Differential Topology | Lecture 1 by John W. Milnor

Soon after winning the Fields Medal in 1962, a young John Milnor gave these now-famous lectures and wrote his timeless Topology from the Differentiable Viewpoint -www.mat.unimi.it/users/dedo/to... , which has influenced generations of mathematicians. The lectures, filmed by the Mathematical Association of America (MAA), were unavailable for years but recently resurfaced. With Simons Foundation funding, the Mathematical Sciences Research Institute has produced these digital reproductions as a resource for the mathematics and science communities.
Milnor was awarded the Abel Prize in 2011 for his work in topology, geometry and algebra.
The sequel to these lectures, written several mathematical lives - and a Wolf and an Abel Prize later - is "Differential Topology Forty-six Years Later,"- www.ams.org/notices/201106/rtx...
Source of the above information and lecture: www.simonsfoundation.org/scie...
Also quite helpful:
Differential Topology
Lectures by John Milnor, Princeton University, Fall term 1958
Notes by James Munkres - www.maths.ed.ac.uk/~aar/papers...

[@robertwilsoniii2048]

I'm seeing just how important linear algebra is. Slowly. It's truly amazing how math builds on itself, starting way back to the Peano axioms. I'm starting to see the beauty of mathematics, after 20 years of hating it.

[@ivonemilena.2626]

6 4

[@gauravnainwal5026]

I had the same realisation when I went to university. Linear Algebra is very important especially if you are an Analyst or a Geometer.

[@sossupummi]

it just takes the removing of necessity (forced math teaching) and letting people be interested in the subject on their own

[@sv-xi6oq]

@@sossupummi Well said.

[@Itzak15]

It's amazing how clearly you can hear and see this lecture from so long ago

[@charlesklimko492]

Nice "Introduction" music.

[@danielrussell2190]

One half expects him to fly in on a magical flying Ford Galaxie, with a talking shaggy dog in the passengers seat, and then to perhaps crash a little at the front of the classroom, the awkward mad genius he must be as suggested by such a soundtrack. But also, he is only a mathematician.

[@jackozeehakkjuz]

Only a mathematician. Ha. Those people are mad.

[@addemfrench]

I was fuckin jammin to the intro music.

[@aryamanmishra154]

seeing him at my uni is such a moral booster

[@arkapointer]

I can't thank you enough for uploading these. Greetings from a mathematics undergrad from India.

[@chandankar5032]

R u a graduate now ?

[@arkapointer]

@@chandankar5032 Yes. I finished my Bachelor's and my Masters too. I am now a PhD student.

[@chandankar5032]

@@arkapointer sir i am a undergrad now, sir is there a way i can connect with you ?

[@arkapointer]

@@chandankar5032 give me your email ID.

[@sv-xi6oq]

@@arkapointerAwesome! How’s it going and what are your research interests?

[@oet2633]

A singularly beautiful exposition.

[@ptyamin6976]

So wonderfully communicated

[@elenapoma5432]

I really appreciate those videos uploaded. Currently, I'm studying maths at the university and I found out how interesting is geometry ( both differential and algebraic). Moreover, those videos are useful to me, because my thesis concern with what Milnor wrote about differential topology. Great job !!!! :)

[@mikes9012]

It's math, not maths, ok guvnuh

[@acirjunior26]

John Milnor : the greatest of all time

[@rajarshichatterjee3281]

Legend john Milnor !!

[@inkland2003]

beautiful lectures!

[@rbnn]

Brilliant lecture, so well-organized, so clear.

[@Beegeezy144]

I love the way people used to speak.

[@chetorisirabi]

Thank you very much for sharing.

[@Mike.Freeman]

First time I've heard of Milnor was in the Sylvia Nasar's book, "A Beautiful Mind" (5th chapter)

[@liceous]

The projector 💀 love it

[@abhishekkumarsharma192]

Love the way he teaches....but the real feel of mathematics comes when it is done with chalk and talk method

[@alejandraescalante3506]

I am student Mathematics. The video is a great forms topology again place and enjoy the transition. Greetings for Mexico.

[@lukealucard]

lovely thanks so much.

[@kazenorashid5732]

milnor god!

