Touring the Calculus Gallery

1. INTRODUCTION. The premise of this article—what our friends in theatre would call its " conceit " —is that we are about to visit a gallery devoted to the history of calculus. Admittedly no such institution exists, but it is easily imagined. One need only think of an art museum, albeit one whose masterpieces are not canvases but theorems and whose masters are not Courbet and Cezanne but Leibniz and Lebesgue. Our stroll through the Calculus Gallery must be brief, and we can stop only occasionally to examine particular works in detail. Even so, the visit should provide a glimpse of the development of calculus/analysis from its appearance in the late seventeenth century, through its expansion in the eighteenth, to its " Classical Period " in the first two-thirds of the nineteenth, and on to the mature subject of today. Like any museum, we enter through a grand hall whose walls are inscribed with noble sentiments. One, from John von Neumann, catches our eye [16, p. 3]: