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.

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# God Created the Integers: The Mathematical Breakthroughs That Changed History

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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.

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5out of 5Richard Houchin–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.

4out of 5Manuel Antão–If you're into stuff like this, you can read the full review. E = hv: "God Created the Integers - The Mathematical Breakthroughs That Changed History" by Stephen Hawking (Original Review, 2005) Random thoughts while attempting to read the book (the edition is shitty: it's full of typos) In EM theory, which is Lorentz invariant, there's a relation between the magnitudes of the E and B fields for light (not if you use Planck units. The magnitudes of c and h tell you nothing about physics, but a lot ab If you're into stuff like this, you can read the full review. E = hv: "God Created the Integers - The Mathematical Breakthroughs That Changed History" by Stephen Hawking (Original Review, 2005) Random thoughts while attempting to read the book (the edition is shitty: it's full of typos) In EM theory, which is Lorentz invariant, there's a relation between the magnitudes of the E and B fields for light (not if you use Planck units. The magnitudes of c and h tell you nothing about physics, but a lot about biology. I don't claim that's original, BTW. I'm trying to recall who said it first, Monod or Schrödinger, E/B = c. That's quite a magnitude difference of the E over the B already. So if you could gradually increase c the structure of a light beam changes radically. But the reason for c is probably tied to quantum vacuum properties so you've got changes there too. In fact I would find it entirely reasonable not to expect invariance in E and/or B while the early universe was trying to sort out its equilibrium conditions during falling out of the gravitational, electromagnetic, weak forces just after the BB.

4out of 5London–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 workin 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.

4out of 5Will–Tried 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 Tried 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?

5out of 5Jenny Prince–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. 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.

4out of 5Silvio Curtis–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 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.

4out of 5Dallas–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. 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.

5out of 5Ashlee–Hmm...probably another book I will always still be reading.

4out of 5Utsav–This 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 This 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

4out of 5R.W. Erskine–a very good read if you have its understanding. Although Mr. Hawking has some pretty far out ideas.

4out of 5Ryan Smith–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.

4out of 5T Dodson–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 att 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.

4out of 5Laurent–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 cont 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.

5out of 5Austin Castellanos–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. 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.

5out of 5William Crosby–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. 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.

4out of 5Colin–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). 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).

4out of 5Michael Weaver–This 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.

5out of 5Nativeabuse–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. 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.

4out of 5William Schram–"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 "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.

4out of 5Koen Crolla–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 intere 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.

5out of 5Ron Moreland–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!

4out of 5Reid–Renowned 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.

5out of 5Jasmine–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. 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.

4out of 5Manmohan Dash–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.

5out of 5Chaim Ackerman–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. 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.

5out of 5Bill Yates–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.

4out of 5Eben Tonder–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. 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.

5out of 5Owen Lindsell–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. 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.

4out of 5Wolfwest–This is one book I will savour for the rest of my life.I have often referred to it and I always will.This is a book that marries ET Bell with Vakil Naik.A fantastic collection edited by a brilliant physicist.

4out of 5Mads Harpøth–Very enjoyable book, but only the Hawking introductions are straight-forward readable - I used some of the works of Descartes in an essay though. In general a very thorough introduction to the concepts behind the evolution of math.