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Carl Benjamin Boyer
9 quotes
“The Introductio does not boast an impressive number of editions, yet its influence was pervasive. In originality and in the richness of its scope it ranks among the greatest of textbooks; but it is outstanding also for clarity of exposition. Published two hundred and two years ago, it nevertheless possesses a remarkable modernity of terminology and notation, as well as of viewpoint. Imitation is indeed the sincerest form of flattery.”
Carl Benjamin Boyer (1906–1976) first seen 1950 wikiquote, CC BY-SA 4.0 source
Recorded in: On the work of Leonhard Euler, in "The Foremost Textbook of Modern Times" (1950)
“But what, after all, are the integers? Everyone thinks that he or she knows, for example, what the number three is — until he or she tries to define or explain it.”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
Recorded in: As quoted in Everything and More: A Compact History of Infinity (2013) by David Foster Wallace, p. 8
“A Hebrew belief asserted that if Yahweh lays aside his bow and hangs it in the clouds, this is a sign that his anger has subsided. Other peoples have had similar ideas, based upon the tradition that an archer carries his bow with the ends pointing downward when he wishes to indicate his peaceful intentions.”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
“Ptolemy left in his Optics, the earliest surviving table of angles of refraction from air to water. … This table, quoted and requoted until modern times, has been admired … A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order … As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience.”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
“Robert Grosseteste … was born at the decisive moment when Greek and Arabic science became accessible in Latin versions.”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
“Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i.e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle ...”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
“Descartes maintained his confidence in the instantaneity of light. … Yet in his derivation of the law of refraction, Descartes reasoned that light travelled faster in a dense medium than in one less dense. He seems to have had no qualms about comparing infinite magnitudes!”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
“It should be mentioned also that the Hindus, unlike the Greeks, regarded irrational roots of numbers as numbers. This was of enormous help in algebra, and Indian mathematicians have been much praised for taking this step; but one must remember that the Hindu contribution in this case was the result of logical innocence rather than of mathematical insight. We have seen the lack of nice distinction on the part of Hindu mathematicians between exact and inexact results, and it was only natural that they should not have taken seriously the difference between commensurable and incommensurable magnitudes. For them there was no impediment to the acceptance of irrational numbers, and later generations followed their lead uncritically until in the nineteenth century mathematicians established the real number system on a sound basis.”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source
Recorded in: quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189
“Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. … Fermat applied his method … and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite.”
Carl Benjamin Boyer (1906–1976) said by 1976 at the latest wikiquote, CC BY-SA 4.0 source