The Four-Color Problem

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[theprofessionalfence-sitter]

If I recall correctly, the main part of the prove of the four colour theorem was actually done manually: They did a lot of work to show that the problem can actually be reduced to finitely many cases, it just so happened that this finite number was too large to be practical to be checked by hand, so they got a computer to do so.

[markharwood]

Funny how a book about the 4 colour problem was printed in black and white!

[nickm]

Ah yes, I learned about this in persona 5

[novideos]

Finally another great video on this channel!

[notsure]

Cool. Vectors. Thanks for sharing. Ai using vectors to assign points with weights using reinman solutions to fractal framework and innovation started in a book like this once upon a time.

[anthonyvossman]

The "proof" of the theorem rests upon the exact same near-axiomatic principle that the Konisburg bridge problem rests - Any bounded S-one shape in 2D can only be bordered adjacently by either an odd number of like spaces or an even number of like spaces. Inferring a four color maximum generalization for 2D maps is trivial topology from there. (V, F, E, 2) = four numerical metaphors, four colors.
Of course, this will not necessarily generalize to higher dimensional maps because in those cases you are dealing with a multiplicity of faces both interior and exterior. A plane in space has two faces while a polyhedron has many and you must always additionally take into consideration the "color" of the space into which the map is embedded.

The problem that mathematicians seem to be addressing is different and is essentially a problem concerning how to develop an efficient, generalized algorithm to guide the coloring process to any size map of odd or even spatial totality. And this can perhaps only be addressed by a brute force, trial and error verification procedure which relates to a travelling salesman (PvNP) problem .