Embedding a Torus (John Nash) - Numberphile

This videos features James Grime with a little bit of Edward Crane.
More links & stuff in full description below ↓↓↓

Nash shared both the Nobel and Abel Prizes. Full details.

Other mathematicians have done much work in this field (we have focused on Nash in these videos).

NUMBERPHILE

Videos by Brady Haran

[NowhereManForever]

Grime has to be my favorite Numberphile speaker.

[TheMaplestrip]

James Grime is so awesome, probably my favorite Numberphile professor.

[BroadcastBro]

Big thumbs up for Dr James Grime, he's superb in his communication technique

[not.dominica]

"There is no great genius without some touch of madness..." - Seneca
A fitting tribute and explanation of John Nash and his innovative work in mathematics. It is a beautiful thing to be able to appreciate creativity in the harshest of disciplines and Nash truly defines thinking differently.

[Mallyhubz]

You really should get Sharpie to sponsor your vids.

[hermes_logios]

This is the coastline measurement paradox. The length of a coastline is infinite if you use a small enough unit of measurement. The more irregularity you ignore by using a longer unit of measurement, the shorter the final measurement will be. In other words, distance depends on granularity.

It’s what Greek mathematicians called “exhaustion” (measuring geometric curves by dividing them into smaller and smaller units), and what algebraic mathematicians call “calculus.” In topology, the granularity is called “smoothness” of a surface.

[PhilBagels]

Much more important is the question:  Where do you get toric balloons?

[PotatoChip]

Prof. Nash and his wife died in a car accident when coming back from receiving the Abel prize. It's weird to see this wasn't mentioned in the video...

[wiwi]

*Picture of the globe*
"This is flat"

WAIT A SECOND

[SalesforceUSA]

I think his story of triumph over his schizophrenia is the most inspiring aspect of his achievements.

[KTC]

RIP John Nash. Your work helped inspire so many mathematicians and economists. May your legacy continue on for many generations to come.

[sphakamisozondi]

03:54, that joke went over most people's heads at a speed of light 😂

[alsoethan]

'waves' 'hand action'

[DustinRodriguez_]

This was a really interesting video, but also a bit sad.  I had not heard that John Nash died yet.  Major bummer.  I'm from West Virginia, where he was from, and his work in game theory has always interested me.. comes in handy when working with simulations.  His life was fascinating, too, in that he suffered from schizophrenia but after years and years of it he made a conscious decision to stop listening to the voices he heard, analyzing the things they said with reason and ignoring anything irrational.  He was able to, essentially, think himself sane.  That is, to me, absolutely astonishing.  I am very sad to hear that after all of the things he survived in his life, a stupid car accident took him from us.  At least he was able to receive the Nobel prize he so deserved before he left us.

[jOpaaD]

Dr. Grime is so good at explaining complicated things in a simple way.

[gabrielsayers]

James is surely the best Numberphile speaker, he explains it all really clearly, without being patronising and while maintaining the audience's interest through his own evident enthusiasm.

[strengthman]

You know, I know a beautiful quote from John Nash
"It's just a theory, a game theory"

[dharma]

The torus has points of positive, zero and negative Gaussian curvature. The "outer" points are elliptic points (+'ve), the "inner" points are hyperbolic points (-'ve), and there are two circles of parabolic points (0) separating them.

[bobbysanchez]

James Grime is my favorite mathematician who appears on this channel.

[AdrianRowbotham]

This corrugation technique appears to be related to the so-called "π = 4 paradox" - whereby constantly cutting corners out of a square (and out of the resulting shapes each step) gets you to an approximation of a circle where the perimeter is the same as the original square.