I. P (Polynomial Algorithm) Problem vs NP (Non-Polynomial Algorithm) Problem 2: Hodge Conjecture 3: Poincare Conjecture 4: Riemann Hypothesis 5: Yang-Mills Existence and Quality Gap 6: Naville-Stokes. Existence and Smoothness of Equation VII: Birch and Swinnerton-Dyer Conjectures VIII: Geometric Scale Drawing Problem IX: Goldbach Conjecture X: Four-color Conjecture.