Richard Hamilton | The Poincare Conjecture | 2006 34,399 viewsApr 9, 2018

Richard Hamilton | The Poincare Conjecture | 2006 34,399 viewsApr 9, 2018 Graduate Mathematics 24.5K subscribers The Poincare Conjecture Richard Hamilton Columbia University, New York, USA https://www.mathunion.org/icm/icm-vid... The Euler Characteristic The Million Dollar Problem that Went Unsolved for a Century - The Poincaré Conjecture 18,476 viewsJan 15, 2021 7.56K subscribers Topology was barely born in the late 19th century, but that didn't stop Henri Poincaré from making what is essentially the first conjecture ever in the subject. And it wasn't any ordinary conjecture - it took a hundred years of mathematical development to solve it using ideas so novel that they were worth at least a million dollars. Here I talk about the Poincaré Conjecture by introducing fundamental topological concepts like homeomorphisms and homology, and eventually talk about its solution through Ricci Flow. Note: At 12:25, it's 3-Manifold, not 3D Manifold. I don't know what possessed me to say 3D. ------------------------------------------------------------------------- Music Credits: Inspired by Kevin MacLeod Link: https://incompetech.filmmusic.io/song... License: http://creativecommons.org/licenses/b... Wind Of The Rainforest Preview by Kevin MacLeod Link: https://incompetech.filmmusic.io/song... License: http://creativecommons.org/licenses/b... Wholesome by Kevin MacLeod Link: https://incompetech.filmmusic.io/song... License: http://creativecommons.org/licenses/b... The Forest and the Trees by Kevin MacLeod Link: https://incompetech.filmmusic.io/song... License: http://creativecommons.org/licenses/b... Music: https://www.purple-planet.com http://www.bensound.com/royalty-free-... -------------------------------------------------------------------------- Image Credits: Tesseract, 24-cell and Tetrahedral Compound: Robert Webb's Stella software is the creator of this image. A link to the website: http://www.software3d.com/Stella.php.CC BY-SA 3.0 (https://creativecommons.org/licenses/... ), via Wikimedia Commons Klien Bottle Homology: Steelpillow, CC BY-SA 4.0 (https://creativecommons.org/licenses/... ), via Wikimedia Commons John Stallings Photograph: George M. Bergman, CC BY-SA 4.0 (https://creativecommons.org/licenses/... ), via Wikimedia Commons Saddle Shape: Nicoguaro, CC BY 3.0 (https://creativecommons.org/licenses/... ), via Wikimedia Commons -------------------------------------------------------------------------- Sources and Citations: 1) https://people.math.osu.edu/fiedorowi... 2) https://www.math.unl.edu/~mbrittenham... 3) Evelyn Lamb, 'What We Talk about When We Talk about Holes,' Scientific American (https://blogs.scientificamerican.com/... ) 4) http://infoshako.sk.tsukuba.ac.jp/~ha... 5) enry (https://math.stackexchange.com/users/... ), Why is $S_1$ said to "enclose" a 1-dimensional hole if the region it encloses is a (2-dimensional) disk?, URL (version: 2017-06-06): https://math.stackexchange.com/q/2311769 6) Wikipedia contributors, "Homology (mathematics)," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?... ------------------------------------------------------------------------ Chapters: 00:00 - The Euler Characteristic 03:00 - Intro 03:10 - What Even is a Homeomorphism? 05:07 - The Euler Characteristic, Reprise 07:50 - Introducing Homology 09:20 - The need for a Fundamental Group 11:55 - The Conjecture 13:50 - MORE Dimensions 15:05 - Deforming Surfaces with Ricci Flow 17:02 - Ricci Flow 2.0 18:24 - The Million Dollars Chapters The Euler Characteristic 0:00 Intro 3:00 What Even is a Homeomorphism? 3:10 The Euler Characteristic, Reprise 5:07 Introducing Homology 7:50 The need for a Fundamental Group 9:20 82 Comments rongmaw lin Add a comment... ML Guy ML Guy 1 year ago 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. 37 Kinertia Chris West Chris West 1 year ago This channel deserves so many more views and subscribers! Great content! 48 Joonas Pastila Joonas Pastila 1 year ago 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. 9 Kinertia Dylan Parker Dylan Parker 1 year ago "I'll leave that one for you to figure out for yourself" You have wildly over-estimated me, sir! 26 Kinertia Mark Lama Mark Lama 1 year ago This is great! Thank you for giving me at least an intuitive notion of what Ricci flow is! 4 Xavier Gottlieb-Young Xavier Gottlieb-Young 1 year ago 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 5 Kinertia Prasoon Gupta Prasoon Gupta 1 year ago 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? 