Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics

by Ivor Grattan-Guinness

Overview

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.

Product Details

ISBN-13:	9780801892486
Publisher:	Johns Hopkins University Press
Publication date:	11/16/2009
Pages:	392
Product dimensions:	5.90(w) x 8.90(h) x 1.00(d)
Age Range:	18 Years

About the Author

Ivor Grattan-Guinness is a professor emeritus of the history of mathematics and logic at Middlesex University. He is author of Convolutions in French Mathematics, 1800–1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics and editor of the Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, also published by Johns Hopkins.

Table of Contents

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

What People are Saying About This

Amy Shell-Gellasch

Ivor Grattan-Guinness has been a leader in the field for decades. His ideas are at times contentious, which is all the more reason to have them all together in one volume. There is nothing else available like this, because there is no other researcher like Grattan-Guinness. This volume is a must for math historians, math philosophers, and all collegiate libraries.

From the Publisher

Ivor Grattan-Guinness has been a leader in the field for decades. His ideas are at times contentious, which is all the more reason to have them all together in one volume. There is nothing else available like this, because there is no other researcher like Grattan-Guinness. This volume is a must for math historians, math philosophers, and all collegiate libraries.
—Amy Shell-Gellasch, editor of From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom

Editorial Reviews

A good contribution to the literature on the field by its wealth of resources. Readers can get in touch with diverse and many lines of scientific thought and ideas.

ZDM: The International Journal on Mathematics Education - Gilda de La Rocque Palis

A useful introduction into the field of history of mathematics.

Archives Internationale d'Histoire des Sciences - Reinhard Siegmund-Schultze

Here, Grattan-Guinness, one of the world's leading mathematics historians, has written the seminal how-to-book for the history of mathematics . . . This reviewer found the book hard to put down.

Choice

This book will be appreciated by anyone with an interest in mathematical history and education, while the wide-ranging bibliographies for each chapter provide a valuable guide for further reading.

— Paul Taylor

Mathematics Today

In spite of the great variation in themes, the book is quite coherent and gives anyone dealing with the history of mathematics food for thought.

— Teun Koetsier

History and Philosophy of Logic

Here, Grattan-Guinness, one of the world's leading mathematics historians, has written the seminal how-to-book for the history of mathematics . . . This reviewer found the book hard to put down.
—Choice

In spite of the great variation in themes, the book is quite coherent and gives anyone dealing with the history of mathematics food for thought.
—Teun Koetsier, History and Philosophy of Logic

This book will be appreciated by anyone with an interest in mathematical history and education, while the wide-ranging bibliographies for each chapter provide a valuable guide for further reading.
—Paul Taylor, Mathematics Today

A good contribution to the literature on the field by its wealth of resources. Readers can get in touch with diverse and many lines of scientific thought and ideas.
—Gilda de La Rocque Palis, ZDM: The International Journal on Mathematics Education

A useful introduction into the field of history of mathematics.
—Reinhard Siegmund-Schultze, Archives Internationale d'Histoire des Sciences

From the Publisher

In spite of the great variation in themes, the book is quite coherent and gives anyone dealing with the history of mathematics food for thought.

History and Philosophy of Logic - Teun Koetsier

This book will be appreciated by anyone with an interest in mathematical history and education, while the wide-ranging bibliographies for each chapter provide a valuable guide for further reading.

Mathematics Today - Paul Taylor