6 ms·

Differential Topology with Prof. John W. Milnor (1965) [video]

codethief 6y ago
I wish all my math classes had started with beautiful music like that. Also, the way Prof. Milnor started off his class ("In order to start talking about differential topology, I have to first give a few definitions…") really made me chuckle. As a former math student who had to sit through many painful and sloppy math lectures I very much appreciate this no-nonsense (albeit maybe a bit dry & stereotypical) approach to math.
evanpw 6y ago
Also highly recommend his book "Topology from the Differentiable Viewpoint". Or any of his books for that matter; he's a famously good mathematical writer.
- kkylin 6y ago
  I came here to recommend that. And anyone interested in great mathematical writing should read the first few pages of Morse Theory. (The rest of the book is great too, but I especially love the clarity and directness of that opening section.)
- ilyagr 6y ago
  "Topology from the differential viewpoint" is a marvel of a book, and the most accessible one of Milnor's. If you are not quite ready for it, or need some inspiration first, I recommend "Intuitive Topology" by Prasolov (https://bookstore.ams.org/mawrld-4/ https://bookstore.ams.org/mawrld-4/). It is short, has no prerequisites, and communicates the flavor of some of these ideas. (It also covers some knot theory, which is a different subject)
layoutIfNeeded 6y ago
Off topic, but the unsharp mask should have been turned down a notch.
- onecommentman 6y ago
  Can’t be helped. He’s a really sharp guy and you have to overcompensate.
jules 6y ago
These lectures are fantastic, as is his book about Morse theory. Highly recommended. And freely available: https://www.maths.ed.ac.uk/~v1ranick/papers/milnmors.pdf https://www.maths.ed.ac.uk/~v1ranick/papers/milnmors.pdf
- jeffreyrogers 6y ago
  As I'm sure you know, Spivak[0] (whose lecture notes the book is based on) was one of Milnor's advisees at Princeton. I was told by another Princeton PhD who was there shortly after Spivak (may have overlapped, I'm not quite sure) that whenever Spivak had a problem he thought was interesting he would discuss it with Milnor, who invariably had already thought about it and knew the answer. This experience dissuaded Spivak from an academic career because he felt he could never be as good a mathematician as Milnor. At least that's the story I was told. [0]: Same Spivak who wrote the famous Calculus book and a series on differential geometry.
da39a3ee 6y ago
I can recommend setting the background to black in dev tools and putting it fullscreen.
deleted 6y ago
[deleted]

I wish all my math classes had started with beautiful music like that. Also, the way Prof. Milnor started off his class ("In order to start talking about differential topology, I have to first give a few definitions…") really made me chuckle. As a former math student who had to sit through many painful and sloppy math lectures I very much appreciate this no-nonsense (albeit maybe a bit dry & stereotypical) approach to math.

evanpw 6y ago

Also highly recommend his book "Topology from the Differentiable Viewpoint". Or any of his books for that matter; he's a famously good mathematical writer.

kkylin 6y ago
I came here to recommend that. And anyone interested in great mathematical writing should read the first few pages of Morse Theory. (The rest of the book is great too, but I especially love the clarity and directness of that opening section.)
ilyagr 6y ago
"Topology from the differential viewpoint" is a marvel of a book, and the most accessible one of Milnor's. If you are not quite ready for it, or need some inspiration first, I recommend "Intuitive Topology" by Prasolov (https://bookstore.ams.org/mawrld-4/ https://bookstore.ams.org/mawrld-4/). It is short, has no prerequisites, and communicates the flavor of some of these ideas. (It also covers some knot theory, which is a different subject)

layoutIfNeeded 6y ago

Off topic, but the unsharp mask should have been turned down a notch.

onecommentman 6y ago
Can’t be helped. He’s a really sharp guy and you have to overcompensate.

jules 6y ago

These lectures are fantastic, as is his book about Morse theory. Highly recommended. And freely available: https://www.maths.ed.ac.uk/~v1ranick/papers/milnmors.pdf https://www.maths.ed.ac.uk/~v1ranick/papers/milnmors.pdf

jeffreyrogers 6y ago
As I'm sure you know, Spivak[0] (whose lecture notes the book is based on) was one of Milnor's advisees at Princeton. I was told by another Princeton PhD who was there shortly after Spivak (may have overlapped, I'm not quite sure) that whenever Spivak had a problem he thought was interesting he would discuss it with Milnor, who invariably had already thought about it and knew the answer. This experience dissuaded Spivak from an academic career because he felt he could never be as good a mathematician as Milnor. At least that's the story I was told. [0]: Same Spivak who wrote the famous Calculus book and a series on differential geometry.

da39a3ee 6y ago

I can recommend setting the background to black in dev tools and putting it fullscreen.

deleted 6y ago

[deleted]