Shimura-Taniyama conjecture

The Shimura-Taniyama conjecture, also known as the modularity theorem, suggests a deep connection between two areas of mathematics: elliptic curves and modular forms. It states that every elliptic curve defined over rational numbers can be associated with a modular form, a special type of complex function exhibiting symmetrical properties. This link means that properties of elliptic curves can be studied through modular forms, enabling profound insights into number theory. The conjecture was proved in the early 2000s, playing a key role in solving Fermat's Last Theorem and advancing understanding of these mathematical structures.