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Unknown Quantity: A Real and Imaginary History of Algebra
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Unknown Quantity: A Real and Imaginary History of Algebra

3.85  ·  Rating Details  ·  471 Ratings  ·  46 Reviews
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? ...more
Paperback, 400 pages
Published May 29th 2007 by Plume (first published May 2nd 2006)
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Community Reviews

(showing 1-30 of 1,486)
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Koen Crolla
Mar 17, 2010 Koen Crolla rated it really liked it
Shelves: mathematics
Though Derbyshire is a dimwitted douchenozzle on many, many subjects, he managed to write a decent book on algebra.

My original review—before I realised this John Derbyshire was also John Derbyshire, the racist/homophobe/theotard/hypocrite/all-round dipshit who writes for the National Review—was going to mention how the book takes a naïve attitude towards history that's refreshing in this age of nuance and relative rigor (something that's only remotely acceptable because the book isn't about, and
Theresa Leone Davidson
I have written before about my propensity in high school to avoid being challenged in math: once I became intimidated by the work, by 8th or 9th grade, I took the easy way out, never challenged myself, and did altogether poorly in the subject. However, in college I had brilliant professors in the math classes I was required to take and they inspired me to take more than was required and instilled in me a love of the beauty of numbers, formulas, equations, etc. Algebra has always been my favorite ...more
Maurizio Codogno
Nella matematica che si fa a scuola la geometria quanto quanto è comprensibile: le figure almeno le si vede. L'analisi matematica, con derivate e integrali, è appannaggio di pochi (s)fortunati. Ma quello che probabilmente fa odiare a tutti la matematica sono le equazioni e i polinomi; quello che viene chiamato algebra. Un libro come questo, che racconta la storia dell'algebra partendo dai babilonesi per arrivare al ventunesimo secolo, potrebbe essere visto come il fumo negli occhi. Non è così, p ...more
Dec 27, 2007 Jesse rated it really liked it  ·  review of another edition
Shelves: history, mathematics
There's an inherent difficulty in writing a book of this kind; a significant portion of the material that the author is expected to cover is simply out of the range of readers that lack an extensive background in mathematics. It is, in fact, worse than physics, in which metaphors can be used to give the reader some inkling of what's going on, even if they don't completely understand the reasons behind it. That being said, Derbyshire does a worthy job at a devilishly difficult task.

The first hal
Nov 22, 2008 Adam rated it liked it
Unknown Quantity is an interesting book about the history of algebra, but I think its major failing is that it concentrates sufficiently heavily on the mathematics that it's hard to read sections if you aren't already knowledgeable about them. It claims to be aimed at the non-mathematician, but even as someone who has good knowledge of algebra, there were portions of the book (such as the topology sections) that I got very little out of because I wasn't already familiar with the particular branc ...more
Jan 21, 2012 gargamelscat rated it it was ok
Shelves: math, 2012
The book falls between the stools of "popular math" and math treatments but is not rigorous enough to satisfy those interested in the latter and loses those drawn to the former in splurges of (incomplete) equations and hard to follow

On the plus side the potted histories of the various mathematicians encountered are entertaining and the book is reasonably well written.

It did serve the purpose of illustrating the arcane geography of modern algebra but didn't make me interested in it. Somewhat
Jan 28, 2011 Nur is currently reading it
Recommended to Nur by: being a Discrete Mathematics TA
Shelves: non-fiction
"The story of algebra, is the story of civilization itself..."

I stumbled on this book somewhere at Amazon while searching for books to help me become a better TA in undergraduate Discrete Math class. The class is entirely in Japanese, so imagine studying sets and groups and lattices using symbols (read: kanji) you've never seen and had no clue on the reading and meaning.

