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Stephen Hawking

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God Created the Integers: The Mathematical Breakthroughs that Changed History Hardcover – October 4, 2005

by Stephen Hawking (Editor)

4.4 337 ratings

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Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

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Amazon.com Review

"God created the integers," wrote mathematician Leopold Kronecker, "All the rest is the work of Man." 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. Each of the 17 sections opens with a historical introduction of the featured author, and proceeds to a faithful translation of their most famous work. While most mathematicians will already have complete editions of Isaac Newton's Principia or Georg Cantor's Contributions to the Founding of the Theory of Transfinite Numbers, this book is unique in presenting just the best bits of these and other theoretical works. The collection spans 2,500 years and covers a vast range of theories: the parallel postulate, Boolean logic, differential calculus, and the philosophy of the unknowable among them. Dense with numbers, formulae, and ideas, God Created the Integers is quite challenging, but Hawking rewards curious readers with a look at how mathematics has been built. In contrast to the towering physical edifices of great civilizations of the past, Hawking writes, "The greatest wonder of the modern world is our understanding." --Therese Littleton

About the Author

Stephen Hawking's ability to make science understandable and compelling to a lay audience was established with the publication of his first book, A Brief History of Time, which has sold nearly 10 million copies in 40 languages. Hawking has authored or participated in the creation of numerous other popular science books, including On the Shoulders of Giants and The Illustrated On the Shoulders of Giants.

Product details

Publisher ‏ : ‎ Running Press (October 4, 2005)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 1176 pages
ISBN-10 ‏ : ‎ 0762419229
ISBN-13 ‏ : ‎ 978-0762419227
Item Weight ‏ : ‎ 3.05 pounds
Dimensions ‏ : ‎ 6.25 x 2.25 x 9.25 inches

Best Sellers Rank: #788,774 in Books (See Top 100 in Books)
- #345 in Mathematical Logic
- #477 in Mathematics History

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4.4 337 ratings

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Stephen Hawking

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Stephen Hawking's ability to make science understandable and compelling to a lay audience was established with the publication of his first book, A Brief History of Time, which has sold nearly 10 million copies in 40 languages. Hawking has authored or participated in the creation of numerous other popular science books, including The Universe in a Nutshell, A Briefer History of Time, On the Shoulders of Giants, The Illustrated On the Shoulders of Giants, and George's Secret Key to the Universe.

(Stephen William Hawking; Oxford, Reino Unido, 8 de Enero de 1942 - Cambridge, 14 de marzo de 2018) Físico teórico británico. A pesar de sus discapacidades físicas y de las progresivas limitaciones impuestas por la enfermedad degenerativa que padecía, Stephen William Hawking es probablemente el físico más conocido entre el gran público desde los tiempos de Einstein. Luchador y triunfador, a lo largo de toda su vida logró sortear la inmensidad de impedimentos que le planteó el mal de Lou Gehrig, una esclerosis lateral amiotrófica que le aquejaba desde que tenía 20 años. Hawking es, sin duda, un ejemplo particular de vitalidad y resistencia frente al infortunio del destino.

Fue miembro de la Real Sociedad de Londres, de la Academia Pontificia de las Ciencias y de la Academia Nacional de Ciencias de Estados Unidos. Fue titular de la Cátedra Lucasiana de Matemáticas (Lucasian Chair of Mathematics) de la Universidad de Cambridge desde 1979 hasta su jubilación en 2009. Entre las numerosas distinciones que le han sido concedidas, Hawking ha sido honrado con doce doctorados honoris causa y ha sido galardonado con la Orden del Imperio Británico (grado CBE) en 1982, el Premio Príncipe de Asturias de la Concordia en 1989, la Medalla Copley en 2006, la Medalla de la Libertad en 2009 y el Premio Fundación BBVA Fronteras del Conocimiento en 2015.

Alcanzó éxitos de ventas con sus trabajos divulgativos sobre Ciencia, en los que discute sobre sus propias teorías y la cosmología en general; estos incluyen A Brief History of Time, que estuvo en la lista de best-sellers del The Sunday Times británico durante 237 semanas.

La Editorial Alvi Books le dedicó, como tributo y reconocimiento, este espacio en Amazon en 2016.

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J. MOLDOVAN

Forget the flaws. Enjoy it.

