The Four Color Map Theorem - Numberphile

It's not just useful for drawing maps, either: the same principle allows cell towers from interfering with each other, by using four sets of frequencies. Using four sets of frequencies, no adjacent cells have to use the same frequencies.

I love how all this started with some guy filling out a map with colors and noticing that he only needed 4

omg watched this mindlessly 3 years ago when i was in high school then here i am studying graph theory in college coming back to see how it actually works like an hour before midterm

I recall an issue of Scientific American back in about 1974 (more or less) that had an article that purported to show 7 amazing recent discoveries. One was that the best first move in chess was shown to be h4, another was a logical way to disprove special relativity, another was that Di Vinci invented the toilet and another was that someone came up with a map that required five colors. I can't recall the year of the publication, but I can recall the month. The magazine came out on April first......

I never thought I would say this of a mathematician, but I don't believe I could ever tire of listening to James Grime. I actually find myself smiling far more often than was likely ever the case back in my school days. Thank you Dr Grime.

0:04 "It's easy to state" I see what you did there..XD

6:03 careful dude you're gonna summon the devil

11:06 I'm currently studying Actuarial Science at the University of Illinois (same awesome school as Appel and Haken). You wouldn't think the Four Color Map Theorem would show up in an insurance internship, but I showed this theorem to a few of my coworkers and they made a colorblind-friendly map of the U.S. for me to use in a project. Thank you Numberphile!

I learned this in a book called "betcha can't" (which actually has a lot of the problems I've seen on Numberphile). But the story was that the father died and his five sons inherit his land. In the will it says they can divide it up however they want, but each plot needs to be all one piece and must share a border with all four other sons' plots.

everytime i take a test i imagine that he's looking over me and kinda guiding my way to success lol

Enclaves and exclaves can not be considered as the theorem requires contiguous regions. The term "map" in the theorem refers to a physical map as opposed to a political map. This could be confusing to grasp after watching this video as they refer to real-world examples as well as abstractions.

What if it was in 3d? like, with colouring 3d spaces instead of 2d shapes. Maybe filling hollow glass chambers with coloured liquid. How many colours would that take? Would there be a limit?

Yes! James Grime!

3:40 Aww I was hoping for the Chrome logo

I love this mans enthusiasm

Really interesting video; great job! I myself spent a lot of 'doodling' time back in the 80s trying to find a counter example. I also don't like the computer proof for the same reason you stated: it doesn't teach us anything but that some result is true. We don't know WHY it's true. But to me it boils down to a topology problem, not a color problem. I state it thus: The greatest number of closed figures which can be drawn on any 2D surface such as a map or globe in such a way that every figure touches every other figure along a side, is four. You'd literally have to put another figure into the third dimension, making it go above or below the 'plane' to connect it to other figures, thus forcing a 5th color. You simply can't do it any other way. That is what makes the 4 color conjecture true... but, of course, that is not a proof in itself. But I can tell you that I'm done doodling with it. I'm satisfied that eventually, someone will prove it with geometry or more likely topology. Rikki Tikki

"Let's try making a map that requires five colors" second map drawn only has four sections

14:14 look above the o there are 2 yellows

While watching this, I thought at 3:23, you could leave the last quarter circle border unclosed and make a bigger circle around everything. With the existing coloring, it looks like that would need a fifth color. But, after more thinking, it's doable by some shifting on the colors used earlier

Four Color Theorem: Exists Enclaves and Exclaves: I'm about to end this man's whole career