Book Title: "A History of Vector Analysis" by Michael J. Crowe

Title A History of Vector Analysis
Author(s) Michael J. Crowe
Description The Evolution of the Idea of a Vectorial System

On October 16, 1943, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Academy. Meanwhile, in a less dramatic style, a German high school teacher, Hermann Grassmann, was developing another vectorial system involving hypercomplex numbers comparable to quaternions. The creations of these two mathematicians led to other vectorial systems, most notably, the system of vector analysis formulated by Josiah Willard Gibbs and Oliver Heaviside and now almost universally employed in mathematics, physics, and engineering. Yet the Gibbs-Heaviside system won acceptance only after decades of debate and controversy in the latter half of the nineteenth century concerning which of the competing systems offered the greatest advantages for mathematical pedagogy and practice.

This volume, the first large-scale study of the development of vectorial systems, traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers created by Hamilton and Grassmann to the final acceptance around 1910 of the modern system of vector analysis. Professor Michael J. Crowe (University of Notre Dame) discusses each major vectorial system as well as the motivations that led to their creation, development, and acceptance of rejection.

The vectorial approach revolutionized mathematical methods and teaching in algebra, geometry, and physical science. As Professor Crowe explains, in these areas traditional Cartesian methods were replaced by vectorial approaches. He also presents the history of the ideas of vector addition, subtraction, multiplication, division (in those systems where it occurs), and differentiation. His book also contains refreshing portraits of the personalities involved in the competition among the various systems.

Teachers, students, and practitioners of mathematics, physics, and engineering as well as anyone interested in the history of scientific ideas will find this volume to be well written, solidly argued, and excellently documented. Reviewers have described it as "a fascinated volume," "an engaging and penetrating historical study" and "an outstanding book [that] will doubtless long remain the standard work on the subject." In 1992 it won an award for excellence from the Jean Scott Foundation of France.
Dedication "TO MARY ELLEN"
ISBN 978-0-486-67910-5
Book Dimensions Width: 5.5″ (5 ½″)
Height: 8.5″ (8 ½″)
Depth: 0.63″ (5/8;″)
Page Count 306
Contents Chapter One The Earliest Traditions, Chapter Two Sir William Rowan Hamilton and Quaternions, Chapter Three Other Early Vectorial Systems Especially Grassmann's Theory Of Extension, Chapter Four Traditions In Vectorial Analysis From The Middle Period Of Its History, Chapter Five Gibbs And Heaviside And The Development Of The Modern System Of Vector Analysis, Chapter Six A Struggle For Existence In The 1890s, Chapter Seven The Emergence of the Modern System of Vector Analysis: 1894-1910, Chapter Eight Summary and Conclusions, Index
Author Photograph --
Cover Design Paul E. Kennedy
Published November 2, 2011 (Reprint edition)
Publisher Dover Publications (
Manufactured in United States of America. Dover Publications, Inc. 180 Varick Street New York, N.Y. 10014
Copyright © 1967 by University of Notre Dame Press. New material copyright © 1985 by Michael J. Crowe. All Rights Reserved.
Book Format Kindle, Hardcover, Paperback
Quoted Reviews --
Best Seller's List --
Other Dover republication of the edition originally published by Henry Holt & Co., New York, 1911.
Library of Congress
Cataloging-in-Publication Data
1. Vector analysis—History.
I. Title.
CIP Number 93-6116
LC Control Number ????
LC Call Number QA433.C76    1993
DDC Call Number 515″.63—dc20

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A History of Vector Analysis by Michael J. Crowe

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Book Review (Posted on 12-02-2017)

When you think of the word "vector," you may think of the vector objects you create from Adobe Illustrator (I'm experienced in 3D motion graphics design via Cinema 4D, so I've heard of this term before). Or, you might think of Isaac Newton's famous equation F=ma—a vector equation. Cool, so what is a vector and who came up with it? Thank goodness for this book by author Crowe, as he guides us through the history of directional magnitudes.

The gentle writing of this book is enough to keep you reading from start to end. That's a huge part because apparently, these old books featured writing styles that make the author sound pretentious and egotistical. That includes them using words that are seldom used today, even by literary scholars. Saying that, it's a breath of fresh air reading through what seemed like an advanced topic in Mathematics. There isn't much pre-requisite to reading this other than understanding algebra and geometry, but other than that, it's readable.

As for the history, it started with one of my personal favorite contributors to Mathematics, by the name of William Rowan Hamilton and his development of complex numbers and quaternions (via parallelograms). Reads like a classic film, I must say. As the author then talks about Hermann Grassmann, it becomes the longest account in talking about a mathematical figure I have ever read. Why is that? When Grassmann made his ideas and contributions public, the math and science communities weren't fans of it. Even Hamilton himself said that his published books "make great waste paper." As time went on, Grassmann passed away, and it wasn't until now that mathematicians contacted Grassmann's son to see if there are any more of his father's copy of his published works still around. Looked like what was wrong with Grassmann's book was it was too philosophical for most to understand. After some time, the sciences went on to accept the publications and contributions from Josiah Gibbs and Oliver Heaviside. Then came the idea of implementing arithmetic and even calculus to the ideas of vectors. It was briefly explained and demonstrated, but enough not to induce frequent yawns from the reader.

It's a relatively simple and great book. I feel this caters to a very exclusive group of people, namely those venturing in the world of math and physics—areas that require the usages and understandings of vectors. The average [American] citizen doesn't know much about the ideas of vectors, so I can see that people who read and enjoy this book are those who have some math prowess in them, and/or are mathematically curious. Nevertheless, it's a welcome into the more deeper waters of mathematics. Don't worry, this book will not make you drown.

Overall, it's the most gentle writing and introduction to the ideas of how vectors came to be. Who said you can't write about an advanced mathematical topic in an easy way? I enjoyed this book a lot.

Give it a read some time!

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