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

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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, in...

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Bibliographic Details
Main Author: Byers, William, 1943-
Format: Electronic eBook
Language:Inglés
Published: Princeton : Princeton University Press, 2007.
Series:Book collections on Project MUSE.
Subjects:
Mathematics > Psychological aspects.
Mathematics > Philosophy.
Mathematicians > Psychology.
MATHEMATICS > History & Philosophy.
Mathematiques > Aspect psychologique.
Mathematiques > Philosophie.
Cognition numerique.
Mathematiciens > Psychologie.
Electronic books.
Online Access:Texto completo
Table of Contents:
  • Acknowledgments
  • Introduction : Turning on the light
  • Section 1 : The light of ambiguity ch. 1
  • Ambiguity in mathematics ch. 2
  • The contradictory in mathematics ch. 3
  • Paradoxes and mathematics : infinity and the real numbers ch. 4
  • More paradoxes of infinity : geometry, cardinality, and beyond
  • Section 2 : The light as idea ch. 5. The
  • idea as an organizing principle ch. 6
  • Ideas, logic, and paradox ch. 7
  • Great ideas
  • Section 3 : The light and the eye of the beholder ch. 8. The
  • truth of mathematics ch. 9
  • Conclusion : is mathematics algorithmic or creative?
  • Notes
  • Bibliography
  • Index.

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