A Colorful Unsolved Problem - Numberphile

James Grime on the Hadwiger–Nelson problem.

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NUMBERPHILE

Videos by Brady Haran

[mebamme]

With a name like "de-grey", what other field could he be working in but anti-aging?

[Madsy]

Every step I take
Every move I make
Every hexagon
Every time I walk
I'll be counting shades

[ivanabraham]

There seems to be some vague hope in these videos, that, somehow in the comment section, some unknown mega talented kid just posts a solution to all of this.

[Muskoxing]

This week on "EXTREME COLOURING with Dr. James Grime"...

[goatmeal]

This episode of Numberphile brought to you by the Ministry of Silly Walks

[joebloggsgogglebox]

It would be nice if they had drawn the graph at 5:10 to scale. It's impossible to draw without crossing edges.

[faastex]

I love the framed brown paper by Ron Graham in the background

[serkif]

I feel that there should be more introductory courses to graph theory in education. There are so many problems that benefit from thinking about them in graph theory, it is doing students a disservice to leave them in the dark on it for so long.

[JcGross]

Wait, there's a scientist called Grey who's field is anti-aging? That's a sign.

[TheMasonX]

Way to go Aubrey de Grey! I like his work against aging through SENS. It's super cool to see him making mathematical breakthroughs and how it inspired them to find an even better walk

[KayvanAbbasi]

Dr. James Grimes picks the most authentic and beautiful subjects. I enjoy listening to him, every time. Sometimes I watch the SingingBanana as well! :)

[EddyGurge]

It's usually way over my head, but James is so easy to listen to and learn.

[evaristegalois]

I’m still waiting for another big breakthrough
to happen with the Riemann Hypothesis

[Rainofskulz]

Oh yeah my boy Aubrey! I was looking for news on his aging work one day about a year ago and found that he had solved this in his free time. Cool dude. :)

[SlidellRobotics]

Correction - 32 degrees offset for the Moser Spindle. I also suggest checking out the Golomb graph as another comprehensible proof that the answer is at least four. It has ten points rather than seven, but it has a lot more symmetry and an easier mental proof: the offset triangle must have all three nodes of different colors. In order to complete the hexagon in three colors, all three nodes which connect to the triangle must be the same. Ergo, four colors required.

[kinggangrel]

I used to fail almost all of my math classes since year 9 (which was alright though 'cause I originally wanted to study chemistry or foreign languages anyway)

BUT especially Dr. Grime somehow managed to make me a numberphile aswell, his motivation and his enthusiasm are thrilling! Last maths exam for example, I got a score of 90 and I unironically started reading my maths books and doing fun algebra stuff in my spare time.

Odd, but I appreciate it.

[B_B_]

thing I love about puzzles like this is how important parsimony is. finding how few is needed sets a wonderful base line for understanding the situation. even better, it makes it simple to teach others about! gods, i love number puzzles :^)

[gavinmann]

0.53

James: its not something that has been solved
Me: MUST. SOLVE.

[NetAndyCz]

Seems so weird you would need such an insanely long walk to suddenly need the 5th colour. The hex tiling is genius though, did not occur to me that it works with hexagons slightly smaller than 1.

[ixcaliber]

Considering the problem requires you to walk the same distance each step, I don't see how these graphs are useful unless you can also prove the graph can be represented on the plane with every edge having a length of 1. It's quite easy to come up with graphs that do not satisfy this property. Fortunately, the Moser Spindel does have this property, though you have to draw the graph in a very different way than shown in this video, thus the "proof" in this video is incomplete.