What is a Manifold? - Mikhail Gromov

"Manifolds are a bit like pornography: hard to define, but you know one when you see one."
S. Weinberger
--------------------------------------------------------------------------------
2010 Clay Research Conference
What is a Manifold?
Mikhail Gromov
Clay Mathematics Institute
www.claymath.org/video

[@ManWhoLostTooth]

This talk is jam-packed with insane content.

[@aloha5527]

Just amazing.. Beautiful mind.. Good explanation! The mathematical education in Russia was great, , but now greatest russian scientist go abroad..

[@readingRoom100]

That's just sad and needs to be turned around

[@MrKarpovy]

@@readingRoom100 Why? So they would have less time to do math? Russia does not offer optimal conditions for scientists nowadays. And not everyone can be satisfied with a bare minimum, like Perelman.

[@readingRoom100]

​@@MrKarpovy It's unfortunate that we have to communicate in english; I rather speak in Russian or Chinese. At any rate, when understood correctly, my comment meant for the conditions of mathematical research be "turned around". This way, there will be less of a brain drain on Russia, which will in turn benefit the average Russian citizens. However, I guess I do mean that some Russian scientists must "turn around" and go back to Russia, particularly those who are required in the valiant effort to revitalize Russian science. And I imagine that willing leaders among this group would not complain about present conditions, deteriorated as they might be. After all, such leaders work to usher in better conditions.

[@readingRoom100]

@Jayce Decker Wow, it worked! And why does Jerry Hudson and Jayce Decker sound the same person lol

[@NataliaSkorokhod]

Ah! the joys of watching math lectures with built-in KZbin subtitles :D Hours of amusement.

[@vincentzevecke4578]

+Nabil Bouhmad His mathematical papers are very hard to read. His papers are very are not straightforward.

[@M37AL6667]

+Nabil Bouhmad but.. but. but.. but.. but.. these essentially the last question, yow

[@chandrapandey822]

vincent zevecke Haha that's very true I guess that's quite common among Russian Mathematicians except maybe Prelemans paper on Ricci Flow that was very clear and beautiful

[@ashishshukla9760]

Bill Thurston is also there.

[@BartAlder]

non-Aryan table services made me lol.

[@Maria-ms8sr]

one of the most brilliant personalities of our time (but the accent is quite savage to follow, even for a Russian national like myself)

[@JaGWiREE]

I agree, on both notes, lol.

[@spacelogisticsinc468]

To me, his accent is like seasoning on a steak. 👌 - Not a Russian

[@sthetatos]

Try Yuri Manin.

[@souravrakshit4062]

Nice explanation sir

[@ghazan555]

Very nice Talks and I wish , I will do PhD Math (Commutative Algebra or Algebraic Number Theory ) .But I am unable to fined PROFESSOR.. very very nice people are there

[@sanjursan]

Fascinating. But I'm slow. I would love to see a transcript, in English hopefully, so to more easily ponder over each huge idea that he drops like bread crumbs behind as he darts through the forest of that part of mathematics. Any chance?

[@josephzizys]

The conference at which this talk occurred was a celebration of that fact.

[@jnk3775]

Mathematics is always beautiful...!

[@mrtertg2603]

I watched this recently and my intuition is that his talk goes far more deeper than Perelmann s proof of Poincare conjecture in dims 3 . It would be great to be able to follow his way of thinking properly . But I ll come back and try again , it is worth another try .

[@ShivamNadimpalli]

Brilliant!

[@user-jw4ez9xg9u]

I dont understand hardly anything he is saying but wow , brain smashed.

[@tomlynd8836]

At 5:53, is it Cédric Villani by any chance sitting at the left corner?

[@gogyoo]

yep

[@itsRAWRtime007]

wild villani appears

[@Tadesan]

Tom Lynd his accent is also atrocious. do they not teach pronunciation to non native English speakers?

[@seanki98]

His accent is fine

[@seanki98]

Tadesan No, you are not being patronising at all!

[@indunaNo1]

It takes 150 years for math to be turned into tradeable products. Gauss discovered the key mathematics for image and video production in 1800's ( the fast fourier transform) . His ideas power the video we are watching. It will take us another 150 years before Gromov's ideas result in employment.

