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5$\begingroup$ Is this long list of two word answers OK? This almost feels like some sort of spam. $\endgroup$Adrian Barquero-Sanchez– Adrian Barquero-Sanchez2010-06-11 02:39:12 +00:00Commented Jun 11, 2010 at 2:39
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$\begingroup$ Wouldn't it be better to piece them together at least? $\endgroup$Adrian Barquero-Sanchez– Adrian Barquero-Sanchez2010-06-11 02:41:10 +00:00Commented Jun 11, 2010 at 2:41
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22$\begingroup$ It's a big list, proper form is to separate them. $\endgroup$Steve Huntsman– Steve Huntsman2010-06-11 03:06:25 +00:00Commented Jun 11, 2010 at 3:06
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5$\begingroup$ This is an excellent answer. In the 19th century Heawood proved the 5 color theorem and gave a false proof of the 4 color theorem. But his ideas in the proof of the 5 color theorem were the basic starting point for all further progress. $\endgroup$paul Monsky– paul Monsky2010-06-11 10:42:05 +00:00Commented Jun 11, 2010 at 10:42
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9$\begingroup$ Indeed Heawood proved the 5-color theorem. But I'm not aware that he gave an incorrect proof of the 4-color theorem. What he is known for doing is finding a flaw in an 1879 supposed proof, by Kempe, that had stood for 11 years. Perhaps at least as impressive, he determined the "Heawood number" -- an upper bound for the chromatic number -- for every compact surface, and conjectured it was the actual chromatic number. This number turned out to be the actual chromatic number of every compact surface except the Klein bottle, as shown by Ringel & Youngs (except for the sphere) in 1968. $\endgroup$Daniel Asimov– Daniel Asimov2010-06-12 02:12:02 +00:00Commented Jun 12, 2010 at 2:12
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