

Four color problem finally proved without a computer? - amichail
http://arxiv.org/abs/0911.1587

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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.

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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.

