History of Convexity and Mathematical Programming: Connections and Relationships in Two Episodes of Research in Pure and Applied Mathematics of the 20th Century

Abstract

In this paper, the gradual introduction of the concept of a general convex body in Minkowski’s work and the development of mathematical programming, are presented. Both episodes are exemplary for mathematics of the 20th century, in the sense that the former represents a trend towards a growing abstraction and autonomy in pure mathematics, whereas the latter is an example of the many new disciplines in applied mathematics that emerged as a consequence of efforts to develop mathematics into a useful tool in a wider range of subjects than previously. It will be discussed, how and why these two new areas emerged and developed through different kinds of connections and relations; and how they at some point became connected, and fed and inspired one another. The examples suggest that pure and applied mathematics are more intertwined than the division in ‘pure’ and ‘applied’ signals.