In this talk, we discuss the current state and future prospects of computational mathematics, science, and engineering. The numerical simulation of physical, chemical, and biological systems is more and more prevalent in industrial development. Fast mathematical algorithms are used to analyse data in applications ranging from oil prospecting to ultrasound imaging. We examine these wide-ranging fields and how they repeatedly return to a few basic questions in applied math. Current research focuses on generalizing both these questions and their answers in the search for improved algorithms.