The DUMBEST Rule for Maps.

Maps have a rule that incredibly frustrates me, so I'm gonna purposely avoid it. 𓅱

0:00 - WORST Rule
0:30 - Innovator
1:07 - Starting Map
2:38 - Adjustments
3:26 - New Map
4:39 - Finding "Proof"
5:19 - YOUR Maps
5:59 - 3D MINECRAFT MAPS
6:34 - DETERMINATION
7:39 - Ŝ̬ᴜβŜ̬ᴋʀiβ𓅱

[kemcolian]

"people can't prove that it's right. the only way to prove that it's right is to make every single conceivable map ever. you can't do that, nobody can do that"
funfact: people did infact do that, using computers. thats one of the reasons why this proof is so popular, and was questioned when it first came out. nowadays however we have accepted computer based brute forcing as a valid method of proof.

[darreljones]

The 4 color theorem only applies to maps on a plane or sphere. If you draw the map on a torus (doughnut shape), you need seven colors.

[enderboy]

I have an idea: Simply don’t. Make the colors touch, be the true rebel that you are

[itsnottylor]

Oats: there's no proof
Oats: *shown proof*
Oats: I'm not reading that

[caspermadlener]

This guy trying to break the second most famous theorem in the entirety of mathematics, and I love it.

[ampisbad]

love the fact that he looked up a formal proof, saw that it was a formal proof and elected to ignore it, 10/10 video, good luck in your lifes mission, Im sure it will break and/or fix maths

[JoshuaWillis]

As a math teacher, watching this man attempt the impossible so confidently is sending me.

[aultain]

The only thing the 4 color theorem fails in is exclaves(originally i said enclavs, but it was an autocorrect), then you need to use another color.

[Artism_vpn]

The 4 colors theorem will never stop bothering me to death

[Ani_Misc]

If you give a country an exclave between two or three countries, you will need a 5th color. The 4 color theorum only stands to countries with consistent bobrders (no exclaves or enclaves)

[Flightkitten]

If this man actually broke this theorem during a Twitch stream would be funny as hell

[MithicSpirit]

if you allow discontiguous regions (real maps do this for things like the US+Alaska) then the minimum number of colors is unbounded.

[elitettelbach]

The way he so casually just tried to disprove a mathematical theorem on stream is amazing to watch. Appreciate your creativity!

[Starlights]

I like how he says "I am not going to read all that" when he finds formal real proof. He is just ignorant and determined.

[maximilianwarren]

Ahem. The theorem is stated to apply to only 2d maps. A donut requires 7 colors instead of 4. A cube needs 6.

[xtieburn]

Hmm, I wondered if anything about non-Euclidean geometry could get past this, but apparently in graph theory it just doesnt matter.

[quelfth]

So, there are a number of interesting ways that you can do this, although they are all accounted for by the theorem and specifically excluded.
1) The most obvious example is to just make a 5-slice pie. If we consider the corners to be touching, then we need five colors, although the theorem explicitly does not count corner connections.
2) If your map is allowed to be a fractal, then this is possible. I couldn't find an actual example, but the Newton-Raphson fractal seems like a good place to start. Though technically, if you zoom in on this fractal, the shapes _only_ ever touch at corners, so by the standard rules of the map theorem, you could just color the whole thing one color, since corners don't count.
3) The four color map theorem also doesn't work if you draw the map on a donut. On a normal one-hole donut, the number of colors increases to 7, and then adding more holes slowly increases the number of colors required from there.
4) For an example that might actually matter for real-life maps, the four color map theorem does not work if countries are allowed to have separated sections that are part of the same country, but not touching the rest of the country, and that we require the whole country to be one color. So, this is like how Alaska is part of the US, dispite not actually touching the rest of the US. If you have some countries like this, then you could need more than four colors for your map.

[Atlantic-Indi]

My favourite part is when he talks about maps

[ALEGOAnimator]

0:50 if by "super critiqued" you mean killed then yes

[floppy]

You don't have to follow the rule. The fact is that you *can* colour every map in at most 4 colours *IF* the regions aren't disjoint. It's called "Four colour theorem". You can, however, use more than 4 colours if you wish. Or you may *have to* use than 4 colours if there are disjoint regions (which they can be irl). There's no """four colour rule""".
Edit: I watched some more of the video, and uh... yeah. I already told you how to make it need at least 5 colours.