[@indunaNo1]

yes, agreed, applied maths has immediate applications, I was thinking more of the more abstract areas that seem to have a long incubation period.

[@SerBallister]

indunaNo1 I thought Fourier transforms were based off Taylor series ? I could be wrong though.

[@cristhianda-silva8346]

Are you a mathematician man I am from Pincenton's advanced studies institute. I would like to send you several of my works

[@colonelburak2906]

indunaNo1 Even that is not generally true. Example: Gromov hyperbolic graphs are very abstract and discovered recently, but yet they are important in the analysis of social networks, or the design of electrical circuits in modern computers.

[@M37AL6667]

5:41 Matrix failure..

[@vimalk78]

prof cedric villani 5:55 first row corner seat

[@AmalgamatedTensor]

I mean that front row also features Smale, Nirenberg, and Thurston. Pretty OP

[@zukerman87]

explosion of the mind

[@naimulhaq9626]

Resorting to topology to visualize 4 manifold, compels us to take gymnastic lessons from Orangutans, twisting and turning, yet visualization alludes us. Topology provides some deep insights in group theories/number theories etc., but not 4-dimensions. There are other Technics in mathematics, that we can use. Ramanujan raised the q-series to powers of 24 to count all the partition of N (counting for example, all the photons in the universe-which is a QC function), useful in the mathematics of quantum computing, that utilizes infinite points on a circle, providing superposition of infinite states (qubits), enabling 'determinism' of chaotic complexity.

[@juspreetsandhu8446]

@5:58 - A young and keen Cedric Villani in the audience!

[@alexcwagner]

Who spliced frames of Tyler Durden in this video?

[@OnceUponASpace]

Yeah I realised that after the fact - he was making a joke about his former skepticism of it :) Actually I really liked the lecture, the content was fascinating and the guys sense of humour and epistemic humility was inspiring...

[@sura2513]

i can't understand what it mean face Manifolds

[@TheJayJohn85]

I mean as a lay man I think of differential equation as a shape changing form or some shit is this crazy thoughts or what....Anyone who can answer that be much appreciated.

[@TheRevAlokSingh]

I'd say that's a good way to think of it

[@luiselsen3767]

Gromov's non-squeezing theorem of 1982, means rigid geometric theory? 1985 perhaps.

[@bernd32]

...de point about matematik in general is completely...как бы...

[@sergelawrencenko9701]

Surprisingly, there was only one question after the lecture.

[@viktoriahabarova4746]

Приятный

[@doublepin1917]

Михаил Абрамович, это вы?

[@vadimium]

Так много лекций Громова, и нет ни одной с переводом

[@samowarow]

Вадим Цукерман Те, кому эти лекции интересны, английский должны знать по умолчанию. Наука говорит на английском.

[@bobopokomono-nu3gv]

what a treasure.

[@nobonespurs]

oh yeah easy to hear

[@fizikchy]

Greetings to Bill! :))

[@davidwilkie9551]

If there was to be a Feynman type guess at "knowing it when you see it", then it's going to be a Quantum Geometric, sequential order of probability in possibility, as begun for the Polar-Cartesian connection condition. The 1-0 axial-tangential interval divides&multiplies simultaneously in superimposed symmetry of "numberness", because it's about the sequence of e-Pi-i identities, like Cantor's infinities. 1-0D Quantum Fields Modulation Mechanism is visually similar to shapes forming in clouds, except for the complexity of eternity-now Superposition and infinite numerical conglomeration. If the trumpet shaped spacetime of gravity fields is 1-2ness combinations of "pipe", and the cross-section of the x-y 2D orthogonal plane on the 1-0 z axis are 2×2 i pipe sub-sections of 0-1 Superspin, then this is the transition from 1 to 2 to 4 ... pipe Manifolds (?) "As simple as possible, but no simpler"...

[@stoolpigeon4285]

yeah well you would say that

[@comprehensiveboycomprehens8786]

It's pretty entertaining but I don't think that it will catch on.

