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...
| Autor principal: | |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Princeton, NJ :
Princeton University Press
c2007.
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| Edición: | Course Book |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009798203806719 |
Tabla de Contenidos:
- Frontmatter
- Contents
- Acknowledgments
- INTRODUCTION. Turning on the Light
- Section I. The Light of Ambiguity
- Introduction
- Chapter 1. Ambiguity in Mathematics
- Chapter 2. The Contradictory in Mathematics
- Chapter 3. Paradoxes and Mathematics: Infinity and the Real Numbers
- Chapter 4. More Paradoxes of Infinity: Geometry, Cardinality, and Beyond
- Section II. The Light as Idea
- Introduction
- Chapter 5. The Idea as an Organizing Principle
- Chapter 6. Ideas, Logic, and Paradox
- Chapter 7. Great Ideas
- Section III. The Light and the Eye of the Beholder
- Introduction
- Chapter 8. The Truth of Mathematics
- Chapter 9. Conclusion: Is Mathematics Algorithmic or Creative?
- Notes
- Bibliography
- Index