I need a good English textbook to keep me sane, and being a fiction-lover, I certainly hope this book could lift my mood in the
Nishant Pappireddi
Jun 20, 2014 Nishant Pappireddi rated it it was amazing
As someone who has already been exposed to many, if not most, of the ideas in this book, I was hoping that it would be more interesting to me than the usual popular math book. "Unknown Quantity" definitely exceeded my expectations on this. Though there were a couple of parts that annoyed me (e.g., he defines a prime number in a ring as being one with no factors besides units and itself, which was especially bad because he was discussing a non-UFD, where "prime" and "irreducible" are not the same ...more
Jose lana
Dec 09, 2015 Jose lana rated it really liked it
Shelves: science, mathematics
This book is another good work of John Derbyshire;the history of algebra from the babilonians to our days making things understable for those with a background of high school,it makes understable concepts as the complex numbers ,vector spaces ,quaternions ,algebraic structures as rings and gives a very elemental introduction to galois theory and algebraic topology
Jan 25, 2016 Erik rated it really liked it
Well played Mr. Derbyshire. This book *appears* to be a history book, but in fact is a gentle introduction to advanced abstract algebra. It focuses on concepts and patterns rather than slogging through proofs, which is by far the most enjoyable way to learn. Books about mathematics have to be careful about the amount of actual math they include, and this book is on the light side. Derbyshire navigates this well early, but in the later parts of the book I wished the ideas were anchored in actual ...more
Theodosia of the Fathomless Hall
It does suffer from the mathematical tendency to be analytic and without personality, but it familiarizes if not outright teaches a multitude of mathematical principles.

There are math primers for each chapter of the history but one, and then there are the aforementioned history/concept chapters. Occasionally dry wit is added into the fray, with a healthy dose of originality and a fresh outlook. Certainly there are more userfriendly approaches to the discipline -- unless one is fluent in rings,
Jonathan Peto
I reached Chapter 12. I noticed reviews by people with stronger backgrounds in math than I have and decided to abandon ship since they too lost focus during the last quarter.
Jan 24, 2010 Joe rated it liked it
I like the history of mathematics... [turns head away in shame, moist eyes brimming with hot tears of disgrace]
Oct 09, 2015 Rossdavidh rated it liked it  ·  review of another edition
Shelves: red
Subtitle: A Real and Imaginary History of Algebra. This is, more or less, the story of how math got away from us. How it went from a way of counting clay casks of grain given as tribute in Mesopotamia, to a system for analyzing entities which have no physical existence, the nature of which cannot easily be explained, and the usefulness of which (while often, it is eventually discovered, quite substantial) is not apparent even to those who are working on it. It's basically the history of how math ...more
Mary Ronan Drew
Mar 03, 2011 Mary Ronan Drew rated it liked it
Shelves: library-book
Unless you already know what Nine Zulu Queens Ruled China has to do with anything and solve the occasional recreational quadratic equation (as I confess I have been known to do from time to time), this book may not be for you.

However, there are two approaches to this history of algebra. One is for those who are tickled to death with Edwin Abbott’s Flatland and know the significance of 1,1,2,3,5,8,13,21,34,55,89,144,233,377, . . . The other is for folks who would like to know which mathematician
Bryan Higgs
I've read a number of "Math for the layman" books in recent years (including this author's Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, which I reviewed here a while back: This one covers a number of topics and history that I've seen covered in many of those other books.

Surprisingly, I have found the history sections of these books often to be more interesting than the math sections -- I say surprisingly because I
Nov 17, 2008 Natbas rated it really liked it
Recommends it for: people interested in ideas

I am reading a book on Maths, I am about to finish it, and in this book, I found a superb passage:

"I remain completely confident that the labor I have expended on the science presented here and which

hasd emanded a significant part of my life as well as the most strenuous application of my powers, will

not be lost. It is true that I am aware that the form which I have given the science is imperfect and must

be imperfect. But I know and feel obliged to state (though I run the risk of seeming arro
Mar 07, 2012 Randy rated it really liked it
Derbyshire interweaves superficial biographic sketches of the mathematicians with superficial descriptions of their discoveries, alongside Will Durant-esque comments on the world political situation at the time.

I found it very interesting. It will be more interesting for you if you have heard of Descartes, Gauss, Riemann... and if you have a sense of what a function is, a matrix, a ring. You need not be able to manipulate them, but if you can visualize how they work, you will enjoy this book.

