The AI Epiphany The AI Epiphany 2 weeks ago (edited) Beautiful video! Unbelievable work I literally grasped everything in a single pass. Intuitively it's a very simple solution in retrospect - but that's the thing with these asymmetric types of problems. I assume there is a close connection with NP problems here - it's hard to find the solution (exponential complexity) easy to verify it's correct (polynomial complexity). Who knows maybe one of these tools will be used to crack the P=NP problem. Ashish Kumar Ashish Kumar 1 year ago Excellent video .. thanks YouTube thanks Aleph 0 . Please keep making more 2 R G R G 1 year ago Great work and clearly explained 👍👍 1 Cristian Alvarez Cristian Alvarez 1 year ago (edited) This is just awesome, I wish you the best for your channel as this video is as beautiful as the idea behind the proof it presents. =D 1 Maxim Golubev Maxim Golubev 1 year ago thanks for the explanation. I have started this topic countless times but every time I'm drowning in details. good stuff sir. 2 6,022x10hoch23 einsdurchmol 6,022x10hoch23 einsdurchmol 1 year ago I can't describe how glad I am that I found the channel. Thx for the content bro! 1 valor36az valor36az 1 year ago (edited) Amazing explanation can you do similar tutorials on other clay institute problems Cosmic Wakes Cosmic Wakes 1 year ago Great video. Thanks for the presentation. 6 Aleph 0 Velvet Revelation Velvet Revelation 1 year ago Such a simple explanation for so enormous an undertaking. Thank you very much for posting this video. Where can I go to see every proof leading up to the Poincaré Conjecture itself? 2 Aleph 0 LV LV 1 year ago Amazing video. Glad I found this gem of a channel! 2 Aleph 0