On the flip side, the computer proof at least resolves the question of whether a given conjecture is true. The proof of the four color theorem by computer in 19

On the flip side, the computer proof at least resolves the question of whether a given conjecture is true. The proof of the four color theorem by computer in 1976–89 opened the door to simplifications and clarifications of the proof in the decade following. This is not unlike a lot of the difficult proofs of the last century. The receommended path to understanding Wiles's proof of Fermat's Last Theorem begins with Yves Hellegouach's book, Invitation to the Mathematics of Fermat Wiles http://www.amazon.com/exec/obidos/ASIN/0123392519/donhosek http://www.amazon.com/exec/obidos/ASIN/0123392519/donhosek and then Gary Cornell's Modular Forms and Fermat's Last Theorem http://www.amazon.com/exec/obidos/ASIN/0387946098/donhosek http://www.amazon.com/exec/obidos/ASIN/0387946098/donhosek which assumes a graduate student's understanding of number theory and then the reader is ready to actually read Wiles. When I was in grad school, I remember reading a comment from someone talking about looking at her roommate's materials for her PhD in English and realizing that while what she had was comprehensible to her even if she didn't necessarily understand any of it, her own materials for her math PhD were completely unintelligible to outsiders.