How Andrew Wiles Proved Fermat’s Last Theorem
For more than three centuries, Fermat’s Last Theorem remained one of the most famous unsolved problems in mathematics . Although the statement is easy to understand, no one could prove it using elementary methods. Fermat’s Last Theorem states that the equation x n + y n = z n has no non-zero integer solutions for any integer n > 2 . The modern proof, completed by Andrew Wiles in the 1990s, did not study Fermat’s equation directly. Instead, it used an indirect argument and ideas from elliptic curves and modular forms . An elliptic curve is a special type of curve defined by a mathematical equation, usually written as: y 2 = x 3 + a x + b y^2 = x^3 + ax + b where a and b are numbers chosen so that the curve has a smooth shape. Example 1: y 2 = x 3 − x + 1 Example 2: y 2 = x 3 + x + 1 y^2 = x^3 + x + 1 Despite the name, elliptic curves are not ellipses . The word “elliptic” comes from their historical connection to elliptic integrals . The strategy begins by assumi...