Your general statements are correct but your example of Wiles is quite wrong. Wiles ideas and their developments in the general area of &quot;modularity of Galois representations&quot; (which this comment box is too small to explain) led to a huge explosion of results. Taylor&#x27;s work on the Artin conjecture and the Sato-Tate conjecture, Khare-Winterberger proof of the Serre conjecture,...