Feb 10, 2016 Tom rated it did not like it
I found it difficult to follow, especially since most of the book focuses on the biographies of obscure 18th century British mathematicians as opposed to the medieval fundamentals or interesting 20th century advancements, and it turns out that it's because the author is a raging white supremacist.
Oct 21, 2007 Erica rated it liked it
Recommends it for: math nerds
Shelves: fall2007

I checked this out at the library. Wanting to know more history about mathematics (because I have started doing this monthly thing with my students called the "Mathematician of the Month" where they research a famous mathematician that has had some influence over whatever unit they/we are currently learning), I thought this book by Mr. Derbyshire would be a good choice.

BOOOORING. I did get some good tidbits out of it though. 1) Decartes invented the radical symbol for square roots. 2) De
Jan 07, 2016 Mattie rated it liked it  ·  review of another edition
A history of algebra. Because I'm just that kind of nerdy. I feel a little ambivalent in rating this book because I'm not sure I understood some of the math well enough to rate it. That said, any failure to follow the math was, I think, mine, not Derbyshire's.

The sections of the book I liked most were when he tied the developments in the discipline to what was happening in the world at large. I just wish there had been more of this - more contextualization of parallel developments in art, scienc
Nov 15, 2014 AJ rated it it was ok
I'm not really sure who the author was considering as the audience for this book. It's too technical at times for a layperson (and even engineers with PhDs apparently) and not detailed enough for the mathematician. Sometimes it's more like a historical biography of mathematicians and other times more like a math textbook. Additionally, the author broke the 4th wall a lot, and while I don't mind when authors do that, he was kind of annoying. He'd interject to say how he loves drawing figures by h ...more
Apr 15, 2015 Robertbyron22 rated it really liked it  ·  review of another edition
Enjoyed and learned from it. Not as good as his other history of math book, Prime Obsession. Review will be on blog.
Marc Towersap
Nov 09, 2012 Marc Towersap rated it really liked it
I did enjoy this book, a bit of a slog, maybe took 2 months to get through it. I worked through much of the math to ensure I understood it. The history was quite interesting, I really enjoyed the way he walked from the beginning to what's going on today. Makes me want to revisit the stuff I learned but have forgotten! If you don't know much math, this book will be very very difficult to read. I had to recall as best I could what little I remember from my undergraduate physics classes to tackle t ...more
Tracy Black
Jun 17, 2010 Tracy Black rated it really liked it
First, I have to say that as a non-mathematician, I had a terrible time with this. This algebra is not college freshman algebra. There were many topics I lacked a background in, and I spent much time digging through my husband's old math textbooks to gain enough understanding just to follow the book.

It was worth it though. Derbyshire is witty and the book was well written and very interesting. Not quite as good as Prime Obsession, but the math was easier for me to follow in that one, so the it w
Shu Lindsey
Jun 07, 2007 Shu Lindsey rated it it was ok
"[E]very science, when we understand it not as an instrument of power and domination but as an adventure in knowledge pursued by our species across the ages, is nothing but this harmony, more or less vast, more or less rich from one epoch to another, which unfurls over the course of generations and centuries, by the delicate counterpoint of all the themes appearing in turn, as if summoned from the void."
Mar 17, 2009 Michael rated it liked it
Okay, but not as good as "Prime Obsession". It can't seem to decide whether it wants to be a math book or a history book. As a result, it isn't very good at being either. For the math layman (as I am), the more abstract algebra later in the book requires more explanation/background than what the author provides, making it somewhat pointless to read.
Jan 23, 2010 Jessica rated it it was ok
This started out as a more interesting and less technical book on math history than others I have read, but got confusing and technical for the last third of the book or so. It was a good overview of the development of algebra and gave me a few interesting stories to tell my classes.
Jul 16, 2014 Alterstuart rated it really liked it  ·  review of another edition
Bought this for my son to supplement his algebra MOOC, but ended up reading it myself. This book introduces you to some mind blowing ideas, and you don't have to be a human calculator in order to benefit from it.
Roger Hallman
Dec 31, 2009 Roger Hallman rated it really liked it
This is a well-written history of Algebra that, aside from periodic tutorials, focuses on the people who developed this branch of mathematics from ancient Persia and Egypt into the 20th Century.
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