One of the difficult problems: P (polynomial algorithm) problem versus NP (non-polynomial algorithm)
The second question: Hodge conjecture
The third question: Poincare conjecture
The fourth question: Riemann hypothesis.
The fifth question: the existence and quality gap of Yang Mill.
The sixth question: the existence and smoothness of Navier-Stokes equation.
The seventh question: Burch and Swinerton Dale's conjecture.
The eighth question: the drawing problem of geometric ruler
The ninth question: Goldbach conjecture
The tenth question: four-color conjecture