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It is stated in many places that the first published reference to the four-colour problem (aka the four-color problem) was an anonymous article in The Athenæum of April 14, 1860, attributed to de Morgan.

I was poking around in earlier issues of The Athenæum and found this on page 726, June 10, 1854:

    Tinting maps.—In tinting maps, it is desirable for the sake of distinctness to use as few colours as possible, and at the same time no two conterminous divisions ought to be tinted the same. Now, I have found by experience that four colours are necessary and sufficient for this purpose,—but I cannot prove that this is the case, unless the whole number of divisions does not exceed five. I should like to see (or know where I can find) a general proof of this apparently simple proposition, which I am surprised never to have met with in any mathematical work.   F.G.

I cannot find any mention of this item anywhere, so my question is whether this information is new.

As far as I can tell, "F.G." is not identified by the magazine. Two obvious candidates are Francis Guthrie and his brother Frederic Guthrie, who discussed the question starting in 1852. An outside possibility is Francis Galton, who was involved in the problem at a later date (see Crilly, Notes and Records of the Royal Society of London, Vol. 59, No. 3 (Sep. 22, 2005), pp.285-304). So my second question is "who was F.G."?

Added: http://arxiv.org/abs/1201.2852 Suggestions for improvement welcome.

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Brendan, two tiny typos you might take time to fix, since your posting here is likely to get copied and circulated: The publication is spelled Athenaeum (at least that's how it's spelled elsewhere), and I'm guessing there should be an "n" in "distinctness" (or else there should be a "[sic]"). –  Barry Cipra Jan 12 '12 at 15:10
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Since De Morgan (according to Wilson) says that Francis Guthrie brought the problem to De Morgan's attention in 1852, and Galton only seems to have been involved from the 1870's on, it seems a safe bet that F.G is Francis Guthrie. –  paul Monsky Jan 12 '12 at 15:59
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Thanks for this interesting find. And thanks also to Igor for pointing out that it was missing from Wikipedia — I've updated the Wikipedia article. But you know, when you discover a curious omission from Wikipedia, it would probably work more reliably to edit the Wikipedia article yourself so that it is no longer an omission, or at least to leave a pointer to it on the article's talk page, rather than hoping that some other Wikipedia editor happens to randomly pass by and notice your posting. –  David Eppstein Jan 13 '12 at 2:06
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I plan to write a 1-page paper about this, quite soon. –  Brendan McKay Jan 13 '12 at 5:53
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Ok, 2-pages. But I wrote it and sent it to a journal. Wish me luck ;). –  Brendan McKay Jan 13 '12 at 14:08

3 Answers 3

up vote 15 down vote accepted

This is very interesting. Congratulations of finding it -- I'll adapt my 'Four colors suffice' book accordingly in the forthcoming new edition. Brendan, if you write it up, make sure that you always write 'De Morgan' and not the incorrect 'de Morgan'. Robin Wilson

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Thanks, confirmation from an expert that it is new is exactly what I needed. I did spell De Morgan incorrectly in the paper I submitted, but I'll be sure to fix it. Brendan. –  Brendan McKay Jan 22 '12 at 4:43

First, congratulations to Brendan for a remarkable discovery. I think it opens up the possibility of more documentary evidence on the early history of the 4CC. We know that in addition to the famous letter to Hamilton in 1852, DeM also wrote to Whewell (9/12/53) and Ellis (24/6/54) about it. I discussed these letters in a short paper in the Archive for History of Exact Sciences in 1983 (pp163-170). The fact that the letter to Ellis is very soon after the the FG Athenaeum piece raises some obvious questions. Did Ellis write to DeM about the 4CC? Why is the DeM to Ellis letter in the Whewell papers at Trinity? Was there other correspondence stemming from the FG piece?

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Welcome to MathOverflow Norman.... –  Gordon Royle Jan 22 '12 at 9:55
    
I am so happy that, I am in a common place with some best mathematicians. Welcome dear Norman... –  Shahrooz Janbaz Jan 22 '12 at 13:41

I am making this an answer even though it is nothing like an answer simply so that I can include a link to the page in question with a fair guarantee that the URL will not be broken. It is a fantastic find. I have trouble visualizing the meaning of "I was poking around in earlier issues of The Athenæum" after looking at the page itself. I assume you were using various search criteria. I don't know how else you would have found this particular needle in this particular haystack. For those that need strong glasses, the paragraph in question is in the middle column, one paragraph from the top.

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Yes, I was searching in a large magazine database. There were many false hits, so I was lucky to notice the one that mattered. –  Brendan McKay Jan 13 '12 at 15:49

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