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

Other records:
Author/Creator:
Byers, William author.
Edition:
Course Book
Publication:
Princeton, NJ : Princeton University Press, [2010]
Format/Description:
Book
1 online resource : 6 halftones. 48 line illus.
Subjects:
Mathematicians -- Psychology.
Mathematics -- Philosophy.
Mathematics -- Psychological aspects.
Language:
In English.
System Details:
Mode of access: Internet via World Wide Web.
text file PDF
Summary:
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.
Contents:
Frontmatter
Contents
Acknowledgments
INTRODUCTION. Turning on the Light
Section I. The Light of Ambiguity
Introduction
Chapter 1. Ambiguity in Mathematics
Chapter 2. The Contradictory in Mathematics
Chapter 3. Paradoxes and Mathematics: Infinity and the Real Numbers
Chapter 4. More Paradoxes of Infinity: Geometry, Cardinality, and Beyond
Section II. The Light as Idea
Introduction
Chapter 5. The Idea as an Organizing Principle
Chapter 6. Ideas, Logic, and Paradox
Chapter 7. Great Ideas
Section III. The Light and the Eye of the Beholder
Introduction
Chapter 8. The Truth of Mathematics
Chapter 9. Conclusion: Is Mathematics Algorithmic or Creative?
Notes
Bibliography
Index
Notes:
Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)
Contributor:
De Gruyter.
Contained In:
De Gruyter University Press Library.
ISBN:
9781400833955
OCLC:
979779657
Publisher Number:
10.1515/9781400833955 doi
Access Restriction:
Restricted for use by site license.
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