Four color problem finally proved without a computer?

[amichail]

http://arxiv.org/abs/0911.1587

[mbrubeck]

Is there any reason to expect more from this (non-peer-reviewed) paper than from the hundreds like it that have failed before?

Edit: At least it appears to be by an experienced mathematician and (at first glance) fairly coherent. So it should be possible for other mathematicians to review it for correctness.

[jmount]

It is always hard to check these longish proofs. For this one it takes a bit of digging to find what the proof method is (versus what parts are the survey). The method of this write-up seems to be at the end of section 3 on page 20 where Jin Xu has cut a general graph up into smaller parts (which are claimed to be 4-colorable by induction hypothesis) and then needs to show they can be glued back together without ruining the coloring. Adding to the difficulty is the fact that the 4-color theorem is true- so you can't expect to whip up an over all counter-example. You would have to show some step fails to meet the assumptions of the next step.