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In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do-and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications?Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics' exceptional consensus is due to the subject's underlying reality.The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Mathematics --- Mathematics --- Benedetto. --- Black-Scholes formula. --- Eugene Wigner. --- Friedrich W.J. Schelling. --- George Lakoff. --- Gilles Deleuze. --- Hermann Cohen. --- Hilary Putnam. --- Johann G. Fichte. --- Logic of Sensation. --- Mark Steiner. --- Rafael Nez. --- Stanislas Dehaene. --- Vincent Walsh. --- Water J. Freeman III. --- abbaco. --- algebra. --- arithmetic. --- authority. --- cognitive theory. --- combinatorics. --- conceptual freedom. --- constraints. --- economy. --- gender role stereotypes. --- generating functions. --- geometry. --- inferences. --- infinities. --- infinity. --- mathematical cognition. --- mathematical concepts. --- mathematical cultures. --- mathematical domains. --- mathematical entities. --- mathematical evolution. --- mathematical interpretation. --- mathematical language. --- mathematical metaphor. --- mathematical norms. --- mathematical objects. --- mathematical practice. --- mathematical signs. --- mathematical standards. --- mathematical statements. --- mathematics. --- natural order. --- natural sciences. --- nature. --- negative numbers. --- number sense. --- option pricing. --- philosophy of mathematics. --- reality. --- reason. --- relevance. --- semiosis. --- sexuality. --- stable marriage problem. --- Philosophy --- History. --- History. --- Benedetto. --- Black-Scholes formula. --- Eugene Wigner. --- Friedrich W.J. Schelling. --- George Lakoff. --- Gilles Deleuze. --- Hermann Cohen. --- Hilary Putnam. --- Johann G. Fichte. --- Logic of Sensation. --- Mark Steiner. --- Rafael Nez. --- Stanislas Dehaene. --- Vincent Walsh. --- Water J. Freeman III. --- abbaco. --- algebra. --- arithmetic. --- authority. --- cognitive theory. --- combinatorics. --- conceptual freedom. --- constraints. --- economy. --- gender role stereotypes. --- generating functions. --- geometry. --- inferences. --- infinities. --- infinity. --- mathematical cognition. --- mathematical concepts. --- mathematical cultures. --- mathematical domains. --- mathematical entities. --- mathematical evolution. --- mathematical interpretation. --- mathematical language. --- mathematical metaphor. --- mathematical norms. --- mathematical objects. --- mathematical practice. --- mathematical signs. --- mathematical standards. --- mathematical statements. --- mathematics. --- natural order. --- natural sciences. --- nature. --- negative numbers. --- number sense. --- option pricing. --- philosophy of mathematics. --- reality. --- reason. --- relevance. --- semiosis. --- sexuality. --- stable marriage problem.

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Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

Mathematics --- Communication in mathematics. --- Math --- Science --- Language. --- History. --- Alasdair MacIntyre. --- Archimedes. --- Aristotle. --- Bleak House. --- Borel sets. --- Bourbaki. --- Carl Friedrich Gauss. --- David Hilbert. --- Emmy Noether. --- Enlightenment. --- G. E. R. Lloyd. --- Georg Cantor. --- Greece. --- Jean-Pierre Vernant. --- John Archibald Wheeler. --- K-ness. --- L'Algebra. --- Leo Perutz. --- Leopold Kronecker. --- Middlemarch. --- Paul Gordan. --- Plato. --- Rafael Bombelli. --- Robert Thomason. --- ThomasonДrobaugh article. --- Tom Trobaugh. --- abstraction. --- aesthetic contingency. --- algebra. --- automated theorem provers. --- axiomatic mathematics. --- belief. --- chiasmus. --- clues. --- cognitive meaning. --- compound machines. --- computational modeling. --- computer simulations. --- cubic equations. --- deductive mathematics. --- diagramma. --- dreams. --- energeia. --- epistemology. --- existential contingency. --- explanation. --- exploration mathematics. --- finiteness theorems. --- focalization. --- forensic rhetoric. --- formal models. --- geometry. --- ghost. --- ghostwriter. --- group. --- highest common factor. --- imaginary numbers. --- incommensurability. --- intuition. --- irony. --- literary narrative. --- literature. --- machine metaphor. --- mathematical argument. --- mathematical concepts. --- mathematical enquiry. --- mathematical line. --- mathematical modeling. --- mathematical models. --- mathematical objects. --- mathematical physics. --- mathematicians. --- mathematics. --- metanarratology. --- metaphor. --- myth. --- narrative analysis. --- narrative representation. --- narrative subjectivity. --- narrative. --- narratology. --- negative numbers. --- non-Euclidean epistemology. --- non-Euclidean geometry. --- non-Euclidean mathematics. --- non-Euclidean physics. --- non-Euclidean thinking. --- orthe. --- permutation groups. --- perspective. --- poetic storytelling. --- polynomial equations. --- proof. --- quantum mechanics. --- rational enquiry. --- rationality. --- reality. --- scientific inquiry. --- square roots. --- story generator algorithm. --- story grammars. --- story. --- storytelling. --- structural linguistics. --- symbols. --- theology. --- theorems. --- tragic mathematical heroes. --- truth. --- variste Galois. --- vestibular line. --- visions. --- visual line. --- vividness. --- Communication in mathematics