Have one to sell?
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See this image

Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness : A Mathematical Novelette Paperback – 1 Jan 1974

4.8 out of 5 stars 5 customer reviews

See all formats and editions Hide other formats and editions
Amazon Price
New from Used from
Paperback
"Please retry"
£16.25 £24.74

Are You an Author Looking to Publish Your Book?
It's Free, Fast, and Easy to Publish to Kindle, Print and Audio with Amazon Independent Publishing Learn more
click to open popover

Special Offers and Product Promotions

Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.

  • Apple
  • Android
  • Windows Phone

To get the free app, enter your mobile phone number.




Product details

  • Paperback: 128 pages
  • Publisher: Addison Wesley; 01 edition (1 Jan. 1974)
  • Language: English
  • ISBN-10: 0201038129
  • ISBN-13: 978-0201038125
  • Product Dimensions: 13.5 x 1 x 20.3 cm
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Bestsellers Rank: 290,049 in Books (See Top 100 in Books)

Product Description

From the Back Cover

Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness.

The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19

Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created.



0201038129B04062001

About the Author

Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.




What Other Items Do Customers Buy After Viewing This Item?

Customer Reviews

4.8 out of 5 stars
5 star
4
4 star
1
3 star
0
2 star
0
1 star
0
See all 5 customer reviews
Share your thoughts with other customers

Top Customer Reviews

Format: Paperback
A few years ago John Horton Conway of the University of Cambridge hit on a remarkable new way to construct numbers ... Conway explained his new system to Donald E. Knuth, a computer scientist at Stanford University, when they happened to meet at lunch one day in 1972. Knuth was immediately fascinated by its possibilities and its revolutionary content. In 1973 during a week of relaxation in Oslo, Knuth wrote an introduction to Conway's method in the form of a novelette. ... I believe it is the only time a major mathematical discovery has been published first in a work of fiction. ... The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as ``to teach how one might go about developing such a theory.'' He continues: ``Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself.'' ... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other ``real'' value does. The system is truly ``surreal.'' [quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19]
Comment 44 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback Verified Purchase
I've always been a big fan of Knuth. I think it's partly because of his insistence on the aesthetics of maths and not just formal correctness. I came to this book thinking that I was going to learn some new number theory. I guess I did - but this book is *really* about how fun it is to discover and *prove* mathematical concepts for yourself. The book was apparently written in about a week and developed as Knuth discovered the ideas for himself. The material is not very hard, and is probably worth reading through quickly at first and then going back to later, to try your own hand at proving some of the basic properties. My only complaint was it all finishes too soon!
Comment 5 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback Verified Purchase
Conway's system of surreal numbers is one of the most brilliant creations of Mathematics. The system adds to the familiar numbers a vast family of infinite and infinitesimal numbers. It allow you to add, subtract, multiply and divide numbers in this collection, and also to find such things as their seventh roots. The system is amazingly rich.

Knuth imagines two young lovers in the future finding the first clues to the system on stone tablets, and then shows how, from these clues, they begin to reconstruct Conway's system. It gives a feel for what research in mathematics is like. Sometimes, our two lovers make errors and have to retrace some of their steps.

To be sure, you need to think hard to get the best out of the book. You must not feel discouraged that you have to spend a long time proving such things as
0+1 = 1. The system you end up with will blow your mind.

Knuth, computer scientist par excellence, has done an excellent job.
Comment 3 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
Excellent book. I love it. Requires some understanding of mathematics, interest in logic and some effort to understand. This book will not teach you much in the way of useful mathematics, but it should really make you think.
Comment One person found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback Verified Purchase
Brilliant book to help understand surreal numbers. Great starting point for research
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse


Feedback