God Created The Integers: The Mathematical Breakthroughs that Changed History Paperback – October 9, 2007

513 years ago this week, a group of sailors found another continent, new to them and the European world, and full of surprises. The group of mathematicians in this book also found other continents of a different nature, new to them and full of surprises. One can only imagine the excitement when both groups found these new frontiers. One can no longer be a sailor and discover a new continent of land, but one can choose to be a mathematician and discover new continents of knowledge. The good thing about mathematics is that it is limitless: there are always problems that need resolution, and there are always new frontiers to open up. How far one goes in one's travels depends on the degree of creativity and ingenuity one chooses to exhibit. And in this way, mathematics is very akin to art: the path chosen depends on the taste of the mathematician, on the particular hedonic function that he/she chooses.The mathematicians in this book exhibited a lot of ingenuity and creativity, and the author has given the reader a look at their contributions as they themselves wrote them down, thanks to the efforts of the translators. Assuming the accuracy of the translations, the reader gets a view of mathematics through a representative time-window of the thoughts and personalities of some of the major players throughout the history of mathematics. The reader learns of the arrogance of Isaac Newton and Pierre Laplace, the shyness of George Boole, the extreme creativity of Georg Riemann, the computational prowess of Carl Gauss, the politics of Jean Fourier, the self-absorption of Archimedes, the encyclopedic mind of Euclid, the arithmetic of Diophantus, the polymathic nature of the mind of Rene Descartes, and the prolific mind of Augustin-Louis Cauchy.When reading the brief life histories of these individuals with all of their variability and disparate life histories, one is tempted to believe solely in a genetic origin of mathematical talent. Their personalities were very different but their aptitude in mathematics was profound. A great deal of their personal conduct could be viewed as reprehensible from a moral or ethical point of view, and the infighting that occurred among some of them was extremely juvenile. If the biographies of these individuals were rewritten to purposely omit their contributions to mathematics, a neutral reader would probably characterize them as being highly unintelligent. This again raises the debate over the concept of `general intelligence' versus that of `specialized' or `modularized' intelligence. These individuals certainly had a talent for mathematics, but does this talent, indeed the talent possessed by all mathematicians, find its origin in specialized regions in the human brain? If so, is there a correlation between mathematical skills and other types of specialized skills?One is also struck by the difficulty that some of these individuals had in finding suitable employment. The difficulties they faced in finding employment did not discourage them from performing research in mathematics. Too often these days many aspiring and talented young mathematicians complain of not being able to find suitable employment, and even feel they have a right to a tenured position at a major research institution. A reading of this book should put their beliefs in proper perspective and dissuade them from blaming the academic establishment for their failures to obtain employment.When reading the book, one can see the growing tension between applied and pure mathematics in the nineteenth century. Most, if not all of the mathematicians in this book were also very practical people: they could build bridges and design military hardware for example Contemporary (pure) mathematicians rarely have these abilities, and frequently pride themselves on not having them. In addition, some of the mathematicians of this book did not hesitate in indulging themselves in "experimental mathematics". When reading their papers in the book, one is struck by how much they used natural language, in how "wordy" their articles are. The proofs they gave explained the mathematics and did not just expound on them. They did not hesitate to use diagrams or pictures. This is to be contrasted with the manner in which contemporary mathematics is reported in the literature: it considers pictures an anathema, and strict, formalist "Bourbaki" language is to be used (although natural language of course still appears to a large degree).One can only speculate on what would have happened if some of these mathematicians had access to modern technology. What would have happened if Gauss had a calculator? What if Fourier had a music synthesizer? One can only admire their willingness to indulge themselves in difficult and time-consuming calculations, especially in the field of celestial mechanics.The list of the mathematicians in this book does not include any female mathematicians. One cannot blame adversity for this, but one could perhaps blame the unwillingness of the academic community to accept their contributions. This rejection though should not be thought of as directed only to female mathematicians. The individuals in this book had their own subjective preferences on what constituted interesting mathematics. They rejected the ideas they did not prefer and accepted the ones that they did, and they did so independent of the sex of the individual mathematician.The mathematicians of this book definitely set the tone for most of the mathematics that was done in the twentieth century and is being done in the twenty-first. But there is also a huge body of mathematics that was not influenced by them, and these contributions are just as interesting and important. The seventeen mathematicians in this book would no doubt be astounded by some of these developments, for they are very exotic if compared with the content of their mathematical constructions. One of the most fascinating of these developments (influenced to a small degree by George Boole) is automated mathematical discovery. If a book like this is rewritten at the end of the twenty-first century, the list of seventeen mathematicians will probably include some that are not human.

