Routes of Learning

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.

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