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How to Read Historical Mathematics
Techniques for deciphering texts by early mathematicians
Writings by early mathematicians feature language and notations that are quite different from what we're familiar with today. Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. How to Read Historical Mathematics fills this gap by introducing readers to the analytical questions historians ask when deciphering historical texts.
Sampling actual writings from the history of mathematics, Benjamin Wardhaugh reveals the questions that will unlock the meaning and significance of a given text―Who wrote it, why, and for whom? What was its author's intended meaning? How did it reach its present form? Is it original or a translation? Why is it important today? Wardhaugh teaches readers to think about what the original text might have looked like, to consider where and when it was written, and to formulate questions of their own. Readers pick up new skills with each chapter, and gain the confidence and analytical sophistication needed to tackle virtually any text in the history of mathematics.
Writings by early mathematicians feature language and notations that are quite different from what we're familiar with today. Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. How to Read Historical Mathematics fills this gap by introducing readers to the analytical questions historians ask when deciphering historical texts.
Sampling actual writings from the history of mathematics, Benjamin Wardhaugh reveals the questions that will unlock the meaning and significance of a given text―Who wrote it, why, and for whom? What was its author's intended meaning? How did it reach its present form? Is it original or a translation? Why is it important today? Wardhaugh teaches readers to think about what the original text might have looked like, to consider where and when it was written, and to formulate questions of their own. Readers pick up new skills with each chapter, and gain the confidence and analytical sophistication needed to tackle virtually any text in the history of mathematics.
- GenresMathematicsHistory
136 pages, Hardcover
First published January 1, 2010
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Displaying 1 - 5 of 6 reviews
August 10, 2019
One of the phrases you'll often hear repeated like a mantra in mathematics education circles is the maxim, borrowed from biology, that ontogeny recapitulates phylogeny. Applied to mathematics, the idea is that the course of an individual student's development in mathematics mirrors the course of the historical development of mathematics. While perhaps often overextended in discussions of the theory of education, the idea has merit: if you want to develop a deep understanding of mathematics, it's incredibly useful to know something about how that mathematics came to be. If you're struggling to grasp a particular concept or theorem, you may benefit from reading about the mathematician(s) who first proved it.
Unfortunately, many students of mathematics (and I use the term broadly here to also include students of physics or engineering or other related fields of applied mathematics) are not well-schooled in historical scholarship. Our educational system seems very well-constructed to divide students, early in life into "science and math people" and "humanities people," with surprisingly little overlap between the two sets. While there certainly are many scholars in the history of mathematics and courses on the subject are available at universities (indeed, I made sure to include a history course among my electives for my own degree in mathematics), students studying mathematics are often not well prepared for historical scholarship. They're accustomed to using a different set of skills.
This book helps to bridge that gap. Within its pages, the reader will find a concise guide to historical scholarship including chapters on subjects such as: translating historical texts into modern notation, considering the historical circumstances under which a work was completed, and probing the physical properties of a book (independent of the text) to learn about its provenance. Anyone who has any experience with historical scholarship will find the book needlessly simplistic and devoid of novel information. However, students who have some prior experience with mathematics and who are interested in reading historical texts but don't know where to start will find a lot of value in the book's gentle introduction to this sort of research.
The examples provided are likely to be familiar to most students. For instance, the first chapter includes a lengthy section concerning a short excerpt from Newton's Principia. Anyone who has taken an introductory course in calculus will find the mathematical material covered to be quite familiar. This is useful for the student. Learning how to read a historical text by focusing on familiar subjects is a wise decision. However, the reader looking for new content concerning historical mathematics will be disappointed. The book does not contain any discussion of how mathematics actually developed over the millennia, instead merely hinting at the richness of this field of inquiry.
If you are a student of mathematics interested in learning about the history of your field by digging into primary sources, or if you are a teacher of mathematics trying to help your students interact with historical mathematical documents, you will find this book to be of great value. If you're already a historian of mathematics or if you're reasonably confident in your ability to interrogate a historical text, you'll probably find the book, while well-written, ultimately of little use. In other words, this is a guidebook for the student who struggles to translate historical texts; it is not a textbook of historical mathematics. As such, I do recommend it, but only for a limited audience.
Unfortunately, many students of mathematics (and I use the term broadly here to also include students of physics or engineering or other related fields of applied mathematics) are not well-schooled in historical scholarship. Our educational system seems very well-constructed to divide students, early in life into "science and math people" and "humanities people," with surprisingly little overlap between the two sets. While there certainly are many scholars in the history of mathematics and courses on the subject are available at universities (indeed, I made sure to include a history course among my electives for my own degree in mathematics), students studying mathematics are often not well prepared for historical scholarship. They're accustomed to using a different set of skills.
This book helps to bridge that gap. Within its pages, the reader will find a concise guide to historical scholarship including chapters on subjects such as: translating historical texts into modern notation, considering the historical circumstances under which a work was completed, and probing the physical properties of a book (independent of the text) to learn about its provenance. Anyone who has any experience with historical scholarship will find the book needlessly simplistic and devoid of novel information. However, students who have some prior experience with mathematics and who are interested in reading historical texts but don't know where to start will find a lot of value in the book's gentle introduction to this sort of research.
The examples provided are likely to be familiar to most students. For instance, the first chapter includes a lengthy section concerning a short excerpt from Newton's Principia. Anyone who has taken an introductory course in calculus will find the mathematical material covered to be quite familiar. This is useful for the student. Learning how to read a historical text by focusing on familiar subjects is a wise decision. However, the reader looking for new content concerning historical mathematics will be disappointed. The book does not contain any discussion of how mathematics actually developed over the millennia, instead merely hinting at the richness of this field of inquiry.
If you are a student of mathematics interested in learning about the history of your field by digging into primary sources, or if you are a teacher of mathematics trying to help your students interact with historical mathematical documents, you will find this book to be of great value. If you're already a historian of mathematics or if you're reasonably confident in your ability to interrogate a historical text, you'll probably find the book, while well-written, ultimately of little use. In other words, this is a guidebook for the student who struggles to translate historical texts; it is not a textbook of historical mathematics. As such, I do recommend it, but only for a limited audience.
December 31, 2010
I am going to use this book in my history of math class from now on.
December 29, 2022
I've had to think a lot about whether I want to give this three or four stars and in the end...I'm going with four! But, wow, it's really close. There's nothing BAD about it, and in fact the insights it gives into the editorial process (and just the sheer amounts of questions it poses about it) really makes you appreciate it. But at the same time...I really don't need a chapter on "how to use the internet for research"...come on...lol
April 3, 2024
really just a stellar introduction to reading historical mathematics, thanks ben!
January 1, 2013
This book provides a wonderful introduction to working with primary sources in mathematics.
Displaying 1 - 5 of 6 reviews