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Unknown Quantity: A Real and Imaginary History of Algebra Hardcover – May 15, 2006


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Unknown Quantity: A Real and Imaginary History of Algebra + Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
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Product Details

  • Hardcover: 390 pages
  • Publisher: Joseph Henry Press (May 15, 2006)
  • Language: English
  • ISBN-10: 030909657X
  • ISBN-13: 978-0309096577
  • Product Dimensions: 9.1 x 6.3 x 1.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (47 customer reviews)
  • Amazon Best Sellers Rank: #268,583 in Books (See Top 100 in Books)

Editorial Reviews

From Publishers Weekly

This book's title is deceiving, for Derbyshire offers a very real and very entertaining survey of the development of algebra. "Real" and "imaginary" refer to types of numbers, and Derbyshire (Prime Obsession) opens with a basic primer on the various flavors of numbers and polynomials before looking at algebra's development over 3,000 years. As he explains how algebraic notation wended its way from Sumerian scratches on clay to such contemporary mathematical structures as Calabi-Yau manifolds (used by Andrew Wiles to solve Fermat's Last Theorem), Derbyshire introduces readers to the colorful figures who made contributions: Hypatia, whose death in Alexandria at the hands of an angry Christian mob marked the end of mathematics in the ancient world; 19th-century mathematician Hermann Grassmann, who published a 3,000-page translation of the ancient Hindu text the Rig Veda after his work on vector spaces was ignored; and Emanuel Lasker, more famous as the longest-reigning world chess champion than for his contributions to ring theory. This book will appeal to readers who relished the rigorous mathematical discursions interspersed with informal historical vignettes of David Berlinski's A Tour of the Calculus, but less mathematically inclined readers more interested in the history of science will also enjoy it. (May)
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Review

[A] very entertaining survey of the development of algebra. (Publishers Weekly)

--This text refers to the Paperback edition.

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This book can lift you up and make you a better person for having read it.
Donald B. Siano
John Derbyshire's Prime Obsession, the story of the Riemann Hypothesis,was a mathematical tour de force but Mr. Derbyshire has done it again.
Mead C. Whorton Jr.
The author also does a good job of showing the historical context for the development of certain ideas in mathematics.
Jay P

Most Helpful Customer Reviews

118 of 120 people found the following review helpful By Michael Birman TOP 500 REVIEWERVINE VOICE on June 1, 2006
Format: Hardcover Verified Purchase
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.
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97 of 98 people found the following review helpful By Mead C. Whorton Jr. on May 16, 2006
Format: Hardcover Verified Purchase
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.
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46 of 46 people found the following review helpful By R. Lighthizer on June 20, 2006
Format: Hardcover Verified Purchase
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.
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41 of 42 people found the following review helpful By Steven W. Erbach on May 24, 2006
Format: Hardcover Verified Purchase
I had high hopes for UQ. My hopes were not dashed, but I wasn't as uplifted and exalted as I was with Derbyshire's excellent "Prime Obsession". If one comes upon these two books for the first time, one should definitely read UQ first.

As in "Prime Obsession", Derbyshire writes very appealingly about the history of the times and about the mathematicians themselves. The biggest issue is that the book is too small for such a huge subject. It's only 320 pages long with 32 pages of notes.

Derbyshire's portraits of algebraists in his book are uniformly delicious. His bio of Alexander Grothendieck reminded me of the life of former world chess champion, Bobby Fischer. Grothendieck was as unworldly, uninformed, naively opinionated, anti-American, and brilliant as Fischer. We find him now holed up in a remote village in the Pyrenees, where "he is known to come up with ideas like living on dandelion soup and nothing else."

Or Solomon Lefschetz, the algebraic geometer, who lost both his hands in an industrial accident. He was "energetic, sarcastic, and opinionated", and something of a character. His most famous quote: "It was my lot to plant the harpoon of algebraic topology into the body of the whale of algebraic geometry."

I think that Derbyshire had to edit severely. His introduction to "Unknown Quantity" says that it was "written for the curious nonmathematician." Perhaps he should have said, "written for the college math major who decided not to pursue a career in mathematics." I studied math in college but I didn't get a degree.
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