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Surreal Numbers 1st Edition

by
Donald E. Knuth (Author)
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Donald E. Knuth (Author)
3 out of 5 stars 8 customer reviews
ISBN-13: 978-0201038125
ISBN-10: 0201038129
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Product Details

  • Paperback: 119 pages
  • Publisher: Addison-Wesley Professional; 1 edition (January 11, 1974)
  • Language: English
  • ISBN-10: 0201038129
  • ISBN-13: 978-0201038125
  • Product Dimensions: 5.4 x 0.4 x 8.2 inches
  • Shipping Weight: 6.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #151,938 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

34 of 37 people found the following review helpful
Couldn't put it down.
By Shlomo Yona on November 12, 2001
Format: Paperback
This little book, written as a "novel", actually tries to show us that each of us is actually able to be an amature mathematician, and that "pure mathematics" is not that complicated once you get down to the rules.
For readers familiar with group theory notations, this is an easy and fun read.
Byeond the superlatives given all over to the nice and simple manner in which the number system is built in front of our eyes, I would also like to add I have noticed some ideas Knuth wanted the readers to absorb by reading this book of his:
* People too much into civilization need time off to "rest".
* After a long while of "resting" people need brain stimulations.
* The joy and interest in mathematics comes with the discovery, or at least after trying the best you can. Only then can you appreciate what others did in mathematics.
* Teachers in schools would rather tell you about math, and make you takes exams, and will not encourage creativity. This results in that only in graduate school are people allowed (and demanded) to start creating things of their own.
* Solving good math puzzles or solving any problem, is satisfying, and makes you horny!
* definitions proofs to theorems and ideas should be expressed as simple as possible, and they can always be expressed in a simple way.
I could go on with more ideas Knuth wanted to pass to the readers...
I read the book in one time, not putting it down for a minute. The flow of ideas and progress in building the number system (up to the pseudo-numbers) is clear and fun. I actually felt as if I was discovering things myself.
There is a lot which can be "further probed" after readnig the book, and Knuth appeals to teachers to gives seminars based on this text, and guides them how he would want those seminars to be like.
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10 of 10 people found the following review helpful
A fun way to read about a formal mathematical construction.
By Rodrigo Hernandez-Gutierrez on January 2, 2012
Format: Paperback
First of all, a word of advice for the future readers of this book. Do not read it for its story. From the literary point of view, it's bad. Perhaps the only type of reader that will benefit or enjoy this book is the mathematical one.

In this book, you will find an exposition of a construction of a special number system (formally, a proper class of number systems). However, this exposition does not follow the formal or even traditional method employed in most mathematics books. It is told in form of a story. Two characters find a stone inscribed with the axioms of the construction of some "surreal numbers" and spend the whole book thinking what these axioms mean in some intuitive way.

In a mathematician's perspective (rather, my own), it is very entertaining. The characters' point of view is just as that of two mathematicians talking about some problem. And the construction is very interesting from a mathematician's point of view. So, yet again, for a mathematician, it will be like listening to two colleagues talking about some problem. It also has another element cooked for mathematicians: it has a small discussion about the fact that mathematical thinking is not taught until graduate school.

In conclusion, this book is a book about advanced mathematics written in a funny style. Do not expect the story to be good in a literary sense.
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14 of 18 people found the following review helpful
An amusing book that details an interesting subject in math
By Adam Goode on January 31, 1999
Format: Paperback
This book, written in Knuth's classic style, employs a unique dialog to guide the reader through the derivation of the fascinating mathematical topic of surreal numbers. Its short length and humor makes it a must for any math fan interested in the methods used for deriving new concepts in math, and the exercises included make it a useful book for math teachers interested in giving something new to their students. All said, a lovely book.
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45 of 66 people found the following review helpful
One star--the extra is for referring to John Conway as God
By Zachary Strider McGregor-Dorsey on December 10, 2000
Format: Paperback
Stanford mathematician D. E. Knuth, in his slim volume Surreal Numbers, attempts to impart to the reader the notion of surreal numbers by way of a very unusual tactic: the dialogue. The book has two characters-a man and a woman-that, as a couple, have left Western society to find peace and their inner selves on a beach in India. After several months of swimming and picking berries, their intellectual needs begin to weigh heavy on them. In other words, they become bored. As luck would have it, their boredom is halted by the discovery of a stone tablet on the beach near their camp. The tablet reads, in Hebrew, "In the beginning, everything was void, and J. H. W. H. Conway began to create numbers." The tablet continues, giving the basic axioms that serve as basis for the creation of surreal numbers. The rest of the dialogue consists of our lovely couple discovering theorems and properties of surreal numbers using the axioms from the stone tablet. We see them take many wrong paths in their journey, only to realize and correct their errors in moments of sudden and poorly explained revelation. ....
To the math buff, I recommend studying up on these magnificent numbers. However, I do not recommend you use the present text to do so. It does little justice to the beauty of surreal numbers, and does even less in its explanation of their properties. The intention of the author, as he states in the postscript, is to present a math text in such a way that the reader not only learns of the topic discussed, but participates in its development. He sees the common math text as a dry conveyer of theorems and proofs that hides the intriguing and moving path of discovery that resulted in these theorems and proofs. He seeks, in Surreal Numbers, to write a sort of antithesis to this type of book.Read more ›
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