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God Created the Integers: The Mathematical Breakthroughs That Changed History
In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.
1176 pages, Hardcover
First published October 4, 2005
478 people are currently reading
8846 people want to read
About the author
Stephen W. Hawking
242 books12.8k followersStephen William Hawking was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at Cambridge, widely viewed as one of the most prestigious academic posts in the world.
Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD degree in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, paralysed him. After the loss of his speech, he communicated through a speech-generating device initially through use of a handheld switch, and eventually by using a single cheek muscle.
Hawking's scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity, and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Initially, Hawking radiation was controversial. By the late 1970s, and following the publication of further research, the discovery was widely accepted as a major breakthrough in theoretical physics. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics.
Hawking achieved commercial success with several works of popular science in which he discussed his theories and cosmology in general. His book A Brief History of Time appeared on the Sunday Times bestseller list for a record-breaking 237 weeks. Hawking was a Fellow of the Royal Society, a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He died in 2018 at the age of 76, having lived more than 50 years following his diagnosis of motor neurone disease.
Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a first-class BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD degree in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, paralysed him. After the loss of his speech, he communicated through a speech-generating device initially through use of a handheld switch, and eventually by using a single cheek muscle.
Hawking's scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity, and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Initially, Hawking radiation was controversial. By the late 1970s, and following the publication of further research, the discovery was widely accepted as a major breakthrough in theoretical physics. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics.
Hawking achieved commercial success with several works of popular science in which he discussed his theories and cosmology in general. His book A Brief History of Time appeared on the Sunday Times bestseller list for a record-breaking 237 weeks. Hawking was a Fellow of the Royal Society, a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He died in 2018 at the age of 76, having lived more than 50 years following his diagnosis of motor neurone disease.
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Displaying 1 - 30 of 76 reviews
April 24, 2008
I only understood half of the original texts. However, I am convinced that in the event of a zombie apocalypse I will risk my life to ensure that this book survives the catastrophe, for it contains the seeds of all human advancement. Such things should not be taken for granted.
March 7, 2012
Anyone interested in the history and evolution of math and science should pick up this monster tome. It's not a book you're likely to read front-to-back in order, nor necessarily even be able to follow all of the copious amount of equations presented without a very solid math background. However, Hawking explains the importance of each mathematicians accomplishments, gives a solid biography for each of them, and presents some of their most important work in its original form.
I'm currently working through Laplace's work on probability. I find it challenging and slow-going at times, but highly rewarding and a great way to keep my mind vigorously engaged.
Since I'm writing a novel with a math genius as the protagonist, I find this the singularly most valuable reference in my library.
I'm currently working through Laplace's work on probability. I find it challenging and slow-going at times, but highly rewarding and a great way to keep my mind vigorously engaged.
Since I'm writing a novel with a math genius as the protagonist, I find this the singularly most valuable reference in my library.
Currently reading
May 28, 2012Tried to read this and threw in the towel. It's primarily a collection of the crucial mathematical writings from Euclid on. These old texts just aren't that readable.
Hawking's introductions are very interesting, and made me want to learn more about the history of math. But they're too rapid. Dim-witted readers of my ilk need to be coaxed through this stuff.
The stuff on the progression of ancient Greek mathematics is fascinating. The Pythagoreans had a philosophy wherein numbers, and relations between them, underlay all real phenomena. This theory yielded splendid results early on, with the surprising 3-4-5/Pythagorean-theorem thing being their most spectacular success. They let it go to their heads. Their theory fell apart because they couldn't find a way to express the square root of 2 in real numbers. The Babylonians had some tricks to come close: mainly, they had figured out that 7/5 was really, really close. Try it and see for yourself: 49/25 is so close 2 that it hurts! But the Pythagoreans needed to do better than that, because they had made these strong, absolute claims about reality being made up of ratios between real numbers. Attempts to derive a real solution led to contradictions, because the premise was flawed: the square root of 2 just isn't a real number. Euclid's work was an attempt to start anew after this failure.
There is also an interesting aside about Euclid. Hawking notes that the assumptions of Euclidian space -- straight, infinite lines that take up no space, and the like -- were treated for hundreds of years as literally true in the Aristotelian physics of the west. However, Euclid and the Greeks never imagined that they were literally true, because they had a cosmology where everything in the universe was spherical and contained. The post-Einstein understanding of space as curved and the universe as limited just happens to accord with the Greeks' view.
I caught tons of copy-editing errors in the short part I read. Stephen Hawking, I will copy-edit this for you! It's gonna cost, though.
This is an interesting subject and if there exists a more accessible work than this, I would love to read it. Does anybody have a recommendation?
Hawking's introductions are very interesting, and made me want to learn more about the history of math. But they're too rapid. Dim-witted readers of my ilk need to be coaxed through this stuff.
