Also Andrew Wiles' six years of focused worked fundamentally depended on very deep work that Ken Ribet had just completed, which in turn relied on decades of hi

Also Andrew Wiles' six years of focused worked fundamentally depended on very deep work that Ken Ribet had just completed, which in turn relied on decades of highly nontrivial work by Mazur, Katz, and others on modular curves and modular forms, which made surprising connections with other areas of mathematics. Finally, Wiles' first announced proof of FLT was wrong, and Richard Taylor collaborated with him to find a correct and quite different proof. (Disclaimer: I published a book on modular forms, and cowrote papers with some of the people mentioned above.)