Unknown Quantity: A Real and Imaginary History of Algebra | 
 enlarge | Author: John Derbyshire
Publisher: Plume
Category: Book
List Price: $16.00
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Rating:  28 reviews
Sales Rank: 37938
Media: Paperback
Pages: 416
Number Of Items: 1
Shipping Weight (lbs): 0.8
Dimensions (in): 7.9 x 5.2 x 1
ISBN: 0452288533
Dewey Decimal Number: 512.009
EAN: 9780452288539
Publication Date: May 29, 2007
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Condition: New Book. Fast Shipping. May have small remainder mark.
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Product Description
For curious nonmathematicians and armchair algebra buffs, John Derbyshire discovers the story behind the formulae, roots, and radicals. As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel s proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from "this plus this equals this" to "this plus what equals this?" gave birth to a whole new way of perceiving the world. With a historian s narrative authority and a beloved teacher s clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging journey through the development of abstract mathematical thought.
Book Description
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the agesa and it promises to be just what his die-hard fans have been waiting for.“Here is the story of algebra.” With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel’s proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematicsa it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.
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| Customer Reviews: Read 23 more reviews...
 Abstraction brought down to Earth June 1, 2006
Mike Birman (Brooklyn, New York USA)
73 out of 74 found this review helpful
Those of us who read and enjoyed Prime Obsession (even the title has a delicious tabloid flavor, reminiscent of Basic Instinct or Fatal Attraction) may have been most amazed at the very idea of popularizing something as arcane and difficult as the Riemann Hypothesis. What made that book work so well was Derbyshire's brilliant alternation between historical narrative and description with chapters that served as a mathematical primer on number theory and other background material. The mathematically challenged reader could peruse these more technical chapters or leave them be by choice: there was still much knowledge to be gained in either case. For the more mathematically sophisticated, a complete reading of the book served as a reasonably deep (if popularized) analysis of the famous Riemann Hypothesis. Short of tackling H. M. Edward's Riemann's Zeta Function, the classic discussion and much more difficult, Derbyshire provided the most cogent introduction to the RH.
Unknown Quantity is similarly constructed, with historical and biographical material alternating with chapters Derbyshire once again describes as mathematical primers. Although trained as a molecular biologist, I have a fairly strong background in mathematics. I still found much to learn. Especially interesting is the material on Vector Spaces and Algebras, the introduction to Hamiltonian Quaternions, Rings and Fields (with the vista of Abstract Algebra just over the hill) and a short introduction to Algebraic Geometry. I found even more to enjoy. The historical and biographical threads make the unfolding mathematics that much clearer and easier to visualize, hence more enjoyable. Derbyshire has produced another superb book that makes mathematics live and breath. To breath life into abstraction is a great gift. I reread Prime Obsession and will do the same for this newest work. If you find mathematics at all amenable to your taste, I urge you to sample this book. I look forward to being pleasantly surprised by the topic of his next work.
Mike Birman
ALGEBRA THEN AND NOW May 17, 2006
Mead C. Whorton Jr. (Bastrop, LA United States)
70 out of 71 found this review helpful
John Derbyshire's Prime Obsession, the story of the Riemann Hypothesis,was a mathematical tour de force but Mr. Derbyshire has done it again. He has written an extraordinary book which traces the history of algebra from its beginnings in the Fertile Crescent nearly four thousand years ago to such modern day abstractions as Category Theory. To assist the reader who has never encountered higher undergradate mathematics or who has forgotten the content of courses taken long ago, Mr. Derbyshire has provided well written, concise MATH PRIMERS on such diverse topics as Cubic and Quartic Equations, Roots of Unity, Vector Spaces and Algebras, Field Theory, and Algebraic Geometry. These Primers are scattered through the text and serve as guide-posts for the reader as she/he treks through the historical development of Algebra. If you have ever wondered how Algebra began and what groups, rings, fields, vector spaces, and algebras are then purchase this book. The author has also done a wonderful job of bringing alive the many men and women who, through the centuries, created modern day abstract algebra. This is not a light read but the prose and logic are superb. The reader who is willing to invest the time to complete this book will emerge all the richer for completing a thrilling intellectual adventure of the highest order.
Another great read from Derbyshire June 20, 2006
R. Lighthizer (NY, NY)
29 out of 29 found this review helpful
Mathematics is not a topic that is easy to read or write about.
How lucky we are, then, that John Derbyshire has chosen once more to grace us with his talent for writing clear, concise, coherent prose on higher math.
In Unknown Quantity, Derb has again achieved the near-impossible feat of writing an approachable, relatively easy-to-read book on mathematics.
Reading Mr. Derbyshire's mathematical writings allows one to experience some of the awe and majesty of the deepest, most esoteric reaches of higher mathematics. In giving the common reader this chance, he does a service both to mathematics by allowing those who would rarely even hear about such topics to learn something of them and also to the reader by allowing him for a moment to feel smarter than he probably has any reason to.
I cannot disagree with others who found Prime Obsession to be the better read, however this should not be taken as a serious criticism of Mr. Derbyshire or Unknown Quantity. Prime Obsession was helped by its more limited focus - not that the author had any shortage of interesting and enlightening information and insight to share.
