How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics /
Byers, William, 1943-
How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / William Byers. - vii, 415 p. ; 24 cm.
Includes bibliographical references and index.
Introduction : turning on the light -- Ambiguity in mathematics -- The contradictory in mathematics -- Paradoxes and mathematics : infinity and the real numbers -- More paradoxes of infinity : geometry, cardinality, and beyond -- The idea as an organizing principle -- Ideas, logic, and paradox -- Great ideas -- The truth of mathematics -- Conclusion : is mathematics algorithmic or creative? Ch. 1. Ch. 2. Ch. 3. Ch. 4. Ch. 5. Ch. 6. Ch. 7. Ch. 8. Ch. 9.
"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."--BOOK JACKET.
9780691127385 (acidfree paper) 0691127387 (acid-free paper) 9780691145990 (pbk.) 0691145997 (pbk.)
2006033160
Mathematicians--Psychology
Mathematics--Psychological aspects
Mathematics--Philosophy
BF456.N7 / B94 2007
510.92
How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / William Byers. - vii, 415 p. ; 24 cm.
Includes bibliographical references and index.
Introduction : turning on the light -- Ambiguity in mathematics -- The contradictory in mathematics -- Paradoxes and mathematics : infinity and the real numbers -- More paradoxes of infinity : geometry, cardinality, and beyond -- The idea as an organizing principle -- Ideas, logic, and paradox -- Great ideas -- The truth of mathematics -- Conclusion : is mathematics algorithmic or creative? Ch. 1. Ch. 2. Ch. 3. Ch. 4. Ch. 5. Ch. 6. Ch. 7. Ch. 8. Ch. 9.
"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."--BOOK JACKET.
9780691127385 (acidfree paper) 0691127387 (acid-free paper) 9780691145990 (pbk.) 0691145997 (pbk.)
2006033160
Mathematicians--Psychology
Mathematics--Psychological aspects
Mathematics--Philosophy
BF456.N7 / B94 2007
510.92