Why was Andrew Wiles’s first announced proof of Fermat’s last theorem incomplete?

When Andrew Wiles first announced his proof of Fermat’s last theorem in 1993, the mathematical community recognized it as a monumental achievement. However, the initial presentation was incomplete because experts discovered gaps in the complex argument during the peer-review process.12

Wiles had spent seven years developing a proof that relied on connecting elliptic curves and modular forms by proving a special case of the Shimura-Taniyama-Weil conjecture. While the core of his work was sound, the specific technical gaps required further refinement. Wiles collaborated with his former student Richard Taylor to address these issues, successfully completing the proof in 1995. The final, rigorous version was published in the Annals of Mathematics, effectively resolving a problem that had remained unsolved for centuries.123