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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.
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.
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.
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.