The stuff on the progression of ancient Greek mathematics is fascinating. The Pythagoreans had a philosophy wherein numbers, and relations between them, underlay all real phenomena. This theory yielded splendid results early on, with the surprising 3-4-5/Pythagorean-theorem thing being their most spectacular success. They let it go to their heads. Their theory fell apart because they couldn't find a way to express the square root of 2 in real numbers. The Babylonians had some tricks to come close: mainly, they had figured out that 7/5 was really, really close. Try it and see for yourself: 49/25 is so close 2 that it hurts! But the Pythagoreans needed to do better than that, because they had made these strong, absolute claims about reality being made up of ratios between real numbers. Attempts to derive a real solution led to contradictions, because the premise was flawed: the square root of 2 just isn't a real number. Euclid's work was an attempt to start anew after this failure.
There is also an interesting aside about Euclid. Hawking notes that the assumptions of Euclidian space -- straight, infinite lines that take up no space, and the like -- were treated for hundreds of years as literally true in the Aristotelian physics of the west. However, Euclid and the Greeks never imagined that they were literally true, because they had a cosmology where everything in the universe was spherical and contained. The post-Einstein understanding of space as curved and the universe as limited just happens to accord with the Greeks' view.
I caught tons of copy-editing errors in the short part I read. Stephen Hawking, I will copy-edit this for you! It's gonna cost, though.
This is an interesting subject and if there exists a more accessible work than this, I would love to read it. Does anybody have a recommendation?
January 14, 2012
A giant book with a lot to explore, but not very easy to understand. It's a collection of excerpts from the work of famous mathematicians, with very short biographies by Hawking. Even reading this as a senior math major I couldn't follow most of the math in any detail, so I only have an impressionistic sense of most of it. It surprised me most with the earlier mathematicians. I would have expected to understand them because what they discovered are relatively simple things that I mostly learned in high school, but they discuss it in geometrical language that's disorientingly different from modern ways of talking about it. The work and lives of the different mathematicians included from the nineteenth century have a lot of interconnections, but in earlier time periods they're too widely scattered. I'm going to use the list chosen by Hawking as a framework to relate other math history that I read to, but it doesn't make a connected story by itself.
June 24, 2010
If you really want to look like a huge nerd, just whip this baby out at any popular social gathering area, and you'll be amazed at how quickly those who are afraid of mathematics vacate the premesis. With that being said, this book is basically a compilation of the most prominent works by the most prominent mathematicians. I particularly like the short biographical introductions preceding the works themselves.
February 21, 2012
I haven't finished this yet - I wasn't even sure I wanted to check it out. I was perusing the math section to find some calculus texts and brush up before next term starts, and there it was: like Brian Greene's _The Fabric of the Cosmos_, it was too intriguing to ignore.
If you don't think math history can be interesting, I dare you to read the first page and a half.
If you don't think math history can be interesting, I dare you to read the first page and a half.
July 13, 2013
Not for the beginner.
I was lost by page 3. Then I scanned the rest of the book. I had hoped Hawking would explain some of these books in a more understandable way. Nope.
None of these types seem to believe in diagrams. It's all verbal descriptions which, if there is any ambiguity in the writing (which there was: Hawking needed a better editor), made it difficult/impossible to follow the mathematical descriptions and formulas.
I was lost by page 3. Then I scanned the rest of the book. I had hoped Hawking would explain some of these books in a more understandable way. Nope.
None of these types seem to believe in diagrams. It's all verbal descriptions which, if there is any ambiguity in the writing (which there was: Hawking needed a better editor), made it difficult/impossible to follow the mathematical descriptions and formulas.
March 13, 2008
Hmm...probably another book I will always still be reading.
March 18, 2010
It's hard to see what Hawking intended with this book; the works are too inaccessible because of their great age (for the earlier ones) or the advanced mathematics background required (for many of the later ones) to be very enjoyable, and while they do add some historical perspective, spending a few dozen pages summarising them would probably have been more productive than spending a few hundred including translated fragments of them. Many of them are still interesting, but not 1160-pages interesting.
As a review of some of the most important mathematical breakthroughs in history, the book has some odd inclusions (I wouldn't have included Dedekind or Lebesgue, myself), some odd omissions (Pythagoras? Al-Khwārizmī, or any other Muslim mathematician?), some questionable choices of materials, and some peculiar emphases (over a hundred pages each for Euclid and Archimedes, and then Weierstrass gets seven?).
All in all, this book wasn't worth the effort of writing, and probably isn't worth the effort of reading, unless you just read the bios (which would bring this book down from 1160 pages to 120 or so; altogether more reasonable). The breakthroughs described are (mostly) important and (mostly) interesting, but there are better places to learn about them.
