Complex sentence: Mathematicians prefer to avoid proofs with large numbers of cases because these proofs feel inelegant--they leave an impression that the theorem is only true by coincidence, and not because of some underlying principle or connection.
Split into simpler sentences: Mathematicians prefer to avoid proofs with large numbers of cases. A proof with a large number of cases leaves an impression that the theorem is only true by coincidence, and not because of some underlying principle or connection.