Items related to How Mathematicians Think: Using Ambiguity, Contradiction,...
How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics - Softcover
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.
"synopsis" may belong to another edition of this title.
From the Inside Flap
"This practical, hands-on, and significant book makes clear the connections between mathematics and art, and demonstrates why artists need to know mathematics. Viewpoints appeals to students' visual intuition and engages their imaginations in a fresh way."--Barbara E. Reynolds, SDS, coauthor of "College Geometry Using the Geometer's Sketchpad"
"This entire book is a thing of beauty: the mathematics, the visual art, the writing, the exercises, and the organization. The authors' passion and excitement for their subject matter is apparent on every page. I am in awe."--Robert Bosch, Oberlin College
"The book's emphasis on a workshop approach is good and the authors offer rich insights and teaching tips. The inclusion of work by contemporary artists--and the discussion of the mathematics related to their work--is excellent. This will be a useful addition to the sparse literature on mathematics and art that is currently available for classroom use."--Doris Schattschneider, author of "M. C. Escher: Visions of Symmetry"
"Concentrating on perspective and fractal geometry's relationship to art, this well-organized book is distinct from others on the market. The mathematics is not sold to art students as an academic exercise, but as a practical solution to problems they encounter in their own artistic projects. I have no doubt there will be strong interest in this book."--Richard Taylor, University of Oregon
From the Back Cover
"An amazing tour de force. Utterly new, utterly truthful."--Reuben Hersh, author of What Is Mathematics, Really?
"Byers gives a compelling presentation of mathematical thinking where ambiguity, contradiction, and paradox, rather than being eliminated, play a central creative role."--David Ruelle, author of Chance and Chaos
"This is an important book, one that should cause an epoch-making change in the way we think about mathematics. While mathematics is often presented as an immutable, absolute science in which theorems can be proved for all time in a platonic sense, here we see the creative, human aspect of mathematics and its paradoxes and conflicts. This has all the hallmarks of a must-read book."--David Tall, coauthor of Algebraic Number Theory and Fermat's Last Theorem
"I strongly recommend this book. The discussions of mathematical ambiguity, contradiction, and paradox are excellent. In addition to mathematics, the book draws on other sciences, as well as philosophy, literature, and history. The historical discussions are particularly interesting and are woven into the mathematics."--Joseph Auslander, Professor Emeritus, University of Maryland
"About this title" may belong to another edition of this title.
- PublisherPrinceton University Press
- Publication date2007
- ISBN 10 0691150915
- ISBN 13 9780691150918
- BindingPaperback
- LanguageEnglish
- Number of pages648
- Rating
(No Available Copies)
Search Books: Create a WantCan't find the book you're looking for? We'll keep searching for you. If one of our booksellers adds it to AbeBooks, we'll let you know!
Create a Want
