The Concepts of the Calculus

Abstract

IN the historical survey of mathematics, as of any branch of science, it is customary to ascribe a great discovery to one or more individuals. Without, however, seeming in any way to detract from the full credit due to such brilliant researchers, it must not be overlooked that behind every great step forward there is, invariably, an evolutionary development of ideas which renders that step possible. There are periods of suggestion and anticipation which lead to a stage where the nebulous begins to take form and ultimately becomes precise. But the process does not stop here. A new discovery is somewhat analogous to a roughly-hewn article specially designed for some particular purpose; it will not function to its fullest extent until subjected to a refining development in which greater definition is brought forth, with a consequent extension of the field of validity and useful application. Thus, in time, by a mental process of evolution, any discovery, great as it may be, tends to become less prominent as a separate entity. In the words of J. W. N. Sullivan: “A history of mathematics is largely a history of discoveries which no longer exist as separate items, but which are merged into some more modern generalisation”.

The Concepts of the Calculus

A Critical and Historical Discussion of the Derivative and the Integral. By Carl B. Boyer. Pp. vii + 346. (New York: Columbia University Press; London: Oxford University Press, 1939.) 18s. 6d. net.