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I removed several sentences that seemed loaded, contrary to WP:NPOV. Consider the sentence "Even Appel has agreed, in numerous interviews, that it lacks elegance and provided no new insight that has guided future mathematical research", which, to me, is a glaringly biased and completely unsourced statement ("numerous" also seems an exaggeration to make the point). Phrases like "even Appel" are leading. There are a number of mathematicians that do find the proof elegant, so a statement that the major achievement of his career "lacks elegance" needs to be sourced and justified for inclusion. In addition "no new insight" is something of an exaggerated claim. The rather random insertion of his children checking the proof is also not a neutral insertion and violated WP:UNDUE.