[@sv-xi6oq]

Such a clear presenter.

[@siddharthaganguly9286]

It's great to learn the subject from the people who developed it taken it further. Thanks for uploading much appreciated.

[@paololeonetti8329]

Topological topology, great :D

[@steliostoulis1875]

Paolo Leonetti lol

[@Hank-ry9bz]

17:55 parameterizations/coordinate patch; 23:00 mobius

[@Hank-ry9bz]

25:50

[@drbonesshow1]

The days before PowerPoint.

[@68ootani]

J・ミルナーの解析的位相幾何学の講義らしいが、1958年プリンストンで何かの会議の際の収録でしょうか？しかし、こんな彼の講義録が残っているとは、大変面白いですね。ポアンカレに始まる、現代では「トポロジー」と、呼んでいる位相幾何学で活躍したミルナーの本は有名で、しっかり学ぶには論文や著作が好いのですが、映像は別の意味で、新鮮だね。声と映像が見られるとは凄いですね。当時の雰囲気が手に取るように分ります。映像をどうも有難う。1958年ですので、しっかりとネクタイとスーツを着ています（笑）。この辺が時代を感じさせますな～。今の国際会議では、殆んどノータイで普段着で集まりますからね。それからＯＨＰに、何か、フエルトペンで直接書いていますね。この辺も時代を感じさせるものです。

[@despicableone4495]

I cannot speak sorry

[@ivanjorromedina4010]

Does anyone know, which name does he say in 32:12? It doesn't sound like any mathematician I know (whitehead, poincare, betti, riemann, noether, mayer, vietoris,etc) Sounds like a russian or east europe name.

[@koenigmagnus]

Hurewicz

[@preben3453]

He's speaking about Hurewicz. en.wikipedia.org/wiki/Witold_Hurewicz

[@mikes9012]

Love how he just starts the talk without thanking or acknowledging anyone. Classic sperg.

[@mehrdadassar2542]

Here we clearly see what ''expert'' is.

[@StewartMNash]

I think the introduction was wrong. George Bernard Dantzig was the one who did the unsolved statistical problems thinking they were homework problems.

[@itssoblatant]

You are right in thinking that. This was an interesting read: goo.gl/zovB1I

[@dicipulosdenewton3956]

Yes you are right, but that also happened to Milnor.

[@natepolidoro4565]

They had just not yet been graced by The Beatles' "Rubber Soul".

[@stearin1978]

His book about Vinnie the Pooh is much more clear!

[@GastroenterologyPINNs]

How the voice’s clear like nightsky in those days 😢

[@heyyoududeyesu]

I have absolute no idea this guys is talking about. But I am oddly drown to this video.

[@sanjursan]

Daniel Hu: I kinda agree, I was drowned, also!

[@lucasm4299]

@@sanjursan I would recommend looking at real analysis or topology.

[@abajabbajew]

Of course they were only in the beta-testing stages of OHPs in the mid sixties. They were still very rare, costing about $100,000 each and were subject to persistent ink-smearing until NASA could straighten out the fundamental physics of writing on clear, flexible plastic in zero-G. It's what really made it possible to get to the Moon by 1969. By the early seventies, they had become so cheap and reliable to produce that even community colleges could easily justify the $2000/unit price tag and they began appearing in major lecture series like this one. Notice how the audience so calmly takes this technical magic in its stride, where only a few years earlier they might have rushed from the theater, convinced the giant hand was actually coming out of the screen.

[@jordinwang9378]

Paul's 2nd Channel i

[@mastershooter64]

wow

[@LeconsdAnalyse]

You're cute😜

[@davidwilkie9551]

Empirical assertion that emulates Analog Computation?, so it's all a construction of precedents, ..a virtual reality established by repetion of stable actions and consequences. Therefore a subset of time-timing definite statements accepted as enduring definitions.

[@heavycalculus]

Douchebag

[@98danielray]

do you do these kinds of nonsensical shitposts often?

[@despicableone4495]

Fuck you

[@yopenzo]

The guy may be a genius, but he's boring, dry and unpleasant. Maybe he's simply shy, but they are characters like him. that make you abandon the desire to study mathematics.