Tracing the Modern Concept of Convexity

Several manifestations of convexity were studied already in the antiquity. The modern concept emerged, however, only around 1900, notably in the works of Peano and Minkowski. This motivates us to review here some main contributions of the latter. In doing so, we attempt to offer a friendly invitation to the history and concepts of convex analysis. Our emphasis is on convex bodies, extreme points, separation, Minkowski functionals, supports and polarity.