As a review of some of the most important mathematical breakthroughs in history, the book has some odd inclusions (I wouldn't have included Dedekind or Lebesgue, myself), some odd omissions (Pythagoras? Al-Khwārizmī, or any other Muslim mathematician?), some questionable choices of materials, and some peculiar emphases (over a hundred pages each for Euclid and Archimedes, and then Weierstrass gets seven?).
All in all, this book wasn't worth the effort of writing, and probably isn't worth the effort of reading, unless you just read the bios (which would bring this book down from 1160 pages to 120 or so; altogether more reasonable). The breakthroughs described are (mostly) important and (mostly) interesting, but there are better places to learn about them.
August 16, 2014
Contrary to what the title could imply, there is nothing about God and the mathematics in this book (by "and" I mean "intersection", not "union"). It's a collection of short bibliography of Mathematicians, alongside a selection of their most interesting and representative publications for the history of mathematics. The material itself is interesting and refreshing, but the added value of this book is rather poor. The selection of mathematicians is somehow arbitrary and misleading about the continuous development of mathematics. Genius do no appear from nowhere.
June 3, 2013
I honestly should have given this book 1 star, but there was enough interesting stuff to keep it a little afloat. While the intent was great, and the introduction are engaging, the constant egregious errors make it too frustrating for me to read. There were glaring mathematical errors (in a book about math!!!) in the first 5 pages, in italicized "proven" conclusions. Really disappointed that this kind of sloppy work has Stephen Hawking's name on it.
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October 13, 2014This is huge (like, 1100+ pages) and full of math (like, equations, and diagrams, and such) and I doubt I'll ever finish reading it, but the idea of it is so beautiful I had to have it. I expect I'm just going to keep turning the pages as in a trance, eyes glazed as I recite, "sine squared theta plus cos squared theta equals one" over and over...
Compulsive book buying: 1 Efforts at elevating myself out of poverty: 0
Compulsive book buying: 1 Efforts at elevating myself out of poverty: 0
January 11, 2017
a very good read if you have its understanding.
Although Mr. Hawking has some pretty far out ideas.
Although Mr. Hawking has some pretty far out ideas.
September 26, 2022
Should have been my warning to not do a maths degree. Good book though.
July 10, 2019
This book is not at all what I expected, but I managed to enjoy it none the less. The majority of the pages are arduous, complex mathematical proofs that extend in difficulty far beyond my education in university calculus. What remains are the miniature biographies Hawking writes of the 17 featured mathematicians. In short, I really enjoyed the intriguing life stories but had to skip most of the featured works.
December 17, 2020
"God Created The Integers" is a book edited by the late Stephen Hawking. It is a collection of works by mathematicians and physicists like Euclid, Euler, Laplace, etc. Professor Hawking comments on each person's life and work. He does a marvelous job of explaining why this person was essential to mathematics.
For example, scholars agree that Euclid did not originate his results. He was a compiler of information. On the other hand, we have Archimedes. He probably developed the method of exhaustion by himself. Many of the earliest results are quite fascinating. For example, the book has a section that explains how Archimedes estimated the size of the Universe.
This book is excellent, but it has some drawbacks. The main shortcoming is the size of the print is small at times. This book is from 2007. I don't know if there is a newer edition of it.
For example, scholars agree that Euclid did not originate his results. He was a compiler of information. On the other hand, we have Archimedes. He probably developed the method of exhaustion by himself. Many of the earliest results are quite fascinating. For example, the book has a section that explains how Archimedes estimated the size of the Universe.
This book is excellent, but it has some drawbacks. The main shortcoming is the size of the print is small at times. This book is from 2007. I don't know if there is a newer edition of it.
March 26, 2015
What bothered me most about this book, is that the size of the fonts were continually changing - tiny font to medium, to large, to micro. It was unnecessary. This is a reference manual - not a readable or enjoyable book. It should have been organized and titled like a textbook (at the least) and certainly not as a history book or insight piece.
I think most people only buy this book because of the shiny cover, and due to the complicated nature of the interior - they never finish it, but just attribute that to their ignorance (rather than the books unreadability) - then they praise Hawking's intellect. Maybe that was Hawking's intention. He could very well have made the book readable, considering half of the topics are below 6th grade algebra.
I think most people only buy this book because of the shiny cover, and due to the complicated nature of the interior - they never finish it, but just attribute that to their ignorance (rather than the books unreadability) - then they praise Hawking's intellect. Maybe that was Hawking's intention. He could very well have made the book readable, considering half of the topics are below 6th grade algebra.
April 27, 2009
I'm a math freak and I really want to like this (along with Roger Penrose's latest) but it's very long and intensive. I keep planning to set aside a weekend just for these kind of books; sit down with a pencil and paper and get through them all. It'll probably highlight some deficiencies in my math education (even though, I'm a comp sci major that took a large number of math classes).
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July 28, 2011This is a great collection of some of the more significant breakthroughs in theoretical mathematics. Though I appreciated how in the introduction he brought it back to the core and showed the sophistication of the Egyptians and Babylonians and went forward; I wish he had included Euler and Einstein.
