Talk:Four color theorem

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This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: A Class Top Priority  Field: Topology

Archives:

  • Archive 1 - discussions from before July 2005.
  • Archive 2 - discussion about the validity of Ashay Dharwadker's proof of the four color theorem [1].
  • Archive 3 - April 2005–September 2007

Contents

[edit] Purported disproofs

Purported disproof
Purported disproof
Colored with four colors
Colored with four colors
Image:ColorXXXfixed.png
Another purported disproof by User:Fsswsb : Can't be colored with four colors. The black region in the middle might be colored blue after exchanging the small blue and purple to the left and the right of black box. The white box on the upper right side might be colored red, and after flipping the blue and purple, the black one blue, but then, no more color is remaining for the big white in the lower right corner. Ok, one might color the black box on the right green after changing the small green boxes to red. Therefore, I added the big black box.
...correctly colored.
...correctly colored.

The two top diagrams are the purported disproofs added by User:Fsswsb, the two bottom diagrams are correctly colored by me. -- ArglebargleIV 22:38, 1 November 2007 (UTC)


[edit] Fair use rationale for Image:ColorXXX.png

Image:ColorXXX.png is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in this Wikipedia article constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

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BetacommandBot 15:48, 5 November 2007 (UTC)

[edit] Real life examples of non-contiguous regions

The real life examples don't seem to hold. I can color the map of Azerbaijan (with its neighbors), or that of United States, or Russia without using more than 4 colors.Bless sins (talk) 23:28, 10 February 2008 (UTC)

The examples given are examples of enclaves -- regions separated into two or more noncontiguous parts. They aren't necessarily examples of non-four-colorable maps, but a map with non-contiguous regions is not guaranteed to be colorable with four colors. -- ArglebargleIV (talk) 00:10, 11 February 2008 (UTC)

Good ones! I was thinking of a simpler thing, but it didn't work. --Diego Bank (talk) 02:19, 17 May 2008 (UTC)

[edit] Missouri

Does the state of Missouri, with its eight adjoining states, argue against the theory? If not, perhaps an explanation would be in order? JuanFiguroa (talk) 19:29, 21 February 2008 (UTC)

No, it's quite possible to color a map of the 48 contiguous United States with four colors. [2] DanBishop (talk) 04:36, 8 May 2008 (UTC)

No, since there's no requirement that the eight states touching Missouri be all different colors -- just that any pair of states that touch be different colors. The False disproofs section of the article covers that case in a general fashion, but maybe an illustrative thumbnail map or two would be useful. -- ArglebargleIV (talk) 21:17, 21 February 2008 (UTC)

I have issue with the beginning of the article, "states of a country". US is the only country to call its regions 'states', and even that is really a misuse of the word. Perhaps 'provinces', 'territories', 'divisions' and the like. Ashleyjohnston (talk) 17:34, 2 April 2008 (UTC)

Just off the top of my head, and without doing any research, I know that India, Brazil, Mexico, Germany, Nigeria and Australia all use the word "states" to designate political subdivision of the nation. I believe Austria, Sudan and Micronesia, likewise, have states. The US is far from the "only country to call its regions 'states.'" JuanFiguroa (talk) 23:31, 5 April 2008 (UTC)

[edit] Not by Francis Guthrie?!

This site does not agree with wikipedia: http://members.ozemail.com.au/~lucire/documents/Five_colour_theorem.htm

"[...] This is called the four colour theorem, as yet an unproven mathematical curiosity, first put forward by Charles Dodgson who also wrote Alice in Wonderland."

--130.225.56.42 (talk) 07:02, 2 May 2008 (UTC)

Perhaps that's why she should stay a really expensive psych consultant and not a mathematics historian. Not surprising, Wolfram's Mathworld encyclopedic entry sides with the wiki article. Quaeler (talk) 07:41, 2 May 2008 (UTC)

Well, this is what "What is Mathematics?" By Courant & Robbins, 2nd edition, p. 247 has to say about this problem: "The problem of proving this theorem seems to have been first proposed by Moebius in 1840..." is this a mistake? —Preceding unsigned comment added by 83.130.40.64 (talk) 20:57, 3 June 2008 (UTC)

Probably, although that sounds more plausible. I believe our current sources more though. Dcoetzee 05:34, 4 June 2008 (UTC)

[edit] downgrade to B+?

I think this article does not deserve an A class rating. It does not contain a single word about the theorem's proof. Hence the article is not "essentially complete", as the rating criteria say, in my view. If nobody is against, I will downgrade it? Jakob.scholbach (talk) 08:33, 26 May 2008 (UTC)

Oh, I see, there are some words about the proof. But still I think, the proof gets not that much attention as it should for A-class. (this is reflected by its placement in the history section, and also by the pretty little amount of actual mathematics covered in the text). Jakob.scholbach (talk) 12:27, 26 May 2008 (UTC)
To be fair, the proof is extremely complex compared to the usual level of sophistication in Wikipedia math articles - but there's no reason we couldn't attempt to construct an intuitive outline. Dcoetzee 05:20, 28 May 2008 (UTC)
I've added a basic outline of some of the proof ideas in a new section. It was informative for me and I hope it will be for others too. I'll leave the fine details of C- and D-reducibility for the brave soul who wants to try it. Dcoetzee 09:37, 28 May 2008 (UTC)
Great! Jakob.scholbach (talk) 13:38, 28 May 2008 (UTC)

[edit] Loaded word, unwarranted use

The article states that one to have "faith" in the correctness of the compiler and functioning of the hardware. "Faith" is a loaded word - usually refers to belief not based on sufficient evidence to meet criteria of logical/mathematical or scientific justification. This is most certainly not the case here. For the compiler itself, an inductive logical proof can be constructed. For the hardware, in such cases there obviously isn't sufficient evidence to warrant the claim that it didn't/doesn't work properly. This can also be tested. It's not "faith" simply because the epistemic probability is less then 100%, which it is only for analytic truths anyway - and those are vacuous.

In short, I am changing the wording to "in order to believe the proof, one also has to believe (which can be justified or not) that the compiler works as intended and that the were no other errors, such as in the functioning of the hardware, that corrupted the output." 91.67.150.18 (talk) 23:54, 27 May 2008 (UTC) MPhil