CiNii 図書 - Routes of learning : highways, pathways, and byways in the history of mathematics

This seminal collection gathers together many general writings of one of the world's leading historians of mathematics. Organized thematically, these essays ponder the intellectual underpinnings of the field, examine the major topics in the history of mathematics, and recount the bizarre history of pseudomath. Ivor Grattan-Guinness explores how people understand mathematics-the routes of learning they take as they make important discoveries and study mathematical concepts and theories. The essays in the first part of the book discuss the history of mathematics as a field and its central philosophical issues. Those in the next part address the history of mathematics education and its importance to current modes of teaching. In the last section Grattan-Guinness investigates various understudied aspects of math, including numerology, Masonic symbols in classical music, and the links between mathematics and Christianity. This collection includes several essays that are difficult to find anywhere else. All historians of mathematics and students of the field will want a copy of this remarkable resource on their bookshelves.

Preface 1. Searching for Reasons: My Way In and Onward Part I: Highways in the History of Mathematics 2. The Mathematics of the Past: Distinguishing Its History from Our Heritage 3. Decline, Then Recovery: An Overview of Activity in the History of Mathematics during the Twentieth Century 4. On Certain Somewhat Neglected Features of the History of Mathematics 5. General Histories of Mathematics? Of Use? To Whom? 6. Too Mathematical for Historians, Too Historicalfor Mathematicians 7. History of Science Journals: "To Be Useful, and to the Living"? 8. Scientific Revolutions as Convolutions? A Skeptical Inquiry Part 2: Pathways in Mathematics Education 9. On the Relevance of the History of Mathematics to Mathematical Education 10. Achilles Is Still Running 11. Numbers, Magnitudes, Ratios, and Proportions in Euclid's Elements: How Did He Handle Them? 12. Some Neglected Niches in the Understanding and Teaching of Numbers and Number Systems 13. What Was and What Should Be the Calculus? Part 3: Byways in Mathematics and its Culture 14. Manifestations of Mathematics in and around the Christianities: Some Examples and Issues 15. Christianity and Mathematics: Kinds of Links, and the Rare Occurrences after 1750 16. Mozart 18, Beethoven 32: Hidden Shadows of Integers in Classical Music 17. Lagrange and Mozart as Critics of Descartes Part 4: Lollipops 18. Four Pretty but Little-Known Theorems Involving the Triangle Index

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Routes of learning : highways, pathways, and byways in the history of mathematics

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