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The Book of Numbers
The Book of Numbers lets readers of all levels of mathematical sophistication (or lack thereof) understand the origins, patterns, and interrelationships of different numbers.
Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun.
A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof.
Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers.
Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun.
A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof.
Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers.
319 pages, Hardcover
First published March 16, 1995
About the author
John H. Conway
22 books70 followersJohn Horton Conway, often credited as John H. Conway, was a Professor of Mathematics at Princeton University, known for inventing the "Game of Life."
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Displaying 1 - 20 of 20 reviews
January 25, 2021
How to Teach Maths
If I ruled the world of education, mathematics would be taught not as calculation but as numbers, just numbers and their relationships with each other. And this book by Conway and Guy would be a primary text.
Through this text, students would learn not the tedious processes of long division (is that still a thing?) or the mechanism for finding square roots, but the history and poetry of numbers themselves.
In my syllabus numbers would be shown to be objects of aesthetic interest, their associations sources of surprise and beauty. Mathematics would be seen for what it is, a language of great fluidity and interest. It is the Latin of the modern world; its patterns are everywhere.
Mathematics as numbers ties together the domaines of literature and science because mathematics is both literature and science. Numbers tell stories about each other. These stories show how the rules of language work. Numbers also are the way the stories of science are told.
Most important, the understanding of mathematics as numbers would allow students to appreciate the reality of numbers as things separate from other things found in the world. Numbers do not represent, point to, or designate anything but themselves. The only thing behind, within, and beyond any number are other numbers - arguably the most neglected lesson about language in modern education.
Along the way, calculation would be recognised and taught for what it is - poetic expression in numbers. Any further instruction in calculation would, in my syllabus, have a separate track called Engineering - what was formerly called Shop or Vocational Therapy.
If I ruled the world of education, mathematics would be taught not as calculation but as numbers, just numbers and their relationships with each other. And this book by Conway and Guy would be a primary text.
Through this text, students would learn not the tedious processes of long division (is that still a thing?) or the mechanism for finding square roots, but the history and poetry of numbers themselves.
In my syllabus numbers would be shown to be objects of aesthetic interest, their associations sources of surprise and beauty. Mathematics would be seen for what it is, a language of great fluidity and interest. It is the Latin of the modern world; its patterns are everywhere.
Mathematics as numbers ties together the domaines of literature and science because mathematics is both literature and science. Numbers tell stories about each other. These stories show how the rules of language work. Numbers also are the way the stories of science are told.
Most important, the understanding of mathematics as numbers would allow students to appreciate the reality of numbers as things separate from other things found in the world. Numbers do not represent, point to, or designate anything but themselves. The only thing behind, within, and beyond any number are other numbers - arguably the most neglected lesson about language in modern education.
Along the way, calculation would be recognised and taught for what it is - poetic expression in numbers. Any further instruction in calculation would, in my syllabus, have a separate track called Engineering - what was formerly called Shop or Vocational Therapy.
June 3, 2016
I was disappointed in this book. I thought I could have learned a lot more about numbers. Instead I felt like I got numbers thrown at me from literally all different directions. To start, the first chapter where the authors break down some numbers and say where the numbers are seen in languages and in the world; this could have been a really great chapter if there was more emphasis on what some of the words mean and how they are used. Instead there is a few brief explanations and other than that the words are just listed there leaving the reader to look up a large number of words if they wanted to know what they mean. Otherwise, the reader is just reading words and not really understanding the connections the author was trying to make.
Other chapters in the book had great potential and I was really excited to read them, however I found that the authors like to define concepts I already knew and completely breeze over the extremely difficult concepts making most of the book go completely over my head - and I have a math degree, I would think that I should be able to at least get something out of this book!
I think overall I would have like to see more explanations and definitions than formulas. There were countless formulas and most of them were not explained enough to understand what they mean.
I would never have picked this book up if I knew that the audience was probably meant for a person with a math doctorate or extremely well versed in the concepts in the book already - in which case, why read the book. The book jacket was misleading. I had such high hopes for this book.
Other chapters in the book had great potential and I was really excited to read them, however I found that the authors like to define concepts I already knew and completely breeze over the extremely difficult concepts making most of the book go completely over my head - and I have a math degree, I would think that I should be able to at least get something out of this book!
