3. [[P=NP]], which states that the amount of time it takes to check a possible answer to a certain kind of problem is equal to the amount of time it takes to find that answer.
4. The '''Hodge conjecture''', which identifies algebraic structures on certain kinds of complex manifolds.
5. The existence of infinitely differentiable solutions to the [[Navier-Stokes equations]], which would imply certain results about turbulence, an extremely common but not at all understood phenomenon.
6. The '''Birch and Swinnerton-Dyer conjecture''', which states there is a certain level of "simplicity" in the solutions to certain kinds of rational equations.
7. Investigation of the [[Standard Model|Yang-Mills existence and gap]]; specifically, whether Yang-Mills theory predicts particles with negative mass, and whether it contains any contradictions. Demonstrations of either negative-mass predictions or contradictions would provide clues as to how to build a more accurate theory.
[[Category:mathematics]]