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

William Byers

ISBN 10: 0691127387 / ISBN 13: 9780691127385

Editore: Princeton University Press May 2007, 2007

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Dati bibliografici

• Titolo: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
• Editore: Princeton University Press May 2007
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0691127387
• ISBN 13: 9780691127385
• Rilegatura: Hardcover
• Edizione: First Edition.
• Stampa: First Edition
• Condizione: Very Good
• Condizione della sovraccoperta: Near Fine
• Cataloghi dei venditori:
  • 51-SCIENCE

Descrizione articolo

Riassunto

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, andHow 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.

Informazioni sull?autore

William Byers is Professor of Mathematics at Concordia University in Montreal.