How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / William Byers.
"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, in...
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| Format: | Book |
| Language: | English |
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Princeton :
Princeton University Press,
c2007.
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Table of Contents:
- Introduction : turning on the light
- Ch. 1. Ambiguity in mathematics
- Ch. 2. The contradictory in mathematics
- Ch. 3. Paradoxes and mathematics : infinity and the real numbers
- Ch. 4. More paradoxes of infinity : geometry, cardinality, and beyond
- Ch. 5. The idea as an organizing principle
- Ch. 6. Ideas, logic, and paradox
- Ch. 7. Great ideas
- Ch. 8. The truth of mathematics
- Ch. 9. Conclusion : is mathematics algorithmic or creative?