The History of the Calculus and Its Conceptual Development: (The Concepts of the Calculus)
This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.
But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek method of exhaustion and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.
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LibraryThing ReviewUser Review - dogcopter - LibraryThing
Classic. Still my go-to resource for most general topics in the history of mathematics, despite how old it is. Very thorough. Not exactly a fun read though. Read full review
CONCEPTIONS IN ANTIQUITY
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algebra analysis appeared application Archimedes argument Aristotle arithmetic attempt basis calculus called Cauchy Cavalieri century circle clear concept connection considered continuous curve defined definition demonstration derivative determining difference differential early edition elements employed equal equations exhaustion explained expressed fact Fermat figures finite fluxions formal function fundamental Galileo geometrical given Greek History Ibid idea indicated indivisibles infinitely small infinitesimal infinity integral interpretation intuition involved known lack largely later Leibniz less limit limit concept logical magnitude mathe mathematicians mathematics means method motion nature Newton Nicholas of Cusa Opera Oresme Paperbound perhaps period philosophy physical precise present principle problems procedure proof proposition quantities question ratio reason regarded represented respect result rigorous sense sequence significant similar suggested symbols tangent theorem theory thought tion Torricelli triangle ultimate values variable volume Wallis zero