June 20, 2012
Stephen Hawking's commentary placed beside great works of mathematical genius really isn't very good. The collection of works all together like this is fantastic and interesting but his commentary on the works was severely lacking and mostly uninteresting.
October 15, 2024
Llevo unos días leyendo este libro y me hace dudar seriamente si algún día tendré los conocimientos necesarios en matemáticas para poder asimilar y entender todo lo que viene aquí. No me malinterpretéis aunque sea joven le he dedicado muchísimas horas a las matemáticas, he leído la obra de Kline de "Pensamiento matemático..." dos veces completa y también la historia de Boyer y la de Cajori, con algo de esfuerzo pero asimilando estos 3 libros, pero lo que viene y como se explica el autor en este libro está a otro nivel.
Esto no es una simple obra de historia de las matemáticas, apenas le dedica espacio a las biografías, el grueso del libro son las trascripciones de las obras originales de los 17 matemáticos que selecciona y notas a pie de página que ocupan en ocasiones las 3/4 partes de la página con las reflexiones de Hawking, muchas veces contextualizando históricamente, aportando curiosidades o enlazando cosas antiguas con ideas más recientes.
Lo único que puedo decir es que trataré de ojear un poco más el libro y después lo devolveré a la biblioteca pública. Para poder leer hasta la última palabra de todo el libro incluidas las notas tienes que tener un doctorado en matemáticas o en su defecto un CI muy por encima de lo normal. En ambos aspectos no es mi caso.
Esto no es una simple obra de historia de las matemáticas, apenas le dedica espacio a las biografías, el grueso del libro son las trascripciones de las obras originales de los 17 matemáticos que selecciona y notas a pie de página que ocupan en ocasiones las 3/4 partes de la página con las reflexiones de Hawking, muchas veces contextualizando históricamente, aportando curiosidades o enlazando cosas antiguas con ideas más recientes.
Lo único que puedo decir es que trataré de ojear un poco más el libro y después lo devolveré a la biblioteca pública. Para poder leer hasta la última palabra de todo el libro incluidas las notas tienes que tener un doctorado en matemáticas o en su defecto un CI muy por encima de lo normal. En ambos aspectos no es mi caso.
May 23, 2008
This book is an excellent resource for students if they want to know more about where a math concept came from. It also provides background knowledge to many of the mathematical concepts that students are going to encounter in a high school math class. From Algebra to Calculus and beyond it is an excellent tool and highly recommended!
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June 25, 2008Renowned astrophysicist Stephen Hawking goes through the most important mathematical realizations of all time. Extremely technical, but readable because of the historical background and discussion.
This book will open your eyes to the incredible order in every-day life, giving you new appreciation for the complexity in simpleness.
This book will open your eyes to the incredible order in every-day life, giving you new appreciation for the complexity in simpleness.
March 13, 2012
Skimmed through the more technical stuff. This is something I'd want to own, not just borrow from the library (which is what I did) so that I could look through it at my leisure, or when I needed to look something up. Really interesting. Learned some new anecdotes. Began to understand that mathematicians are even crazier than I had assumed.
August 28, 2012
Own this book although not yet started reading. This one is a great compilation of mathematical concepts and theorems needed for practising mathematicians, physicists and engineers incase they are also inspired scinetist and/or have good time to brush their knowledge with concepts of mathematics from a super-intellect.
June 5, 2015
This book contains well written and fascinating short biographies of the greatest mathematicians throughout human history.
They serve to introduce over 1000 pages of math essays that are too ancient or too advanced to be of interest to most people.
This book must weigh close to 10 pounds. Still, you can finish the biographies in an evening. They're a good read.
They serve to introduce over 1000 pages of math essays that are too ancient or too advanced to be of interest to most people.
This book must weigh close to 10 pounds. Still, you can finish the biographies in an evening. They're a good read.
July 31, 2015
Look at the number of pages in this book. It is a tome. I sort of finished the book, since I read all of the biographies. But I only skimmed through the original mathematical papers. No doubt Hawking read and understood very word that he included in the process of editing. Kudos to him. I admire him greatly.
August 27, 2009
It is amazing to work through the development of mathematics with one as gifted as Stephen Hawking! From the earliest Greek "dilemmas" to the modern day thought and how these thoughts impacted our world.
March 4, 2012
Only read the start of this. Seems good, but you have to have a lot of time to read it as it's essentailly just a reprint of all the major works of mathematics interspersed with comments from Hawking.
November 2, 2013
Interesante libro que recoge los escritos originales de los matemáticos más importantes de todos los tiempos. No se dejen llevar por el nombre de "Hawking" como autor, su participación se limita a una breve introducción biográfica de cada autor, después vienen los textos originales...
Displaying 1 - 30 of 76 reviews