The Hodge conjecture is a fundamental question in algebraic geometry, a branch of mathematics that studies geometric properties of solutions to polynomial equations. It proposes a relationship between the topology of a non-singular projective algebraic variety and its algebraic cycles. Specifically, it suggests that certain classes of cohomology can be represented by algebraic cycles. This conjecture was formulated by the British mathematician W.V.D. Hodge in the mid-20th century. It remains one of the central open problems in mathematics, with implications for various fields, including number theory and string theory. Solving it could deepen our understanding of the connections between geometry and algebra.