Hodge conjecture
In 1924, before Hodge even made the conjecture in 1950, Solomon Lefschetz ForMemRS proved it for codimension 1. In other words, every Hodge class in H²(X, ℚ) is algebraic. By duality, this also shows that every Hodge class in Hⁿ⁻²(X, ℚ) is algebraic. Thus, if the dimension of X is 1, 2, or 3 the Hodge Conjecture is true. The Clay Mathematics Institute, and other drummers-up of the Hodge Conjecture as "a hard problem", just want to find proofs for this X, of 4 and higher.