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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics - Couverture rigide

Byers, William

 
9780691127385: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Couverture rigide
ISBN 10 : 0691127387 ISBN 13 : 9780691127385
Editeur : Princeton University Press, 2007

Synopsis

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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À propos de l'auteur

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

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Éditeur
Princeton University Press
Date d'édition
2007
Langue
anglais
ISBN 10 
0691127387
ISBN 13 
9780691127385
Reliure
Relié
Nombre de pages
424
Coordonnées du fabricant
non disponible
Personne responsable
non disponible