While Andrew Wiles’s success with Fermat’s Last Theorem is often celebrated as a balance between creative insight and strict logic, one might argue that this portrayal oversimplifies the dynamic. In practice, intuition can be fundamentally at odds with rigorous proof; imaginative leaps might lead to elegant ideas but can equally mislead if not eventually anchored in formal validation. Critics contend that the eventual triumph lay more in painstaking, labor-intensive verification than in harmonious collaboration between two distinct modes of thinking, suggesting that it is the dominance of rigor—and not a seamless blend—that ultimately secures mathematical truth.