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William Byers, “How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics”

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

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	How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematic 425 pages \| Dec 12, 2006 \|ISBN:0691127387 \| DJVU \| 6 Mb[/center]Product Description:To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even al ...
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	Science/Engineering Foundation Mathematics for Non-Mathematicians Milo Shott “Foundation Mathematics for Non-Mathematicians" Open University Press \| 1990-02 \| ISBN: 0335092136 \| 240 pages \| PDF \| 8,4 MB depositfiles.com filefactory --- No mirrors, please --- thank you much
	Science/Engineering Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. GrosholzPublisher: Oxford University Press, USA \| Number Of Pages: 250 \| Publication Date: 2007-10-18 \| ISBN-10: 0199299730 \| PDF \| 2 MbEmily Grosh ...
	Mathematicians and Their Times (Mathematics Studies) Semiparametric Regression (Cambridge Series in Statistical and Probabilistic Mathematics)Elsevier Science Ltd \| ISBN: 0444861351 \| 1981-09 \| PDF \| 354 pages \| 23 Mb Science abounds with problems where the data are noisy and the answer is n ...
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	How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematic 425 pages \| Dec 12, 2006 \|ISBN:0691127387 \| DJVU \| 6 Mb[/center]Product Description:To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even al ...
	The Banach-Tarski Paradox (Encyclopedia of Mathematics and its Applications) Author: Stan WagonPublisher: Cambridge University Press (1993)Binding: Paperback, 272 pagespricer: $45.00ISBN-10: 0521457041editorialreviewsThis volume explores the consequences of the paradox for measure theory and its connections with gr ...

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