6 5W Plus H 5W Plus H 1 year ago Excellent vid! Beautifully well done explanations and top-notch quality! 3 Kinertia 3Liter 3Liter 9 months ago To shut yourself away and focus on something until you solve it, that's dedication. 3 Nando Alves Nando Alves 1 year ago (edited) 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. 3 Kinertia Simson616 Simson616 1 year ago 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... 3 Ambuj Tyagi Ambuj Tyagi 1 year ago 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. 2 richard slater richard slater 4 months ago 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. Pierre Fromont Pierre Fromont 1 year ago Your animations are so beautiful ! What softwares do you use to make them ? 5 Shreyas JV Shreyas JV 1 year ago This was really well done! Kudos to you man! Kishore Chhetri Kishore Chhetri 1 year ago (edited) Brilliant content with smooth explanation ! Please keep it up. 1 Arkadyuti Sarkar Arkadyuti Sarkar 1 year ago 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. 2 analógico analógico 2 months ago Oh my god you explained it so well, thank you! Jin Jun Liu Jin Jun Liu 1 year ago The quality of your videos are amazing man! 3 Rahul Kumar Rahul Kumar 10 months ago well i am a biology student and came here just out of curiosity and i was awestruck by the way you explained it .. SUBSCRIBED LeBusiness LeBusiness 1 year ago 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. 1 yogesh shahi yogesh shahi 3 months ago Brilliant mann just keep going YouTube takes some time to reach you to the people who actually loves it... Don't stop keep going ❤️ Harran Singh Harran Singh 1 year ago Great to see more videos, keep it up! 11 no name no name 1 month ago I am surprised this doesn't have more views. Great video! Marco Cecchi Marco Cecchi 1 year ago (edited) 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! Stanislav Matusevschi Stanislav Matusevschi 5 months ago Great piece of work, nice job World Of Reality World Of Reality 7 months ago I really appreciate your content. 🤍 Ram Sundaram Ram Sundaram 1 year ago And here I thought topology was the same as topography 1 Cycklist Cycklist 1 year ago Wonderful visuals. What a superb video. netomdam netomdam 10 months ago I really like your videos, keep it up May Piatt May Piatt 1 year ago inb4 10k subs for the people who are coming from 1 mil! This channel is going places fs 4 Kinertia PimThePhysicsGuy PimThePhysicsGuy 1 year ago Wonderful! 1 Shubham Vishwakarma Shubham Vishwakarma 1 year ago Great content, but mediocre minds will never catch it .That's why few subscribers and less views. Omar gaber Omar gaber 1 year ago You are so genius💖 1 Calvin Jackson Calvin Jackson 4 months ago I still did not get why the man rejected the prize? What was his reason? Vineel Vineel 10 months ago Amazing video.... I have no words... Prasoon Gupta Prasoon Gupta 1 year ago Bhai bhai! People like you make indians proud! 1 Nachiketa kumar Nachiketa kumar 10 months ago Please bhaiya, make a playlist on topology and string theory... Please please please accept my request 🙏🙏🙏🙏 John St Fleur John St Fleur 2 months ago A PERFECT WOMAN. jimmy cricket jimmy cricket 7 months ago (edited) My one year old can make a spherical shape out of a doughnut shape. No problem. Abhishek Tiwari Abhishek Tiwari 1 year ago 3:00 what's the tune name, btw liked the video 👍, make one on yang miller's and reimann too 5 MG MG 4 months ago What’s the third way to draw the line around the thing???? I’m going insane I can’t figure it out AVINASH SPARROW AVINASH SPARROW 10 months ago Best EXPLAINed man jabunapg 1 jabunapg 1 5 months ago Great explanation Shaun Modipane Shaun Modipane 1 year ago (edited) I see you were interested in the poincaré conjecture Hadi 46290 Hadi 46290 1 year ago Your videos are amazing 👍👍 2 Ricky Ardo Ricky Ardo 4 months ago Did you make a massive error? [look at the frames between 1:39 and 1:50] Manish Kumar Manish Kumar 1 year ago Waooo keep it going 🙌 Mark Summers Mark Summers 1 year ago Very nice job my friend... 1 Naufil Sakran Naufil Sakran 1 year ago great work.... Leo4580 Leo4580 8 months ago Great video 1 Migz Leon Migz Leon 5 months ago Good stuff... Gekkkoin croe Gekkkoin croe 2 months ago Thank you Math is fun by Biki Sharma Math is fun by Biki Sharma 1 year ago Great content .. 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