I think overall I would have like to see more explanations and definitions than formulas. There were countless formulas and most of them were not explained enough to understand what they mean.
I would never have picked this book up if I knew that the audience was probably meant for a person with a math doctorate or extremely well versed in the concepts in the book already - in which case, why read the book. The book jacket was misleading. I had such high hopes for this book.
April 20, 2007
lots of silliness in numbers. makes good toilet reading and horrible party conversation topic. this is personal experience; don't make the same mistakes.
May 4, 2015
the best book I have ever read wheverything.ich contains various intriguing
July 29, 2015
Everything you didn't need to know about numbers.
July 27, 2017
A spectacular book. After a delightful chapter on etymology and number names (researched more deeply than any I've read) and a second chapter on geometric inspired groups of numbers (not just the triangular numbers everyone's heard of, but also numbers like the rhombic dodecahedral numbers), the book is just full of jaw-dropping deep facts about various types of numbers. And it's not just an encyclopedia of numbers--there are explanations and proofs as well. In fact, every time I came to a famous theorem whose proof I've known, Conway and Guy spring some paper-folding argument on me to prove the theorem in the most elementary and eye-catching way possible. There are also some original results and formulas in the book too that I guarantee you haven't seen before.
Of course not everything is proved--it's not a textbook. There's just the right amount of rigor, with an exhilarating pace leading to the climactic final chapter on infinite ordinals/cardinals and the surreal numbers. This chapter gives the best explanation of the infinite ordinals and their arithmetic for the layperson (or even math major) that I've ever seen. And the surreal numbers are explained just enough to get me to research them more.
This book may not be for everyone. With the exception of a couple of the chapters it's a very difficult book, with sometimes very terse explanations. It would appeal most to bright high school students in a math club, or students of higher mathematics. I would even venture to say that professional mathematicians would get something out of this book. But even if you don't understand everything (I could use a second reading regarding some of the explanations), you'll get something out of this book and you'll be dazzled and enticed to learn more about math.
Of course not everything is proved--it's not a textbook. There's just the right amount of rigor, with an exhilarating pace leading to the climactic final chapter on infinite ordinals/cardinals and the surreal numbers. This chapter gives the best explanation of the infinite ordinals and their arithmetic for the layperson (or even math major) that I've ever seen. And the surreal numbers are explained just enough to get me to research them more.
This book may not be for everyone. With the exception of a couple of the chapters it's a very difficult book, with sometimes very terse explanations. It would appeal most to bright high school students in a math club, or students of higher mathematics. I would even venture to say that professional mathematicians would get something out of this book. But even if you don't understand everything (I could use a second reading regarding some of the explanations), you'll get something out of this book and you'll be dazzled and enticed to learn more about math.
January 20, 2014
It is rare indeed to find a book that presents some fairly serious mathematics without getting too technical yet without trivialising it either. I have a maths degree but there was quite a lot here that I hadn't met before, including Eisenstein integers.
It is difficult to say who this book would appeal to: perhaps a very intelligent and dedicated teenager or a maths graduate in search of diversion and inspiration. I doubt the the average adult layman could cope, and even regular readers of Martin Gardner might struggle. There are just too many ideas in one slim volume. The arguments are subtle and even I couldn't follow all of them: the sections on trancendental numbers and infinities, for example.
But if you want to meet the whole spectrum of what mathematicians regard as numbers, here they are!
It is difficult to say who this book would appeal to: perhaps a very intelligent and dedicated teenager or a maths graduate in search of diversion and inspiration. I doubt the the average adult layman could cope, and even regular readers of Martin Gardner might struggle. There are just too many ideas in one slim volume. The arguments are subtle and even I couldn't follow all of them: the sections on trancendental numbers and infinities, for example.
But if you want to meet the whole spectrum of what mathematicians regard as numbers, here they are!
November 30, 2019
Cool intro to number theory. Discusses quite a lot of things without going too deep inside any of them. However, this isn't quite a popular level book. The topics covered are somewhat on an intermediate level, and that, coupled with the fact that it doesn't go too deep into any, makes it hard to follow in places.
