Sir Michael Atiyah: “The Soluble and the Insoluble” What do we mean by a solution to a problem? This is both a philosophical question, and a practical one, which depends on what one is trying to achieve and the means, time and money available. The explosion in computer technology keeps changing the goal posts. I will reflect on these issues, primarily from the viewpoint of an elderly mathematician. The opinions expressed in this video do not necessarily reflect the views of the Heidelberg Laureate Forum Foundation or any other person or associated institution involved in the making and distribution of the video.