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How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics

Author: William Byers
Publisher: Princeton : Princeton University Press, ©2007.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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,  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: William Byers
ISBN: 9780691127385 0691127387 9780691145990 0691145997
OCLC Number: 73502041
Awards: Runner-up for Choice Magazine Outstanding Reference/Academic Book Award 2007
Winner of Library Journal Best Sci-Tech Books in Mathematics 2007
Short-listed for Choice's Outstanding Academic Titles 2007 (United States)
Description: vii, 415 pages : illustrations ; 24 cm
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.
Responsibility: William Byers.

Abstract:

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  Read more...
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Ambitious, accessible and provocative...[In] How Mathematicians Think, William Byers argues that the core ingredients of mathematics are not numbers, structure, patterns or proofs, but ideas...Byers' Read more...

 
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