👉 One of the most remarkable accomplishments in modern mathematics is Andrew Wiles's proof of Fermat's Last Theorem (FLT), a problem that had gone unsolved for over 350 years. Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Wiles, with the help of Richard Taylor, demonstrated that FLT holds true for all integers n > 2 by proving a special case of a more general theorem known as the modularity theorem for elliptic curves. This proof is a masterpiece of number theory, combining deep insights from algebraic geometry, modular forms, and Galois representations. The proof involves constructing a complex relationship between elliptic curves and modular forms, ultimately showing that if FLT were false, it would lead to contradictions in these mathematical structures. This breakthrough not only resolved a centuries-old puzzle but also showcased the profound interconnectedness of various branches of mathematics.
