Enlightening symbols: a short history of mathematical notation and its hidden powers / Joseph Mazur

Incluye índice: páginas 269-285

Introduction.. Definitions.. Note on the Illustrations.. Part 1 Numerals.. 1. Curious Beginnings.. 2. Certain Ancient Number Systems.. 3. Silk and Royal Roads.. 4. The Indian Gift.. 5. Arrival in Europe.. 6. The Arab Gift.. 7. Liber Abbaci.. 8. Refuting Origins.. Part 2 Algebra.. 9. Sans Symbols.. 10. Diophantus's Arithmetica.. 11. The Great Art.. 12. Symbol Infancy.. 13. The Timid Symbol.. 14. Hierarchies of Dignity.. 15. Vowels and Consonants.. 16. The Explosion.. 17. A Catalogue of Symbols.. 18. The Symbol Master.. 19. The Last of the Magicians.. Part 3 The Power of Symbols.. 20. Rendezvous in the Mind.. 21. The Good Symbol.. 22. Invisible Gorillas.. 23. Mental Pictures.. 24. Conclusion.. Appendix A Leibniz's Notation.. Appendix B Newton's Fluxion of xn .. Appendix C Experiment.. Appendix D Visualizing Complex Numbers.. Appendix E Quaternions.. Acknowledgments.. Notes.. Index

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. eng