 Sergei Gelfand and Yuri Manin remarked around 1988 in their "Methods of homological algebra", that unlike Galois symmetries acting on other cohomology groups, the origin of "Hodge symmetries" is very mysterious, although formally, they are expressed through the action of the fairly uncomplicated group formula_71 on the de Rham cohomology.Since then, the mystery has deepened with the discovery and mathematical formulation of mirror symmetry.A variation of Hodge structure (,) is a family of Hodge structures
parameterized by a complex manifold "X".