Now time for the contents. The first chapter is an interesting discussion on how pervasive numbers have become in the human world, and shows some words which you wouldn't expect originated from numbers (e.g., distribution, triumph, finger et cetera). The remaining chapters include discussions on the interplay between numbers and geometry, combinatorics, primes and congruences, Farey diagrams, continued fractions, the complex plane, transcendental numbers, and infinities.
Now time for the contents. The first chapter is an interesting discussion on how pervasive numbers have become in the human world, and shows some words which you wouldn't expect originated from numbers (e.g., distribution, triumph, finger et cetera). The remaining chapters include discussions on the interplay between numbers and geometry, combinatorics, primes and congruences, Farey diagrams, continued fractions, the complex plane, transcendental numbers, and infinities.
May 22, 2013
A really weird book--takes a fairly non-rigorous approach, as if written for non-mathematicians, but gets pretty complicated nonetheless. I assume it's for people who are just really fascinated by numbers, but I'm not really sure who the audience is. Invariably, there's a plethora of fascinating facts and theorems, particularly from Number Theory, ranging from the first-semester undergraduate type, all the way up to some things I never ran across even in grad school. Rather encyclopedic, in some sense. Lots of fun.
April 24, 2018
We are in 1995, Conway is showing off numbers. Many of them. He warms us up pointing out that civilization has been using numbers everywhere and there are a bunch of composed words out there. And it took a great intellectual leap to see numbers as abstract entities. Then the numbers zoo broke loose. Many clever people started to create recipes for sequences of numbers. The fun here comes from the relations among numbers and geometric forms. Conway very often explain these relations using geometric isomorphisms making this book imaginary, transcendental, surreal, infinite, fun!
June 4, 2013
Delightful. I guarantee that if you are at all interested in math, you will find at least one chapter interesting. I can't say with any certainty which it will, be though. The writing is fun, and detailed enough that you can follow the (simplified) proofs they provide, but not so dense as to be a deterrent. Also, lots on prime numbers; this stuff is fascinating, folks!
Read
March 19, 2020The author thinks we readers are good at math. So some gaps are left for the readers to think. They are not always obvious, but most are manageable. However, after encountering some typos, it is hard to figure out if we were thinking along the wrong direction or we are just staring at another typo.
April 9, 2019
This was fun, varyingly thorough, usually interesting, and often provided good discussion fodder. I’ll probably bust this out when people are over some day, to talk about some numeric curiosity or another. I’m excited to read On Numbers and Games, and hope there’s not too much overlap.
November 16, 2010
Un must per ogni matematico che si rispetti. C'è di tutto, compresi i numeri surreali.
August 16, 2012
For anyone who wants to remind themselves that Math can be interesting.
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December 3, 2013929.1 CON
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April 26, 2016Numbers
August 25, 2024
This will be a 'marmite' book for most readers, you will either love it or hate it. I am in on the first camp, this book is mathematical beauty from start to finish.
Two major caveats though:
1) It is not 'accessible' - I have struggled to understand sections where I did not have the required mathematical background.
2) Many concepts are introduced and developed quite quickly, and I have struggled at times to read more than a paragraph in one hour, trying to figure out what was going on.
But if you are a non-mathematician, you will feel new parts of your brain getting activated and exercised.
Two major caveats though:
1) It is not 'accessible' - I have struggled to understand sections where I did not have the required mathematical background.
2) Many concepts are introduced and developed quite quickly, and I have struggled at times to read more than a paragraph in one hour, trying to figure out what was going on.
But if you are a non-mathematician, you will feel new parts of your brain getting activated and exercised.
January 24, 2023
Very whimsical and fun. With sometimes deep mathematics explained in such a way that any sufficiently curious person could understand after possibly a few thoughtful pauses. The book goes just into enough detail to tickle the mind, without getting lost in formality. The ideal bedside read that will give you ideas to think about as you sleep without overwhelming you.
January 20, 2024
Confusing in several places even for folks with a strong math background. This is probably the source from which Vsauce and 3Blue1Brown draw their ideas for YouTube videos.
Displaying 1 - 20 of 20 reviews