The Weil conjectures are a set of important hypotheses in algebraic geometry proposed by the mathematician André Weil in the 1940s. They relate to the properties of algebraic varieties over finite fields and connect these properties to number theory. The conjectures suggest deep relationships between geometry, topology, and arithmetic. These conjectures were proven in the 1970s by Pierre Deligne, among others, and are fundamental to the development of modern mathematics. They have implications for the study of zeta functions of varieties and have influenced various areas, including number theory and mathematical physics.