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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
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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--19Surreal 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
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2 of 2 people found the following review helpful
Format:Paperback
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!
1 of 1 people found the following review helpful
Format:Paperback
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.
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.
43 of 55 people found the following review helpful
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]
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