Problem (1): P (polynomial algorithm) problem vs NP (non-polynomial algorithm) problem (2): Hodge conjecture problem (3): Poincare conjecture problem (4): Riemann hypothesis problem (5): Yang-Mills. Existence and Quality Gap (VI): Existence and Smoothness of Naville-Stokes Equation (VII): Burch and Swinerton-Dale Conjecture (VIII): Drawing Geometric Ruler (IX): Goldbach Conjecture (X): Four-color Conjecture.