Poincare Conjecture and Ricci Flow | A Million Dollar Problem in Topology 

0:20 “By the end of this video you’ll understand exactly what it is” - how dare you overestimate me, sir

As an engineer, I can tell you with cerainty that it's true for small angles.

Disclaimer: there are easier ways to make a million dollars

The question is: WHO CARES? Well, Poincares.

Ricci Flow always sounded like a rapper name to me...

Man your effort is appreciated. I hope your channel grows.

I do wonder what Perelman is up to these days. Again, supremely good content! I've seen a lot of the Poincaré videos on RU-vid; your effort exceeds them all! Great presentation 👍👍

He solved "Thurston Geometrization Theorem", Poincare Conjecture is just one case of it.

THANK YOU. Geez it’s impossible to get someone to give a straightforward answer about what this even is lol

This is definitely my favorite channel on youtube. Thank you for your hard work.

You are literally the only youtuber to whom i let the ads play full length. Amazing content, keep it up!

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 👏

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!

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

I can't describe how glad I am that I found the channel. Thx for the content bro!

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.

A new gem has emerged on RU-vid! Thanks for the video :)

Amazing. Lots of effort were put into this, truly a great video; thank you!

Absolutely killer video man that was awesome. Really felt like understood it after watching it and was thinking the whole time about how it might relate to physics.

I have never seen such an understood video about something so complicated. Congratulations.

That's a great explanation of a surreal complex topic. I'm amazed. I guess the comparisons with 3b1b are warranted.

Finally a nice video about this topic! Thank you so much!

What an awesome channel; I hope you'll get the publicity that you deserve.

Best visualisation on the topic i've ever seen! Thank you!

Wow... this channel gives exceptionally well made explanations.. please keep going!

thanks for the explanation. I have started this topic countless times but every time I'm drowning in details. good stuff sir.

3b1b: Finally, a worthy opponent, our battle will be legendary.

This video deserves million views. Quality content.

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! :)

What an incredible video, your channel deserves to be huge

The visual effects are awesome 🤩It really offers me a invitation into learning Ricci flow 🥳

Pretty cool, I actually vaguely comprehended that - thanks for the great explanation and visualization.

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...

Very interesting, informative and worthwhile video.

Amazing video. Glad I found this gem of a channel!

another awesome video buddy!

This was brilliant and deserves a lot more views the one thing I didn't understand was actually the very ending I'm not a mathematician I can barely add and subtract but this was a beautiful and intuitive proof

What an explanation! Amazing! Thank you so much for this brilliant content.

Thanks man. Outstandingly clear.

Excellent video .. thanks RU-vid thanks Aleph 0 . Please keep making more

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.

Awesome videos Man!!

Great video. Thanks for the presentation.

Sick animations man! Good job

Great work and clearly explained 👍👍

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

Absolutely amazing and concise explanation!

Thanks man, that was a great explanation, though I would’ve loved more details on the surgery part.

The RU-vid algorithm just recommended me your channel and man it is simply amazing, can't wait for more videos to come out :)

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 .

This video is super well done! Hope you'll get more subs.

excellent explanation, thank you so much!

Great video! Love it.

This was helpful. Thank you much

Incredible video! Very illuminating even to a layperson like myself! Can't thank you enough for the effort! Is it possible to explain (at the level of this video, of course) whether this argument generalizes to other dimensions, and if not, why? Once again, thank you very much for creating such wonderful educational content! I wish you all the best 😊

This is so cool! Thank you for the video.

Thank you for this wonderful video! :-)

A very nice Video, thank you for explaining the great ideas from Gregori Perelman 😀

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.

Excellent!!!

Iam happy that I found this channel

Well done! Nice channel!

Amazing explanation!

This video is a triumph of modern mathematics

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

I understood that! Even though not good at understanding complex maths/problems. Thank you :)

Thank u for this one...💯❤

Great video!

The most daunting problems in mathematics oftentimes have the most elegant solutions.

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.

This was a fantastic video, thanks! One thing I was missing, however, is a reasoning for why n=3 was so much more difficult.

Loved it truly👍

incredible video, you guys are amazing

It is important to mention that Perelman completed Hamilton's program. The idea of Ricci Flow with Surgery was already floating around, Perelman just finished the job.

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.

Amazing Vid .. Thank you Creating it..

Man that was awesome

Oh man!!! Beautiful indeed, isnt´it. Let me tell you that I didn´t have any idea about Perelman contribution. Great!! Now I think I understand why he didn´t accepted the million dollar prize. Ricci flow was really relevant for him. As for me I think it is a quiestion of humbleness. But what a humble guy!!!!!

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.

Brilliant!

Did he solved N=3 or N=4? I’m confused.

Simplicity at its core 💯💯

Awesome video

Take a pan of water and try heating the pan, drop some oil randomly, and observe the motion of oil blobs as the temperature increases. Discrete oil bubbles coalesce to form larger circular blobs of oil, eventually to largest possible. If the container size is large, the oil drop not only maintains circular shape, but keeps on increasing in size. This seems like a nice physical process for Ricci flow. The g and R properties can be shown to be preserve the flow equations, until turbulence destroys everything to make it point like oil drops.

That's a very simple and cute video for beginners. I hope you will get more attentions.

Wow great channel .. Nice explanation

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.

Best explanation!

Wow glad I discovered your channel. You’re going to be the next 3blue1brown.

I hope to become such a fantastic mathematician in the future!

Excellent

Amazing explanation can you do similar tutorials on other clay institute problems

This concept reminds me of how glass condenses when its heated up; regardless of its initial shape it always wants to end up as a sphere with enough time and heat.

Amazing video ..... 👍👍👍👍

This, super short explanation of the ideas behind the proof of the Poincare conjectute, is brilliant and also deserves a prize. I had written a short explanation of the proof of the Poincare conjecture for physicists. It got 1325 reads at arXiv.org. Knowing what this is all about in details, I freely admit that for the unassumed readers it is best among the best. This is an example of how books on math should be written for school children. Only late Martin Gardner would be able to come close to this gem.

The inversion/eversion of the circle is best model for our manifold.

amazing content, wow

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?

When I see Ricci Flow in the title, I subscribe :D

Simplifying such intricate math takes some grt effort ..... kinda what this video does here.