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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.
392 pages, Hardcover
First published August 14, 2009
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August 28, 2025
This is a meta-history of mathematics (a history of its history) with some of Grattan-Guinness' suggestions on which areas of the history of mathematics have been neglected. In a lot of ways, this is a kind of guidebook on how historians of mathematics and people interested in the history of mathematics should approach the subject.
One question Grattan-Guinness thinks the writing historian should ask is suggested by one of the chapter titles, "History of Science Journals: 'To Be Useful, and to the Living'?" This chapter comes after a few chapters giving a survey of the history of the history of mathematics, and Grattan-Guinness (who worked as an editor of a history of science Journal, Annuls of Science) wrote the piece thinking of some gaps in its coverage. He says,
"[One] imbalance that greatly disturbs me is the excess emphasis on the achievements of the undoubtedly Very Great Men. Sometimes the impression is almost that only Euclid, Aristotle, Ptolemy, da Vinci, Harvey, Copernicus (the number of celebratory volumes around 1973 for him was ridiculous), Kepler, Galileo, Newton, Leibniz, Darwin, Einstein, and a few others had any brains. There are dozens of significant figures in my own tiny area of interest alone on whom very little work has been done. In this respect it will be good if journals are not useful to the living, if it means accentuating these imbalances and continuing to neglect the very many other sides of the subject."
This collection also includes a well regarded essay titled: "The Mathematics of the Past: Distinguishing Its History from Our Heritage". Grattan-Guinness highlights in this essay, the point that sometimes when the history of mathematics is written or taught (and science too), ideas and theories that were used 200 years ago, say, are given meanings or importance that they didn't have at the time they were made. He introduces and explains the difference between two (both perfectly good) readings of a mathematical theory or notion: 1) its history, which deals with "the details of the development of [a notion]: its prehistory and concurrent developments; the chronology of progress, as far as it can be determined and maybe also the impact in the immediately following years and decades"; and 2) its heritage, which deals with "the impact of [a notion] on later work, both at the time and afterward, especially the forms that it may take, or be embodied in, in later contexts. Some modern form of [the notion] is usually the main fucus, with attention paid to the course of its development."
In short, this book is a fantastic introduction to the history of (the history of) mathematics. I especially enjoyed the chapters on the history of numerology and (since I quite enjoy geometry) the exposition of a few obscure theorems about triangles.
One question Grattan-Guinness thinks the writing historian should ask is suggested by one of the chapter titles, "History of Science Journals: 'To Be Useful, and to the Living'?" This chapter comes after a few chapters giving a survey of the history of the history of mathematics, and Grattan-Guinness (who worked as an editor of a history of science Journal, Annuls of Science) wrote the piece thinking of some gaps in its coverage. He says,
"[One] imbalance that greatly disturbs me is the excess emphasis on the achievements of the undoubtedly Very Great Men. Sometimes the impression is almost that only Euclid, Aristotle, Ptolemy, da Vinci, Harvey, Copernicus (the number of celebratory volumes around 1973 for him was ridiculous), Kepler, Galileo, Newton, Leibniz, Darwin, Einstein, and a few others had any brains. There are dozens of significant figures in my own tiny area of interest alone on whom very little work has been done. In this respect it will be good if journals are not useful to the living, if it means accentuating these imbalances and continuing to neglect the very many other sides of the subject."
This collection also includes a well regarded essay titled: "The Mathematics of the Past: Distinguishing Its History from Our Heritage". Grattan-Guinness highlights in this essay, the point that sometimes when the history of mathematics is written or taught (and science too), ideas and theories that were used 200 years ago, say, are given meanings or importance that they didn't have at the time they were made. He introduces and explains the difference between two (both perfectly good) readings of a mathematical theory or notion: 1) its history, which deals with "the details of the development of [a notion]: its prehistory and concurrent developments; the chronology of progress, as far as it can be determined and maybe also the impact in the immediately following years and decades"; and 2) its heritage, which deals with "the impact of [a notion] on later work, both at the time and afterward, especially the forms that it may take, or be embodied in, in later contexts. Some modern form of [the notion] is usually the main fucus, with attention paid to the course of its development."
In short, this book is a fantastic introduction to the history of (the history of) mathematics. I especially enjoyed the chapters on the history of numerology and (since I quite enjoy geometry) the exposition of a few obscure theorems about triangles.
Displaying 1 of 1 review