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Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century, by Victor J. Katz, Karen Hunger Parshall
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What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century.
Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era.
Taming the Unknown follows algebra's remarkable growth through different epochs around the globe.
- Sales Rank: #355552 in Books
- Published on: 2014-07-21
- Original language: English
- Number of items: 1
- Dimensions: 1.43" h x 6.45" w x 9.58" l, .0 pounds
- Binding: Hardcover
- 504 pages
Review
"An excellent book; its accurate historical and pedagogical purpose offers an accessible read for historians and mathematicians."--Raffaele Pisano, Metascience
"Well written and engaging with a wealth of useful material and a substantial bibliography for further reading, this book is a valuable resource for anyone with a serious interest in the history of algebra. With Taming the Unknown, Victor Katz and Karen Parshall have created a comprehensive synthesis of recent research on the subject, accessible to mathematicians, historians of mathematics and anyone involved in the teaching of algebra."--Adrian Rice, BSHM Bulletin
From the Back Cover
"Taming the Unknown is well written and informative, and will satisfy any reader with an interest in the history of algebra. Striking just the right balance between general overview and technical detail, this book is a pleasure to read."--Joseph W. Dauben, City University of New York, Graduate Center
"This original and high-quality book is a significant contribution to the history of mathematics. It will be useful to scholars doing research in the history of mathematics, as well as to a broader readership that includes mathematics teachers, advanced undergraduate or graduate students, and mathematicians."--Leo Corry, Tel Aviv University
"This fine survey of the history of algebra is clearly and engagingly written. It will become the standard reference on this topic by virtue of its scholarship, coverage, and readability."--Tom Archibald, Simon Fraser University
About the Author
Victor J. Katz is professor of mathematics emeritus at the University of the District of Columbia. Karen Hunger Parshall is professor of history and mathematics at the University of Virginia.
Most helpful customer reviews
10 of 10 people found the following review helpful.
A Powerful and Modern Narrative on Algebra.
By G. Arnell Williams
In recent times, much exceptional work often in the form of articles has been written on the nature and history of algebra: What is algebra truly about? What role did symbolism really play throughout its history? Are there three distinct phases in the evolution of algebra: rhetorical, syncopated and symbolic? Or only two: rhetorical and symbolic? Or should we look for a different classification scheme entirely? Excellent research is being done in many places throughout the world on these and other important questions.
This excellent and well-researched book joins this current tradition by providing one of the most powerful historical narratives of algebra that I have yet seen. In regards to its history on elementary algebra, the book strikes the nice balance between providing sufficient technical details without overwhelming the reader. It also goes into very nice depth and detail in discussing the extensive contributions to algebra of medieval mathematicians.
Another highlight of the book is its detailed discussion of the connection between the revolutionary work in algebra of 16th century mathematicians and the revolutionary work in analytic geometry, calculus and physics of 17th century mathematicians & scientists. This is a powerful and important transformational bridge that is often glossed over in many books. Taming the Unknown tackles these particulars head-on; and in an insightful and nuanced fashion that sets it apart from the pack.
The book also excels in its demonstration of how the study of the algebraic structure of equation solving in the 17th through early 19th centuries gradually transformed into the modern abstract algebraic study of mathematical structures in general.
All in all, Katz & Parshall are to be commended for having written a remarkable book. One of their stated goals is to show how the algebra of the past (much of which is now codified in the x’s & y’s in today’s school algebra courses) led to some of the modern algebra of today (now taught to “advanced college-level students”). A noble aim which, in my opinion, they have in great measure achieved.
If you are someone seeking a deeper conceptual understanding and appreciation of the history and/or structure of algebra in its many phases, then this book (written in the form of a tightly woven and explanatory story) is for you!
1 of 1 people found the following review helpful.
I rate this book, Taming the unknown, as ...
By Francis Bacon
I rate this book, Taming the unknown, as a magnificent 5 star book.
I applaud the authors for the hard work and academic excellence
that they put into their book. To see the historical unfolding of the
mathematical roots of algebra across so many cultures, makes for
fascinating reading. The quest for solving for the unknown, reveals the
universal aptitude of scholars across Egyptian, Mesopotamian, Greek,
Chinese, Islamic and European cultures in giving us this heritage. This
book is a treasure to have on my book shelve.
1 of 1 people found the following review helpful.
Great book!
By Rachael Bro
I actually didn't purchase this book on Amazon but I did use it for a class and really enjoyed it so I thought I might as well post a review. The authors did a great job at organizing their book as well as presenting information to the reader. Even though I was required to read it for class, I found myself not hating that I had to read for class. It's interesting to read about history from a mathematical view.
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