👉 The failed attempt at proving Fermat's Last Theorem (FLT) by Andrew Wiles in 1994 was based on a connection between FLT and elliptic curves, but it relied on a flawed assumption that all modular forms could be "decomposed" into simpler components. Specifically, Wiles's proof required a special kind of modular form called a "semistable elliptic curve" to be broken down into simpler ones, but he incorrectly assumed this decomposition could always be achieved. This assumption overlooked a critical case where the decomposition fails, leaving a gap in the proof that Wiles later resolved by introducing new techniques and clarifying the conditions under which the decomposition is valid. The failure stemmed from an overreliance on a narrow interpretation of modular forms and their interactions with elliptic curves, which Wiles later corrected by broadening his approach to encompass more general scenarios.