[@infinit42652]

На русском, я так понимаю, такой лекции не предвидится ? Спасибо Михаил Леонидович.

[@ticTHEhero]

Никаких лекций тебе

[@mikhailmikhailov8781]

Маэстро Микаэль Громов дает лекции только на франсуа ун инглиш, если тебе не нравится, ехай в Нью Йорк или Париж и жалуйся там ему лично, что он говорит на языке мировой науке со своими иностранными коллегами, а не на русском.

[@BaronStClair]

is this darwin

[@OnceUponASpace]

Oops! Sorry prof - Poincare conjecture has been proved, so it's probability of being true is now 1 XD

[@shoopinc]

MEASUREMENT UPDATE

[@jarekkurczewski-wasp3069]

What is a Manifold = Ⓠ ♔ Spinor and Plateau billiards­ = Ⓠ ♔ 1 2 3 4 Mathematical Structures arising from Genetics and Molecular Biology = Ⓠ ♔ 1 2 3 4 5 6 Probability, symmetry, linearity = Ⓠ ♔ Michał Gromov = ♛

[@jedediahjehoshaphat]

He's like the Slavoj Zizek of Mathematics

[@PelczarTomasz]

Outstanding topic is : How the Helium by "natural powers" had created iron etc and made our sun ...

[@tyler-iy4jk]

a topology with an atlas duhh

[@manooko]

robert bryant in the audience.

[@user-yq1zw3nw5s]

ㄷㄷ

[@thabangjosephkotelo8243]

What is a manifold?Well its like folding a page,but more than one time..............lool

[@neildhan]

Well I liked it at least. It maybe took 4 months, but you get a thumbs up now. :)

[@jeanblanco9773]

The theory of sphere is belony it doesnt explained the mass irregularity on the quantum theory

[@florin604]

yet accurate

[@abhiramdeva1417]

There are a lot of manifolds in pornography

[@jimelias5046]

Great! I know know what a "foil menufolt" is, in that strange language of "teepolougy"!

[@TheJayJohn85]

Ignore that last comment as soon as he was on about the groups and abelian and all sorts of shit I don't understand I tuned in. Why is youtube linking me all these damn videos lol. I understand how geometry is connected to topology well its like a extension but I still don't understand these transform and shit man this is crazy shit to get from a cartesian plane you'd think they find a easier way to describe shape and transforms....translations or whatever. I mean wtf is a manifold its a field which is a shape of some description? Excuse me I am a lay man that keeps getting these types of videos on my youtube feed I probably should not watch them,

[@comprehensiveboy]

I agree, it's difficult to decide whether the difficulty lies in the thing itself or the failure of various people to explain it.

[@Chasmify]

I don't understand what you expected? This is obviously directed towards mathematicians.

[@RougeWaterPoloPlayer]

gromov sounds exactly like zizek

[@mappingtheshit]

+RougeWaterPoloPlayer LOL, totally different accent, manner, and for god's sake, totally different subject

[@avinashbandpatte3630]

How mathematician sit quietly and leasning what othere mathematician is saying but physicist not like that he starting tebate on that😁

[@jesuschristignorantracistf387]

WHY IS IT WHEN THEY ZOOM IN ON THE AUDIENCE SOMEONE IS PICKING THERE NOSE OR THERE EYE S OR THERE EAR AND THEN EAT IT GET A SANDWICH AT THE LUNCH ROOM WILL YA OR THEIR SCRATCHING SOMETHING AND SNIFF THERE FINGER LIKE WE DONT SEE IT .I HAD A TEACHER WHEN I WAS IN DETENTION AFTER SCHOOL SHE WOULD EAT HER EYE WAX AND FINISH HER MEAL WITH NOSE PUDDING FOR DESERT

[@BaronStClair]

is this guy trolling

[@jordans962]

Hey, that orangutan is not nearly as exceptional as me! 🇧🇬, 🇧🇬🇺🇸,🇺🇸,🇺🇸🇧🇬.

[@mechwarreir2]

I can't understand shit, i dont even know if I can trust closed captioning.

c'mon! Beardo's accent sounds nice. I'm a non-native and still understand him. You should try chinesse's accent.

