1. What is the current status of the Collatz Conjecture, and what approaches have mathematicians used to try to solve it?

2. What are some examples of algebraic cycles that are known to satisfy the Hodge Conjecture, and what makes these examples different from cycles that do not satisfy the conjecture?

3. What are some open questions related to the Navier-Stokes Equations, and what progress has been made towards understanding these questions?

4. What are some implications of a solution to the P versus NP Problem, and what approaches have been used to try to solve it?

5. What are some potential consequences of a proof or disproof of the Riemann Hypothesis, and what progress has been made towards a solution?