[JadeNB]

> Heh. I suppose we've proved it, but this author doesn't accept this proof as an explanation for why it's true.

I think that this is a reasonable philosophical position; given the heavily computer-based nature of the proof, even mathematicians who might accept that (say) the proof of the solubility of odd-order groups explains 'why' they are soluble are reluctant to accept this (the 4-colour proof) as a 'true' explanation.

Even if you have no problem with computer-generated proofs, I think that there is a big gap, for professionals and amateurs alike, between proof and explanation.