Leseprobe
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
How Mathematicians Think
William Byers
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Naturwissenschaften, Medizin, Informatik, Technik / Geometrie
Beschreibung
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.
Kundenbewertungen
Science, Parity (mathematics), Informal mathematics, Counterexample, Mathematical proof, Cardinality, David Hilbert, Mathematical induction, Ambiguity, Complex number, Natural number, Notation, Consciousness, Contradiction, Existential quantification, Philosophy of science, Axiom, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Geometry, Conjecture, Theory, Variable (mathematics), Parallel postulate, Infinitesimal, Logical reasoning, Continuous function, Line segment, Subset, Mathematical theory, Irrational number, Scientist, Sign (mathematics), Logic, Mathematician, Real number, Analogy, Philosophy of mathematics, Theorem, Algorithm, Calculation, Approximation, Series (mathematics), Result, Thought, Mathematics, Summation, Integer, Addition, Rationality, Equation, Cardinal number, Quantity, Actual infinity, Randomness, Reason, Rational number, Emergence, Pure mathematics, Derivative, Mathematical practice, Quantum mechanics, Principle, Complexity, Gödel's incompleteness theorems, Dimension, Proof by contradiction, Euclidean geometry, Paradox, Inference, Scientific theory