"resolution of the four-color conjecture
by Appel and Haken in 1976 (though it is now reproven with less need for
computer verification by N. Robertson, D. P. Sanders, P. D. Seymour and
R. Thomas),"

This should be rephrased. Even in the newer proof, there are still  
portions (in particular, the reducibility phase) which are  
essentially impossible for a human to verify. I vaguely remember a  
statistic like: 20 minutes on a desktop machine, maybe 10 years ago.  
So I would say, in practical terms, there is just as much need in the  
newer proof for computer verification as there was with the Appel +  
Haken proof.

Also some nitpicky things.....:

"something isn't done to reverse this trend" => "something is not  
done to reverse this trend"

"the Kepler's conjecture" sounds awkward, unless I'm missing some  
standard usage. Either "Kepler's conjecture" or "the Kepler  
conjecture"? (Wikipedia uses the latter.)

"defense department" => "Department of Defense"

Finally, I share Tom's concerns about the sentence "No journal would  
make a statement like Mathematica....". I'm wondering if you could  
make more explicit exactly what kind of statement the journal could  
make, which you would consider isomorphic to Mathematica's statement.  
It's not quite clear to me what such a statement would be.

david


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