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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

3.90  ·  Rating details ·  671 ratings  ·  49 reviews
Perfect for history buffs and armchair algebra experts, Unknown Quantity tells the story of the development of abstract mathematical thought.

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
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Paperback, 400 pages
Published June 1st 2007 by Plume Books (first published May 2nd 2006)
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Average rating 3.90  · 
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 ·  671 ratings  ·  49 reviews


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Koen Crolla
Mar 17, 2010 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
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Jafar Isbarov
According to Wikipedia, there are 13 branches of math, 6 of which fall into the realm of pure mathematics. Algebra is just one of these. So is there any merit in reading a book about history of this small corner of the mathematical universe? Of course, this is a large understatement on part of algebra – it definitely is not a “small corner” of math. On the contrary, it perhaps the largest and the most interconnected field of it. But it is still not whole of it, right? Why not go for some general ...more
Jesse
Nov 24, 2007 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
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Jose Moa
Oct 09, 2015 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
Jake
Aug 12, 2019 rated it liked it
Shelves: math
yet another book that has a subject in its title without understanding how people of the subject do things.
History.
At the start of the book he already mentioned he used only a few sources. What was it a large encyclopedia and a few texts on the history of math. Truly, that is how how to do these things.

to develop a balanced view of any subject, one must read widely on that subject, and maybe even in general. I do not get the sense that the author cared much to do this.

I though, am not
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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
Nishant Pappireddi
Jun 18, 2014 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 ...more
Adam
Nov 19, 2008 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 ...more
AJ
Jun 17, 2012 rated it it was ok
Shelves: stem, non-fiction, 2012
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 ...more
Nur
Jan 28, 2011 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
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gargamelscat
Aug 20, 2011 rated it it was ok
Shelves: 2012, math
5/10
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
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Lance Johnson
May 04, 2019 rated it it was amazing
This book was excellent. It was recommended to me by a math professor who found out that I enjoy the history if mathematics as much as I enjoy the math itself. This book strikes a nice balance between explaining the material and maintaining a compelling narrative. Other math history books have learned a bit too far in one direction or another, but this one felt right. It does focus specifically on algebra rather than analysis or geometry, but those topics do appear from time to time.
Joe
Jul 01, 2008 rated it liked it
I like the history of mathematics... [turns head away in shame, moist eyes brimming with hot tears of disgrace]
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.
Keenan
Dec 28, 2018 rated it really liked it
I bought this book 10 years ago to the date with a Chapters gift card I received for my birthday. I've had enough math training in the interim to appreciate what this book tries to offer some perspective into, and thought it would be time to finally open up this dusty novel.

Ultimately this book does a good job for a popular mathematics book, a bit of history, a few interesting anecdotes, good overall approachable descriptions of some tricky concepts in algebra. But as good as the descriptions of
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Rossdavidh
Apr 18, 2014 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
Natbas
Nov 17, 2008 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
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Mary Ronan Drew
Feb 07, 2011 rated it liked it
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
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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: http://www.goodreads.com/review/show/...). 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
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Randy
Nov 24, 2011 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.

The
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Erik
Jan 25, 2016 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
Marc Towersap
Aug 31, 2012 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 ...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,
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Erica
Oct 21, 2007 rated it liked it
Recommends it for: math nerds
Shelves: fall2007
10/21/07

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)
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Mattie
Dec 08, 2013 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,
...more
Tracy Black
Jun 11, 2010 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
...more
Shu Lindsey
Jun 03, 2007 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."
Michael
Mar 17, 2009 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.
Alterstuart
Jul 16, 2014 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.
Jessica
May 11, 2009 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.
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