I just couldn't put this book down. I was so absorbed that I even missed my station and had to catch a train back. The biographies mixed with mathematical explanations and an outline of the significance of each work is brilliant. It gives one an insight into how context-dependent genius really is.I knew that the book had flaws because I read these reviews a while ago. But so what! You wouldn't use this book for reference or as a text book. It's meant to be entertainment and entertaining it is. If you can understand the maths and the significance of the selected papers you can enjoy it without worrying too much about everything being crossed and dotted.I knew the biographies of many, but not all, of these men. Of the ones I didn't know, my favorite is George Boole. The description of his unusual career and the amazingly clear and readable paper on symbolic logic are worth buying the book for. I almost choked up when I read how he died.Anyway, in our age or irrationality and ignorance we need more books like this to show us that we can rise above it all.

This book is a many-in-one exposition of some of the biggest works in mathematics and it does it well. Kudos to Stephen Hawkings for carefully choosing works that lay out the progression of mathematical ideas for all of us to see. Of course, it does not include all the important works in mathematics...no single book can. What it gives is a reference guide of sorts, a road map of mathematical history with certain markers on the way; these markers are what constitute the chapters of this book. Follow up each of those chapters/works - it will give you plenty to study on if you happen to be genuinely interested in mathematics.However, this property of the book as reference guide is also its main shortcoming: you WILL need to follow up on the works unless you have prior knowledge on the subject matter. Otherwise you will find the works quite puzzling. For example, I did not get heads or tails of what Galois was trying to convey with his seminal work on permutation groups until I read a history on the origins of group theory in the work of Abel. Even more so, you will find Godel's groundbreaking work on logical incompleteness inaccessible without prior knowledge (if not academic background) on mathematical logic and non-naive set theory (Cantor's work as presented is not enough for a background in non-naive set theory. To begin with, it predates even the naive set theory of Frege which is not presented in the book, let alone non-naive set theory which came about later to fix naive set theory).

I've only had this book a month and inasmuch as it's encyclopedic in what it does cover, I cannot write anything at all comprehensive. I haven't read my entire Britannica either. I can only be very impressed with the book's selections and its thoroughness in presenting some very special mathematicians, both their lives and their ideas. There's not much attempt to balance the presentations. The chapter on Boole is long, the chapter on Riemann is short.I wonder, however, how Hawking could omit Galois, the youngster who invented modern algebra, and Euler, the most prolific of analysts, both of whose developments had great influence on modern physics.The book would benefit with an index.Should you put it on your reference shelf? Yes.

The author was a genius so I'm not judging any of his work obviously. What I find a bit disappointing with this book is that it alternates between being a sort of archive and some history and commentary. I think it's weird to have these binned into one as they have separate audiences. Also the format is somewhat odd. Odd variations in font sizes, etc.

As dense as you'd expect this book to be. One could consider this the abridged Bible of documented achievements in mathematics over the last 2 and a half millennium. Granted this is a ridiculously hard book to read (at-least for me, an undergraduate student of Astrophysics), but its interesting to delve into now and then particularly when you want a solid grounding in the proofs of the mathematical techniques that are used so often.

Very useful to have such a well-chosen list of brilliant originals to hand. Of course it is for professional mathematicians.

Stephen Hawkings is an amazing scientist but the book is complex and the equations really hard to understand. I spent days try to understand them but im biologist :(, maybe thats why.

Having read several books by and about Stephen Hawking, I felt I owed it to myself to read more about the mathematical breakthroughs that made his - and other scientific greats - work possible. However, the first chapter made me realize that this book would be a more extended project, as my own math background is so limited. Paper and pencil and time are necessary.