Colouring Numbers - Numberphile

Fields Medallist Sir Timothy Gowers discusses Van der Waerden's theorem.
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NUMBERPHILE

Video by Brady Haran and Pete McPartlan

[jannegrey]

I have to re-watch it, because I didn't get the difference between length and step in the beginning. It felt rushed or shy. I'm not saying it's bad, but it can be missed.

[pbp]

I’m blown away how useful the animations are. They really keep the train on the rails moving forward.

[TamaraTkacova]

Such an interesting way of viewing arithmetics, I like how he explained it

[ojaimark]

I can’t stop laughing at the little sound as the progression humps are being animated.

[ChonGeeSan]

This explanation wasn't clear at all. I'm sure it can be done better. Talk a bit slower, cover important details when they need to be covered, etc...

[realdealsd]

Maybe I am missing something but it seems a rather intuitive conclusion. You have a finite number of colors which to color an infinite number of positions. Eventually you will cover all the possible permutations of colorings and eventually you will repeat all those permutations any number of times.

[whatisthis]

Numberphile: **Uploads at 5 am**
Me: i don't need sleep, i need *_ｎｕｍｂｅｒ_*

[gavin]

I seriously enjoy listening to this guy teach. Please find excuses to get him on the channel more!

[mlkin]

how does he look so old and yet so young at the same time?

[joao]

I appreciate the fact that the curves connecting the terms of the progressions are much like Cycloids.

[thomasanderson]

Fascinating!  I hope you do more videos on Van der Waerden's theorem, and on Ramsey theory in general

[ProfOmarMath]

It's intriguing how the best upper bounds for W(r, k) are power towers.

[ajaxmajor]

there were 4 or 5 different times where i was completely lost in this video. he kinda explained something and then went a direction that i could not follow and made no sense to me. like those six killer examples things? what? those aren’t the only possibilities and why does it matter if we flip the colors around. uncharacteristically confusing.

[adityakhanna]

This video just made me realize that just like this, lying on my bed, about 5-6 years ago I used to binge watch numberphile, just loving all the beautiful results, quite obliviously. Now, I'm doing mathematics in University. Gosh, hindsight is weird

[Thror]

This reminds me of the "forest fire" sequence from your "Amazing Graphs 2" Video with Neil Sloane. v=o8c4uYnnNnc?t=220 for reference. It has similar arithmetic progression constraints.

[FlutterBug]

my understanding of this is, since we are using all of the integers, all of the multiples of those integers are in there too, so no matter what multiple you are trying to use, it will always come up, because it's just. inherently there somewhere

[polares]

Brady you are the greatest interviewer ever

[ErixTheRed]

So this must apply to pi where you use numbers instead of colors. I.e. you can always find a single number x spaces apart y many times in a row at that spacing.

[craigwynnphoto]

"This red here was a forced move, " chess player spotted

[cwaddle]

Another fields medalist added to the numberphile hall of fame