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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.
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)
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. --このテキストは、 ハードカバー 版に関連付けられています。
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. --このテキストは、 ハードカバー 版に関連付けられています。
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最も参考になったカスタマーレビュー
3 人中、3人の方が、｢このレビューが参考になった｣と投票しています。
形式:ハードカバー
代数学を中核に据えて、色々な人物の織り成す人間模様を描いた本である。数の代わりに文字を用いることを始めた人達として、Descartes, Newton, Leibniz, Viete等が、方程式から群への動きに貢献して人達として、Lagrange, Cauchy, Abel, Ruffini等が、環論に貢献した人達として、Noether, Hilbert, Kummer, Dedekind等が、幾何学方面に足場を持ちながら何らかの意味で代数学と大きな関係を持った人物として、Lie, Klein, Poincare, Plucker等が、現代代数学の中心にいた人物として、Lefschetz, MacLane, Zariski, Grothendieck等がとりあげられている。前近代からも、３次方程式の一般解を見つけたCardanoやイラン＝イスラム文化を代表するOmar Khayyamあたりが取り上げられている。代数幾何学を話題にしているのに、イタリア学派がやけにあっさりとした扱いしか受けていなかったり、上記の人物の選択にはちょっと首を傾げる点も多々あるが、こういう素人が素人のために2次資料を駆使して書き上げた本に、そこまで要求するのは酷というものだろう。いずれにしてもepisodes集として十分楽しめるつくりになっている。私にとって印象深かったのは、Grothendieckの天才が生きていく上での救いようのない不器用さと表裏一体になっていることと、古代に文化の中心であったエジプトのAlexandriaの滅亡に至る経緯であった。最近は高校でも線形代数を勉強し、２次正方行列についてはCayley-Hamiltonの定理あたりまで勉強するが、そういうものが形成されていく１９世紀のイギリスの話は高校生にも十分楽しめる作りになっている。是非一読を薦めたい。
Amazon.com で最も参考になったカスタマーレビュー (beta)
Amazon.com:
42件のカスタマーレビュー
109 人中、108人の方が、｢このレビューが参考になった｣と投票しています。
Abstraction brought down to Earth
2006/6/2
形式:ハードカバー|Amazonが確認した購入
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
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
94 人中、93人の方が、｢このレビューが参考になった｣と投票しています。
ALGEBRA THEN AND NOW
2006/5/17
形式:ハードカバー|Amazonが確認した購入
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.
45 人中、45人の方が、｢このレビューが参考になった｣と投票しています。
Another great read from Derbyshire
2006/6/21
形式:ハードカバー
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.
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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