1 2 Andy Magid, Letter from the Editor, in Notices of the AMS, November 2005, American Mathematical Society, p.1173.
↑ Boyer, Carl B. (1991). “The age of Plato and Aristotle”. A History of Mathematics . John Wiley & Sons, Inc. tr. 86. ISBN0-471-54397-7. Plato is important in the history of mathematics largely for his role as inspirer and director of others, and perhaps to him is due the sharp distinction in ancient Greece between arithmetic (in the sense of the theory of numbers) and logistic (the technique of computation). Plato regarded logistic as appropriate for the businessman and for the man of war, who "must learn the art of numbers or he will not know how to array his troops." The philosopher, on the other hand, must be an arithmetician "because he has to arise out of the sea of change and lay hold of true being."
↑ Boyer, Carl B. (1991). “Euclid of Alexandria”. A History of Mathematics . John Wiley & Sons, Inc. tr. 101. ISBN0-471-54397-7. Evidently Euclid did not stress the practical aspects of his subject, for there is a tale told of him that when one of his students asked of what use was the study of geometry, Euclid asked his slave to give the student threepence, "since he must make gain of what he learns."
1 2 Boyer, Carl B. (1991). “Apollonius of Perga”. A History of Mathematics . John Wiley & Sons, Inc. tr. 152. ISBN0-471-54397-7. It is in connection with the theorems in this book that Apollonius makes a statement implying that in his day, as in ours, there were narrow-minded opponents of pure mathematics who pejoratively inquired about the usefulness of such results. The author proudly asserted: "They are worthy of acceptance for the sake of the demonstrations themselves, in the same way as we accept many other things in mathematics for this and for no other reason." (Heath 1961, p.lxxiv). The preface to Book V, relating to maximum and minimum straight lines drawn to a conic, again argues that the subject is one of those that seem "worthy of study for their own sake." While one must admire the author for his lofty intellectual attitude, it may be pertinently pointed out that s day was beautiful theory, with no prospect of applicability to the science or engineering of his time, has since become fundamental in such fields as terrestrial dynamics and celestial mechanics.
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