23 Quotes by Carl B. Boyer

Voltaire called the calculus "the Art of numbering and measuring exactly a Thing whose Existence cannot be conceived."See Letters Concerning the English Nation p. 152

Definitions of number, as given by several later mathematicians, make the limit of an infinite sequence identical with the sequence itself. Under this view, the question as to whether the variable reaches its limit is without logical meaning. Thus the infinite sequence .9, .99, .999,... is the number one, and the question, "Does it ever reach one?" is an attempt to give a metaphysical argument which shall satisfy intuition.

In making the basis of the calculus more rigorously formal, Weierstrass also attacked the appeal to intuition of continuous motion which is implied in Cauchy's expression -- that a variable approaches a limit.

Thus the required rigor was found in the application of the concept of number, made formal by divorcing it from the idea of geometrical quantity

Leibniz in this respect had perhaps even less caution than many of his contemporaries, for he seriously considered whether the infinite series 1 -1+1-1+... was equal to 1/2.

Recognizing that geometry is entirely intellectual and independent of the actual description and existence of figures, Fontenelle did not discuss the subject fro the point of view of science or metaphysics as had Aristotle and Leibnez.

These results were obtained by making up tables in which were listed the volumes for given sets of values of the dimensions, and from these selecting the best proportions.

Most of his predecessors had considered the differential calculus as bound up with geometry, but Euler made the subject a formal theory of functions which had no need to revert to diagrams or geometrical conceptions.

Carnot, one of a school of mathematicians who emphasized the relationship of mathematics to scientific practice, appears, in spite of the title of his work, to have been more concerned about the facility of application of the rules of procedure than about the logical reasoning involved.