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