415 pp., vii. '1' in number line. Contents in three SECTIONS and nine chapters, following Introduction, "Turning on the Light": I: THE LIGHT OF AMBIGUITY 1. "Ambiguity in Mathematics"; 2. "The Contradictory in Mathematics"; 3. "Paradoxes and Mathematics: Infinity and the Real Numbers"; 4. "More Paradoxes of Infinity: Geometry, Cardinality and Beyond"; II. THE LIGHT AS IDEA 5. "The Idea as an Organizing Principle"; 6. "Ideas, Logic and Paradoxes"; 7. "Great Ideas"; III. THE LIGHT AND THE EYE OF THE BEHOLDER 8. "The Truth of Mathematics"; 9. "Conclusion: Is Mathematics Algorithmic or Creative?"; Notes, pp. 389-397; Bibliography, pp. 399-405; Index, pp. 407-415. Black cloth with brilliant gilt lettering on spine. Dustwrapper not price-clipped ($35.00), illustrated with green chalice-shape on most of front cover, with title lettering in black, edged in yellow, across middle front cover, above subtitle in smaller white letters, all superimposed upon chalice, on lower half front over; author name lettering in thin, smaller maroon letters across top front cover. (NO previous owner names; NO remainder marks.) Absolutely FLAWLESS artifact and dustwrapper. Gift-Giving Quality. Laid in news clipping (NO offsetting): 6 Letters to the Editor of the New York Times, 7 31 2012, prompted by Andrew Hacker's Sunday Review piece, "Is Algebra Necessary?".

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Bibliografische Details

Titel: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Verlag: Princeton University Press, Princeton and Oxford
Erscheinungsjahr: 2007
Sprache: Englisch
ISBN-10: 0691127387
ISBN-13: 9780691127385
Einband: Hardcover
Auflage: 1st Edition
Druck: 1st Printing
Zustand: New
Zustand des Schutzumschlags: New

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To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically - even algorithmically - from one black-and-white deduction to another. Yet, mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, "How Mathematicians Think" reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and "How Mathematicians Think" provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, "How Mathematicians Think" shows that the nature of mathematical thinking can teach us a great deal about the human condition itself

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William Byers is professor of mathematics at Concordia University in Montreal. He has published widely in mathematics journals.

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