Mathematics as an Engine for Computational Sciences

The situation with the success of quantum computers is analyzed and a conclusion is made about the need to develop quantum computing regardless of the development of the corresponding computing base. Particularly highlighted is the role of new mathematics associated with functional integrals as a means for quantum computing. The problems of the Feynman formulation are described and it is shown how to construct an approach that allows the generation of quantum algorithms. The prospects for this approach for creating a qualitative theory of partial differential equations are indicated.