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A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.

Mathematics --- History. --- History --- Philosophy and science. --- Mathematics. --- Mathematical logic. --- Algebra. --- Geometry. --- Philosophy of Science. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Euclid's Elements --- Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Annals --- Auxiliary sciences of history --- Math --- Science --- Science and philosophy

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The twentieth century is the period during which the history of Greek mathematics reached its greatest acme. Indeed, it is by no means exaggerated to say that Greek mathematics represents the unique field from the wider domain of the general history of science which was included in the research agenda of so many and so distinguished scholars, from so varied scientific communities (historians of science, historians of philosophy, mathematicians, philologists, philosophers of science, archeologists etc. ), while new scholarship of the highest quality continues to be produced. This volume includes 19 classic papers on the history of Greek mathematics that were published during the entire 20th century and affected significantly the state of the art of this field. It is divided into six self-contained sections, each one with its own editor, who had the responsibility for the selection of the papers that are republished in the section, and who wrote the introduction of the section. It constitutes a kind of a Reader book which is today, one century after the first publications of Tannery, Zeuthen, Heath and the other outstanding figures of the end of the 19th and the beg- ning of 20th century, rather timely in many respects.

Academic collection --- #GGSB: Filosofie (20e eeuw) --- Phenomenology --- Philosophy, Modern --- Philosophy --- Phénoménologie --- Science --- Greece --- History --- To 1500 --- Science [Ancient ] --- Historiography --- Mathematics [Ancient ] --- Mathematics --- Mathematics. --- History. --- Philosophy. --- Philosophy and science. --- Popular works. --- History of Mathematical Sciences. --- Philosophy, general. --- Philosophy of Science. --- Popular Science, general. --- Science and philosophy --- Mental philosophy --- Humanities --- Annals --- Auxiliary sciences of history --- Math --- Filosofie (20e eeuw) --- Phénoménologie

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515.12 <09> --- 515.12 <09> General topology--Geschiedenis van ... --- General topology--Geschiedenis van ... --- Topology --- History. --- History --- Topology - History. --- Topology. --- Mathematics. --- Philosophy and science. --- History of Mathematical Sciences. --- Philosophy of Science. --- History, general. --- Science and philosophy --- Science --- Annals --- Auxiliary sciences of history --- Math --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear

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This is an outstanding collection of original essays. All of them concern the history and philosophy of mathematics and physics in the years from 1870 to 1930. More specifically, they are intellectual histories of the interactions between the three disciplines, philosophy, mathematics and physics, in that period. And as the essays bring out, what a period it was: of both ferment and synergy, heat and light! Most of the giants - especially Helmholtz, Hertz, Poincare, Hilbert, Einstein and Weyl - are here: engaging not just in physics and mathematics but also in philosophy, often together, or with figures like Schlick. The editors are to be congratulated on a major contribution to our understanding of one of the most complex but fertile periods in the history of all three disciplines. - Jeremy Butterfield, University of Cambridge This stimulating volume covers a wide range of topics which are of direct interest to anyone who thinks about the curious relation between mathematics and the natural world. Philosophers often pose interesting questions about the "dispensability" of mathematics to science. But they too often overlook the wealth of philosophical perplexities that can arise in detailed examples and case studies, both contemporary and historical. This volume refocuses our attention by addressing a number of topics connected to applied mathematics, any one of which is worthy of every philosopher’s attention. - James Robert Brown, University of Toronto What to make of neo-Kantianism in its hey-day, from 1840-1940? It was the most prolific of times and the most seminal, it was the most muddled and confused, it is philosophy working at its hardest with science and most damagingly against science. It is examined here episodically, as it engaged individual scientists: Helmholtz, , Hertz, Poincare, Minkowski, Hilbert, Eddington and Weyl. If Einstein is not in their number, he had to contend with their influence, and anyway he transformed their agenda. The essays on these figures are glinting in their focus and scholarship. Whatever one thinks of neo-Kantianism, this book is history and philosophy of science at its best: mathematically and physically informed, historically engaged, and philosophically driven. - Simon Saunders, University of Oxford Ten first-rate philosopher-historians probe insightfully into key conceptual questions of pre-quantum mathematical physics, from Helmholtz and Boltzmann, through Hertz and Lorentz, to Einstein, Weyl and Eddington, with an interesting aside on the rarely studied philosophy of Federigo Enriques. A rich and effective display of what the critical history of science can do for our understanding of scientific thought and its achievements. Roberto Torretti, University of Puerto Rico.

History of philosophy --- Pure sciences. Natural sciences (general) --- Theory of knowledge --- History of physics --- filosofie --- epistomologie --- Mathematics --- geschiedenis --- Philosophy of science --- wetenschapsgeschiedenis --- wiskunde --- epistemologists --- fysica --- Philosophy. --- History. --- Philosophy and science. --- Mathematics. --- Physics. --- Philosophy, general. --- History of Mathematical Sciences. --- History of Science. --- Philosophy of Science. --- History and Philosophical Foundations of Physics. --- History of Philosophy. --- Science and philosophy --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Math --- Annals --- Auxiliary sciences of history --- Mental philosophy --- Humanities --- Mathematical analysis --- Physics --- Causality (Physics) --- Foundations. --- 517.1 --- Philosophy and science --- Normal science --- Logic of mathematics --- Mathematics, Logic of --- Causality --- Heisenberg uncertainty principle --- Nuclear physics --- Quantum theory --- 517.1 Mathematical analysis --- Philosophy --- Causality (Physics). --- Philosophy (General). --- Foundations

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Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.

Science, general. --- History of Science. --- History of Philosophy. --- History of Mathematical Sciences. --- Science --- Philosophy (General). --- Sciences --- History. --- Histoire --- Science (General). --- Science_xHistory. --- History & Archaeology --- History - General --- Leibniz, Gottfried Wilhelm, --- Mathématiques --- Mathematics --- Critique et interprétation --- Philosophie --- Philosophy --- Mathematics. --- Philosophy. --- Criticism and interpretation. --- Mental philosophy --- Math --- Logic of mathematics --- Mathematics, Logic of --- G. G. L. L., --- L., G. G. L., --- Leibnitius, Godefridus Guilielmus, --- Leĭbnit︠s︡, G. --- Leĭbnit︠s︡, Gotfrid Vilʹgelʹm, --- Leibnitz, Godefroy-Guillaume, --- Leibniz, G. W., --- Leibniz, Georg Wilhelm, --- Leibnizius, Godefridus Guilielmus, --- Leibnizius, Gotfridus Guilelmus, --- Lithuanus, Georgius Ulicovius, --- Ulicovius Lithuanus, Georgius, --- לייבניץ, גוטפריד וילהם, --- לייבניץ, גוטפריד וילהלם, --- Leibniz, Gottfried Wilhelm von, --- Von Leibniz, Gottfried Wilhelm, --- Leibnitz, Gottfried Wilhelm --- Leibniz, Gottfried Wilhelm --- Humanities --- Annals --- Auxiliary sciences of history --- Philosophie. --- Mathématiques --- Critique et interprétation