[@OrangutanNationz]

Dribble....

[@anatolykarpov2956]

His accent is very hard to follow with😢

[@samueldeandrade8535]

Subtitles.

[@iop151]

I can't understand this accent

[@AZTECMAN]

Painful to watch: many visual glitches. Difficult to listen to: thick accent. Confusing: wandering train of thought. Maybe this guy is really good (and it went over my head), but I wouldn't recommend this video to anyone unless I was trolling.

[@alexduval4740]

Continuing to calculate to an infinite point... to perfection (story of modern math), meanwhile reality collapses around you... Has the patron of this video actually seen or experienced working with any living matter ever, anything at all?, anytime?, why worry about possible genetic relationships revealed by your "nuisance" science.

[@CarmenEverywhere]

His english is incomprehensible. What he is saying is so disjonted

[@florin604]

I can understand perfectly, and english is my 3-rd language.

[@steliostoulis1875]

@@florin604 me too

[@remlatzargonix1329]

Carmen Everywhere .....Not really. I have no problem understanding his English.

[@monoman4083]

Rubbish

[@wonggaakeoi7168]

shut your fucking mouth up!!! 收你個聲 死蠢

[@sdfdsf4162]

r u from UK, sir&

[@Appmaths2008]

Nothing transparent, not good presenter...sorry but losing time of the listeners...

[@embracingchina1744]

If you are a student visiting from McMaster University, I have this to say ESPECIALLY to you. As a long-time math student, I would respect a lot of what he is saying. However, the truth is that jobs are difficult to get in math, pay is minimal and competition is incredibly high. I question why we should learn or even care about this if none of this will be used by almost any of us to help support ourselves and our families and pay the bills. These are the real-life and important issues, NOT this garbage! And I say this as a long-time math student. THIS IS GARBAGE!!!

[@GavinoFelix]

Well, when the mathematician in question is not only an Abel Prize recipient but has a Permament position at IHES, maybe we proles' would best listen a little harder...

[@embracingchina1744]

Gavino Felix I assume you are mathematician, because your response is completely ambiguous and unrelated to my comment. Good for him that he has a permanent position at IHES, but only a very small percentage are so fortunate and prestigious. The rest are Postdocs (i.e., Temp Workers) who usually have few real life skills that may be demanded in industry, or struggling to find good careers. I question and regret learning all this abstract nonsense when there is little demand for it in the job market and even less demand for it in real life. Bottom line is that for the majority of us, knowing this nonsense DOES NOT PAY THE BILLS!!!!!! I don't know how much more clear I can be.

[@GavinoFelix]

Jason Haradyn I definitely agree with you w/r/t the American Education System/Capitalism taking advantage of post-docs, adjunct professors, etc. What really moves me about this lecture (and the few other 'casual' lectures of his posted on youtube) is that he has nothing to prove and no one to impress - we're getting a once in a lifetime chance to witness a 'great mathematician' not constrained to rigor and formality. More and more I'm realizing that math is and never was just the theorem-proof style presented in textbooks. Textbooks and rigor are great and wonderful, but there's something lost when the social element (talking to other people excited about math, shooting ideas off of one another, 'going out on a limb' with an idea...) of math is silenced. Unfortunately, my opinions, sentiments, reactions, etc. are likely heavily distorted by the fact that I'm in my late 20's and going to school at a community college here in the States. Between stocking grocery store shelves and enduring the U.S. required 'calculus' track before I'm permitted to study 'more advanced mathematics', i'm pretty worn down by the time I find myself with free time. It's just comforting to know that somewhere in the world, people are permitted and encouraged to think without constraints.

[@embracingchina1744]

Gavino Felix Great comment, with some amazing insights. I just want people to know that these days they must consider the education they are receiving and also choose education that has minimal gaps with careers. Unfortunately, the gaps between pure mathematics and the job market, i.e., the real world, are too large, which these days makes me question -- Why?? Why the large gaps? Why do I even care about this theory? Why? Unfortunate, but reality.

[@gigiduru125]

If you can learn all that math, you can surely get a decent job in software development, data science or whatever if you start learning about those fields.