Differential Topology | Lecture 1 by John W. Milnor

Nice "Introduction" music.

Thank you very much for sharing.

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

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.

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。

I was fuckin jammin to the intro music.

A singularly beautiful exposition.

The days before PowerPoint.

lovely thanks so much.

Brilliant lecture, so well-organized, so clear.

beautiful lectures!

milnor god!

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

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.

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 !!!! :)

You're cute😜

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

So wonderfully communicated

Topological topology, great :D

Legend john Milnor !!

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.

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

John Milnor : the greatest of all time

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

seeing him at my uni is such a moral booster

His book about Vinnie the Pooh is much more clear!

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

The projector 💀 love it

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

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

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

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

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

Such a clear presenter.

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

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.

It is interesting to see so many middle aged people in the audience.

Smooth lecture