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 KZfaq; 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

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

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 👏

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

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!

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

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 KZfaq! Thanks for the video :)

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

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

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

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

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

This video deserves million views. Quality content.

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

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

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

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

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

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

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

another awesome video buddy!

Thanks man. Outstandingly clear.

What an incredible video, your channel deserves to be huge

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

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...

Awesome videos Man!!

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! :)

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

Sick animations man! Good job

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

Absolutely amazing and concise explanation!

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

This was helpful. Thank you much

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

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.

Excellent video .. thanks KZfaq thanks Aleph 0 . Please keep making more

Very interesting, informative and worthwhile video.

Great video! Love it.

Great work and clearly explained 👍👍

This is so cool! Thank you for the video.

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

Thank you for this wonderful video! :-)

excellent explanation, thank you so much!

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

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

Great video. Thanks for the presentation.

This video is a triumph of modern mathematics

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.

Excellent!!!

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 .

Iam happy that I found this channel

Thank u for this one...💯❤

Amazing explanation!

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

The sound is messed up near the end

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

Man that was awesome

Well done! Nice channel!

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.

Loved it truly👍

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.

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.

Great video!

Amazing Vid .. Thank you Creating it..

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

incredible video, you guys are amazing

Brilliant!

Best explanation!

Amazing video and content! What program do you use to make the animations?

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 😊

Simplicity at its core 💯💯

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

i love watching these kinds of videos and confusing myself

how do you make these geometry animations? 3b1b does it but less with the dough style shape you used.

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!!!!!

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

Awesome video

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

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.

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.

Excellent

How is his solution homeomorphic if he cuts monolitic object? And what is n7 dimension?

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

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.

How did he cut the object and replace part of it with a sphere?

So, in the begining of the solution, you take apart the singularity with another surface, like you do with divergence theorem and stokes in calculus 3? Is it something like this? but a few orders of magnitude higher. Im preparing for a double diploma in math and engineering, any answer will e appreciated.

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

Hey can you tell me your editing software and software which you use for creating the graphics.

n=3 is one of the greatest parts of mathematics