In financial mathematics, finding solutions to the associated partial differential equations (PDEs) or stochastic differential equations (SDEs) is an important task as it significantly reduces computational costs. While various mathematical techniques such as Fourier transforms can be used to find solutions, most differential equations are intractable. However, recent advances in computational science, in particular the integration with deep learning, are gradually making feasibility in financial mathematics more attainable. This talk will present a number of these research efforts, focusing on topics in financial mathematics. It will also explore further directions for progress, including solutions for non-Markovian process-based SDEs.