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...

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Hlavní autor:	Byers, William
Médium:	E-kniha Kniha
Jazyk:	angličtina
Vydáno:	Princeton, N.J. ; Woodstock Princeton University Press 2010
Vydání:	1
Témata:	Actual infinity Addition Algorithm Ambiguity Analogy Approximation Axiom Calculation Cardinal number Cardinality Complex number Complexity Conjecture Consciousness Continuous function Contradiction Counterexample David Hilbert Derivative Dimension Emergence Equation Euclidean geometry Existential quantification Geometry Gödel's incompleteness theorems History & Philosophy Inference Infinitesimal Informal mathematics Integer Irrational number Line segment Logic Logical reasoning Mathematical induction Mathematical practice Mathematical proof Mathematical theory Mathematician Mathematicians Mathematicians > Psychology MATHEMATICS Mathematics > Philosophy Mathematics > Psychological aspects MATHEMATICS / History & Philosophy Natural number Notation Paradox Parallel postulate Parity (mathematics) PDZ Philosophy Philosophy of mathematics Philosophy of science Principle Proof by contradiction Psychological aspects Psychology Pure mathematics Quantity Quantum mechanics Randomness Rational number Rationality Real number Reason Result Science Scientific theory Scientist Series (mathematics) Sign (mathematics) Subset Summation The Unreasonable Effectiveness of Mathematics in the Natural Sciences Theorem Theory Thought Variable (mathematics) Scientific theory Subset Series (mathematics) Rational number Counterexample Logical reasoning Result Complexity Gödel's incompleteness theorems Mathematical theory Mathematical induction Calculation Axiom Contradiction Paradox Addition Real number Approximation Cardinality Consciousness Rationality Conjecture Scientist Inference Continuous function Principle Algorithm Thought Existential quantification Cardinal number Irrational number Informal mathematics Derivative Philosophy of science Summation Ambiguity Natural number Sign (mathematics) Philosophy of mathematics Line segment The Unreasonable Effectiveness of Mathematics in the Natural Sciences Theory Science Mathematics Notation Reason Actual infinity Mathematical proof Pure mathematics Emergence Theorem Analogy Logic Proof by contradiction Euclidean geometry Equation Quantity Dimension Infinitesimal Mathematician Complex number Variable (mathematics) Geometry Integer David Hilbert Parity (mathematics) Quantum mechanics Randomness Mathematical practice Parallel postulate
ISBN:	0691127387, 9780691145990, 9780691127385, 0691145997, 1400833957, 9781400833955
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