Unknown Quantity's goal of presenting a readable, reasonably approachable history of algebra is definitely met, but it would probably require a book several times the length of this one to properly explore all the intricacies of the story with the thoroughness that Mr. Derbyshire could. That book might not be as broadly marketable but I feel it would be gladly received by those of us who have discovered Derb's genius.
If you have any interest in math or the history of human thought, you cannot go wrong with Unknown Quantity.
Modern Maths Phobia cured January 2, 2007
Wu Bing (Singapore)
25 out of 27 found this review helpful
I learned the Modern Algebra 28 years ago in the very university of "The Last Theorem of Fermat" in Toulouse, France (Classe Preparatoire aux Grandes Ecoles, Lycee Pierre de Fermat - Mathematiques Superieures et Mathematiques Speciales). These were the 'darkest' years of my study life when we slogged for 2 years learning the abstract Modern Algebra and Analysis. The French are "Maths lovers" people, given 100+ streets in Paris are named after their mathematicians.
I remembered the Maths were taught in the form of arcane and boring Axioms/Theorems. starting from Set Theory (Ensemble), Group (Groupe), Ring (Anneaux), Field (Corps), Vector Space (Espace Vectorielle), Affine Space(Espace Affine), Matrix, Topology, etc. The toughest Grandes Ecoles Entrance Exams (Concours) demanded the students master these maths abstract concepts in order to solve difficult maths questions in long-hour written and oral Papers. Many bright top students, after scoring brilliant results to enter the prestigious Ecole Polytechnique (the one which failed twice Evariste Galois!), shied away from Maths in their life later because of this "Maths Phobia". What a shame and waste of maths talents.
After reading The "Unknown Quantity", I always ask "If only these Maths were taught in the similar interesting way", we could have actually loved and enjoyed it in our entire life.
Derbyshire has introduced many 'revolutionary' Maths teaching ideas:
1) Group, Ring (Ideal) and Field are presented in a non-traditional reversed order of all Maths text books. He said: "Field is a more common place kind of thing than a Group, and therefore easier to comprehend." I agree 100% when I read this book without any difficulty to follow.
2) Many enlightening 'tips' e.g. NZQRC (Nine Zuru Queens Rule China), helps my teenage children grasp instantly the intrinsic Number Theory over a dinner talk.
3) 'Vector Space' was presented in a refreshing manner, without bothering us with the difficult theorem, which helps us understand the linear (in)dependence, hence linear algebra and its importance in application.
4) Chapter 8 "The Fourth Dimension" on Hamilton's Quaternions (1,i,j,k) and the intriguing story of the discovery (page 151) at Brougham Bridge on one Monday, 16th Oct, 1843.
5) Why x is the predominant used unknown variable in equations (Chapter 5, Page 93), because the french printer ran short of letters (y and z are commonly used in French language).
6) The reason behind the eccentric choice of letters (a,h,b,g,f,c, skipping i and e) for coefficients in conic equation: ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 was uncovered in the matrix on Page 245 (another maths tip: "All hairy guys have big feet") and Page 248 (homogeneous coordinates).
7) The Yin-Yang view of Geometry vs Algebra. Geometry is for Space and Algebra for Time (Sequence of transformation).
I had spent my entire 1 week holidays in end December till 1 Jan 2007 reading this book. No regret of time wisely spent. I urge all who are "curious nonmathematicians" to follow me.
This book has cured my 28 year-Modern Maths Phobia!
Cornelius
Excellent historical grounding of the most basic of math subjects November 9, 2006
P. J. Hartwick (Tucson, AZ)
18 out of 19 found this review helpful
If you're like most folks, you took algebra in high school and within a week you learned to stop wondering "why" something was like it was or how "they" figured out some rather abstract idea. Instead, you just memorized the definitions and the "tricks" that were presented as "teaching", without ever really understanding the "why" of it all. We tend to forget that it took a lot of people thousands of years of thought to produce what we have today between the covers of a basic algebra book. And the subject is taught in such a way that we feel slightly guilty if we don't immediately "get" some idea or concept that actually was a long time in the making. The problem only compounds as we take more math courses, since algebra is a key language for all of them. What to do?
Read John Derbyshire's book! Take it slowly, with a pencil and pad next to you; don't just read the book, digest it! His thoughtful inclusions of somewhat detailed explanations of building block material is especially helpful. Even if you're past the point of needing to know anything about math, let alone algebra, it'll be good exercise for the brain and it'll help with other tasks that you do use every day -- like trying to remember someone's name or phone number right after you heard it! I took my first algebra course almost 50 years ago (can it be?) and I often found myself saying "if only they had presented it this way back then, I could have actually LEARNED something!. The "teachers" I had for those first courses in high school were uniformly bad, so I shouldn't have expected them to convey what they didn't have: understanding.
Incidentally, if you know someone just starting out with high school math, this book would be a nice gift to help fill the gaps. Who knows? It might even motivate them to go further. In a society when mathematical literacy is becoming increasingly critical to personal and societal success, the schools are doing an ever-poorer job of meeting the need. Books like this help fill that gap.
Highly recommended.
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