The Hodge conjecture is difficult because complex submanifolds are very rigid objects (since they are described by polynomials). In truth, it is very hard to construct complex submanifolds, and there are hardly any of them. Proving that submanifolds exist with out constructing them (an exceedingly handy kind of oblique reasoning) https://dailybookmarkhit.com/story19389486/how-metode-can-save-you-time-stress-and-money