Hodge conjecture

The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.

1. Why is the Hodge conjecture important?
2. What is the Hodge conjecture problem?
3. How many unsolvable math problems are there?

Why is the Hodge conjecture important?

One reason to believe the Hodge conjecture is that it suggests a close relation between Hodge theory and algebraic cycles, and this hope has led to a long series of discoveries about algebraic cycles.

What is the Hodge conjecture problem?

In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties.

How many unsolvable math problems are there?

In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics (Hilbert's problems), a number of which have now been solved, but some of which remain open. In 1912, Landau proposed four simply stated problems, now known as Landau's problems, which continue to defy attack even today.