Andrew Wiles’s journey in proving Fermat’s Last Theorem demonstrates that transformative discoveries emerge when imaginative insight meets meticulous analysis. His work was driven by an inner conviction—a spark of intuition—that hinted at hidden structures in mathematics. Coupled with decades of rigorous effort, this creative insight enabled him to bridge gaps between abstract theory and formal proof. In this way, Wiles’s achievement exemplifies the balanced fusion of intuition and rigor, illustrating that the pursuit of truth requires both the freedom to imagine and the discipline to verify.