Hodge Conjecture Millennium Problem Solved?

In the twentieth century, mathematicians developed powerful methods to study the shapes of complex objects by approximating them with simple geometric building blocks of increasing dimension. These techniques proved so useful that they were widely generalized, producing tools that helped classify many mathematical objects—though the geometric origins became obscured, and some added pieces lost direct geometric meaning.The Hodge Conjecture claims that for certain well-behaved spaces called projective manifolds (smooth projective algebraic varieties), the pieces known as Hodge cycles are actually rational linear combinations of geometric pieces called algebraic cycles.Although the topic seems far from actuarial science, applications may arise through discrete Hodge theory on graphs and simplicial complexes, which turns these geometric ideas into computable linear-algebraic tools.