# Human checkable proof of the Four Color Theorem?

Four Color Theorem is equivalent to the statement: "Every cubic planar bridgeless graphs is 3-edge colorable". There is computer assisted proof given by Appel and Haken. Dick Lipton in of his beautiful blogs posed the following open problem:

Are there non-computer based proofs of the Four Color Theorem?

Surprisingly, While I was reading this paper, Anshelevich and Karagiozova, Terminal backup, 3D matching, and covering cubic graphs, the authors state that Cahit proved that "every 2-connected cubic planar graph is edge-3-colorable" which is equivalent to the Four Color Theorem (I. Cahit, Spiral Chains: The Proofs of Tait's and Tutte's Three-Edge-Coloring Conjectures. arXiv preprint, math CO/0507127 v1, July 6, 2005).

Does Cahit's proof resolve the open problem in Lipton's blog by providing non-computer based proof for the Four Color Theorem? Why isn't Cahit's proof widely known and accepted?

Cross posted on MathOverflow as Human checkable proof of the Four Color Theorem?

• It's on MO, too. Nov 3, 2010 at 13:27
• The question presupposes that Cahit's claimed proof is actually correct. Nov 3, 2010 at 13:52
• I don't understand why is there so much appeal for a human checkable proof of this result? Why aren't people demanding a human checkable proof that 615789648168*54681684648 = 33672415350625446924864? (If you can actually do that yourself then triple the number of digits.., it's just an example to illustrate my question anyway)
– anon
Nov 3, 2010 at 17:03
• Muad, I think that what people want most of the time is insightful proof - proof that not only tells us "it's correct" but also helps us understand WHY it is correct. A human-verifiable proof is not, of course, always an insightful proof; but it's a start. Nov 4, 2010 at 16:40
• I don't think it's fair to think of all computer verified proofs as non-insightful. The Appel-Haken proof of the 4-color theorem is insightful: it says all you need to use is discharging. I don't see why thousands of cases is any less insightful than 4 cases. Nov 4, 2010 at 23:07