Unknown Quantity: A Real and Imaginary History of Algebra | 
 enlarge | Author: John Derbyshire
Publisher: Plume
Category: Book
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Rating:  27 reviews
Sales Rank: 180643
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Media: Paperback
Pages: 416
Number Of Items: 1
Shipping Weight (lbs): 0.8
Dimensions (in): 7.9 x 5.3 x 0.9
Dewey Decimal Number: 500
Publication Date: May 29, 2007
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Condition: Brand new! Beautifu!! May have a small remainder mark (ink mark) along the edge. gift quality, crisp, clean, multiple copies available, prompt shipping, excellent service.
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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.
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| Customer Reviews: Read 22 more reviews...
 Abstraction brought down to Earth June 1, 2006
Mike Birman (Brooklyn, New York USA)
72 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)
68 out of 70 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)
27 out of 28 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.
A Chatty History of Algebra July 29, 2006
Walter Fekula (New York, NY USA)
21 out of 22 found this review helpful
"Unknown Quantity" is a history of algebra presented in Derbyshire's chatty, sometimes quirky style. It is compulsively readable. I kept stopping to remind myself I was reading a HISTORY OF ALGEBRA--and enjoying it! The math is kept at a decently low level. If you can get the idea of a polynomial (Derbyshire explains it up front), that will get you through most of the book. The explanation of groups is painstaking and pretty good, and I am fairly sure I got the main idea about rings and fields, too--though I'm afraid he lost me with "p-adic numbers." There is a strongly geometric angle in the later part of the book. This gives you some attractive diagrams--look at 13-2, the "ampersand curve," or 13-3, which beautifully illustrates the meaning of "variety"--but I found myself wondering whether the author was falling back on geometry because the algebra was just getting too hard to present to his chosen audience ("the curious nonmathematician"). When Derbyshire gets to the 20th century he pretty much gives up on trying to explain what the algebraists are doing, and concentrates on the personalities and the historical background. From the little he does tell us about 20th-century algebra, it's hard to see that he had much choice. I still have no idea what Alexander Grothendieck did in his day job, but he sure sounds like a fascinating character. Best chapter: "The Leap into the Fourth Dimension." I now understand what multi-dimensional spaces are all about and why people started thinking about them. Best chapter title: "Lady of the Rings" (that's Emmy Noether, another fascinating character). Best photograph: Hypatia--is this the first algebra book to include a picture of a naked woman? Best footnote: No. 142. (As with "Prime Obsession," the footnotes are wonderfully readable.) Still, "Unknown Quantity" shows even more clearly than "Prime Obsession" did that Derbyshire is at heart a novelist. I wish he'd give us another novel. Anyone who can make the history of algebra interesting is a born story-teller!
Modern Maths Phobia cured January 2, 2007
Wu Bing (Singapore)
25 out of 28 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
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