Hilbert's 15th problem called for a rigorous foundation of Schubert's enumerative calculus, where the main focus and long standing part is Schubert's problem of characteristics. In the course to secure the foundation of algebraic geometry Van der Waerden and Andre Weil attributed the problem to the determination of the Chow rings of flag manifolds.? In this talk I will give an overview of the background, content, and resolution of Hilbert‘s 15th problem. Our main results are a formula solving Schubert's problem of characteristics, and a system? description computing the Chow rings of flag manifolds. We illustrate the effectiveness of our formula and algorithm via explicit examples.