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

By:

Sign Up Now! Already a Member? Log In
You must be logged into Bookshare to access this title. Learn about membership options, or view our freely available titles.

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.
Copyright:
2007

Book Details

Book Quality:
Publisher Quality
Book Size:
424 Pages
ISBN-13:
9781400833955
Related ISBNs:
9780691150918, 9780691127385, 9780691145990
Publisher:
Princeton University Press
Date of Addition:
Copyrighted By:
Princeton University Press
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
History, Nonfiction, Mathematics and Statistics, Philosophy
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

Reviews

No Rating Yet