Aspects of mathematical science in modern life Professor PH Potgieter Department of Decision Sciences : Departement Besluitkunde Inaugural lecture : Inkulumo yokwethulwa : Intreerede Senate Hall, University of South Africa 2 October 2007, 19:00 Mnumzane ohloniphekileyo, Kollega(s), dankie vir die gawe inleiding en vir u teenwoordigheid. 1 Introduction The message of this lecture is perhaps best summarised by the subtitle of an article from the September 13 issue of The Economist: Consumers and companies increasingly depend on a hidden mathematical world. I shall substantiate this assertion and try to explain, without going into much detail, how some of the mathematical and modelling work that is of interest to me relates to modern civilised life. It is hardly necessary to point out the substantial contribution of mathematics to design and optimisation in manufacturing, in physics—where there is little to improve on Eugene Wigner’s 1960 paper “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”—and, through the application of powerful computers, in computational chemistry and biology. Rather, I shall mention some applications that are closer to one of the central ar- eas in the Department of Decision Sciences where I work—Operations Research—and to the closely related areas of Theoretical Computer Science and also to Finance and Economics. My interest is less in the manufacturing of the machines and gadgets, the use and utility of which can hardly be better illustrated than by the cellphone-talking car driver in Nairobi that is sip- ping on a cold Appletiser made from apples grown 5 000km away near Grabouw, than in how the same machines can be organised, allocated and managed using algorithms so as to improve and optimise their utility for the individual or a group of individuals. The word utility is used here without implying any Benthamite inclinations or sympathy for grand social experiments. As I hope to make clear, I see the influence of the mathematical sciences as pervasive and descriptive but not prescriptive. 1