Mathematics, from its earliest days, has always benefited from the healthy tension between theory and application. But who or what defines the particular areas for exploration, as well as the mathematical toolbox, of practising applied mathematicians? Should applied mathematicians seek elegance and truth in the order of the universe, or be happy to work on ‘dirty problems’?
In this highly selective and somewhat opinionated talk, I shall offer a few thoughts and observations about the changing nature of applied mathematics from the nineteenth century to the present day. This will be discussed in the context of significant developments within society; the expansion of universities and the subjects studied therein; and changes to industry, commerce and technology.
Unfortunately, there will not be time to illustrate or motivate this talk with specific examples of major research advances; however, I hope that the talk will stimulate others to consider how we keep mathematics relevant and impactful and whether the subject divisions within mathematics are now becoming obsolete.
* This talk is adapted from the Institute of Mathematics and Its Applications’ Gold Medal Lecture given in June 2025.