How to Read Historical Mathematics by Benjamin Wardhaugh (PDF)

Description

Techniques for deciphering texts by early mathematiciansWritings 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.Introduces readers to the methods of textual analysis used by historiansUses actual source material as examplesFeatures boxed summaries, discussion questions, and suggestions for further readingSupplements all major sourcebooks in mathematics historyDesigned for easy referenceIdeal for students and teachers

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐You will find this book to be a great, quick read. The intent is to encourage you to read the original mathematics typically written in words versus more modern math written in equations. The style is guided learning. I liked how the author breaks down the “code” of old mathematics. It would have been nice to have more examples, but after finishing the book, it is easy enough to find my own examples. The author provides a lot of sources to pursue for further research in the form of notes. I was happy the author did not go too far back in time, and felt sticking with math from 1500’s to !800’s was enough to get started. The other important information presented was on how to put the writing in context. The issue here is value. Sure you could spend a semester with the Katz book, or consider two nights with this book. I found the this book to be an enjoyable read, and would encourage you to give it a try.

⭐Very interesting book. I would never have picked it up “just because,” but because I was writing a paper for an upper-level mathematics seminar, I did find it a helpful resource. Essentially it introduces a reader to the types of historical mathematics materials out there, and how to differentiate between them when investigating topics in mathematics for research.

⭐The book title and summary are misleading with respect to content. If you are about to buy, take some time to figure out what is actually in the book, particularly the review by Adams. A more accurate title would be “miscellaneous remarks about old books; mostly light reading.” There is some example translation to modern notation in the first chapter, but this will not empower you to translate nor guide you to where translation is best best presented.

⭐Contrary to what you might expect from the book’s title, what this book, How to Read Historical Mathematics, does not contain, to mention the absence of only three broad topics, is:(1) a discussion of how the concept of number has changed from the Greeks to the present, and the implications for understanding the differences or controversies in the use of number and hence also controversies in the numerical range of algebraic methods from the past to the present;(2) a discussion of how the abstract nature of modern mathematics differs from classical mathematics, the “historical mathematics” of the title, and the implications for reading less abstract and non-abstract, pre-modern mathematics, which exists, so to speak, at a different conceptual level;(3) a discussion of how criteria of justification or concepts of proof and rigor have fluctuated from the period of the ancient Greeks through the intervening ages into the present, and the implications for what counts for understanding, and thus the possible historical differences in levels of cognition.None of this is discussed in the book. To mention is not to discuss. Each one of those topics is deep and broad. Wardhaugh splashes about in the kiddy pool instead. What the book in fact contains is simple advice such as:(1) to try to translate the text into modern notation without changing the meaning (yet he doesn’t discuss the differences between mathematical world-views and seems to believe the student will be magically enlightened on this through the course of translation work, not historical study);(2) to consider how modern notation has meaning for a modern reader that may differ from the meaning which similar or identical historical notation may have for the original readers, and how non-notational mathematics may itself differ in meaning or differ in meaning from what would seem to be a modern notational equivalent (yet he doesn’t discuss this beyond mentioning it, and even then, not as overarching as this);(3) to try to discover the context of the text, meaning who, what, when, where, why, and how (yet he doesn’t explain what possible contexts would actually matter, nor why nor how);(4) to examine the vehicle of the text, eg. book, professional journal, diary, scratchpad, clay tablet etc., and to consider what, then, may have been the purpose of the text and for whom may it have been written (yet he doesn’t explain how that helps in understanding the mathematics of the text, which, one would think, is the first point of reading historical mathematics);(5) to try to recover the original version of the text if the text under study is a copy (yet he doesn’t discuss this beyond a mere mention of how a copy may differ from an original and to refer very briefly also to the student’s making of a copy and the editorial choices that may have to be made).This is really a silly book, to be mean about it. It’s written in a condescending style as if the reader is a child who needs to be patted and congratulated for learning the most simple principles, and who at the same time has an intellect that might take an active interest in reading from Newton’s Principia. I can’t imagine who the author thinks needs or will appreciate this book. It’s shallow, it’s patronizing, it’s facile, and it’s off the mark.

⭐auch wenn das in Deutschland nicht mehr zu stimmen scheint. Während man sich hierzulande allzuoft an Hermeneutik und Kontext abarbeitet versteht man im Ausland unter “Mathematikgeschichte” das harte Studium der Quellen und ihre historische Einordnung. Wardhaugh hat ein schönes kleines Büchlein über den Umgang mit Quellen vorgelegt, das jedem Anfänger nur zu empfehlen ist. Ein Wermutstropfen ist nur der geringe Umfang. Mehr als ein Einstieg in dieses wichtige Thema ist es also nicht.

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