Reviewed in the United States on August 30, 2007

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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.

21 people found this helpful

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djavan

Book with the Spirit of Philosophy...

Reviewed in the United States on January 27, 2014

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This is an excellent masterpiece in writing and perfect in logical development and gives a reader a perspective to envision the progress of the sciences through the prism of the history of mathematics. Dr.G., Naples, FL.

2 people found this helpful

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Dr. Lee D. Carlson

17 people discover 17 new continents

Reviewed in the United States on October 16, 2005

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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.

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Josh

Intimidating, yet rewarding comprehensive book.

Reviewed in the United States on September 25, 2014

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This book is truly a work of art. From his detailed to general knowledge about the history of mathematics, he gives the advanced mathematician an opportunity to see through the eyes of the great. This is not for beginners though. Even around mathematics majors and extremely high level scientists, many flee from the area when I pull this book out. It's thick and intimidating, but if you can sit and read parts of it at a time, it's greatly rewarding.

4 people found this helpful

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Don Hudson

math

Reviewed in the United States on March 20, 2010

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Math, math, everywhere there is math. I have not finished this book. I will be a long time finishig this book, but it is great reading for an 11 hour flight to Europe. This is a book that can be read several times and more can be learned each time read. Not a late night book, it stirs the brain into overdrive!

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rezaul karim

sweet

Reviewed in the United States on July 7, 2020

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Very quick delivery, book is in wonderful condition thanks credible books

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Joseph Horton

He could have done something new...

Reviewed in the United States on January 25, 2006

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Stephen Hawking seems to like the limelight. Hey--if I had ALS, maybe I'd be willing to steal other peoples' ideas and not give them credit, too. No, come to think of it, I woudln't.

Some years ago, William Dunham wrote and exceedingly unusual and charming book, Journey Through Genius. It was a collection of famous theorems, their proofs, a slice of life of the time, often lemmas and corrolaries, etc. A unique gem, it stood out among other books that challenge the busy, but modern mind. I had to read it with a notepad next to me--I didn't always believe it until I proved it myself.

And now guess who discovered the great idea but the incessantly novel Mr. Hawking! Had he limited his treatments to mathematicians that Dunham hadn't covered, maybe there would be an excuse, but in several cases, e.g., Kantor's transfinite numbers, he just duplicates it.

I gave this 3 stars because, if it had stood alone, it would have been good. I took away stars because it was just this side of plagiarism.

22 people found this helpful

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Oceanus

I loved this book

Reviewed in the United States on July 14, 2016

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I loved this book. It was incredibly interesting and although it did have a lot of typo's, the content is what matters and what I appreciate. As someone who LOVES maths and its history, I highly recommend this book.

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Dr. T.

Hawking Reloaded? – Breakthroughs in Mathematics.

Reviewed in Germany on May 9, 2021

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Das vorliegende Werk, das von Stephen Hawking herausgegeben und kommentiert wurde, ist eine Sammlung von Auszügen aus berühmten mathematischen Originalarbeiten aus einem Zeitraum von über 2000 Jahren.

Die Beiträge reichen von Euklid, Archimedes und Diophantos , über Descartes und Newtons Pricinpia, mit denen die Neuzeit eingeleitet wird, Fourier ist einer der ersten, der neue analytische Methoden auf physikalische Probleme angewandt hat. Die Disquisitiones leiten schließlich die Mathematik des 19. Jahrhunderts ein, jenem Werk, mit dem Gauß die Zahlentheorie erstmals auf eine systematische Basis stellte. Mit Cauchy, Weierstraß und Dedekind setzt sich eine zunehmende Strenge in der Mathematik durch. Riemann ist der einzige, der in dieser Sammlung gleich mit drei Veröffentlichungen vertreten ist, dazu gehört auch sein Arbeiten zur Anzahl von Primzahlen. Die Aufsätze von Gödel und Turing sind Meilensteine der Mathematik des beginnenden 20. Jahrhunderts, die mit den Methoden der Formalisierung Begriffe wie ‘Beweisbarkeit‘ und ‘Berechenbarkeit‘ mit den Mitteln der Mathematik selbst untersuchen und zu erstaunlichen Ergebnissen gelangen. Merkwürdig – oder lustig – ist allerdings, das der Titel aus einem Zitat Kroneckers, der nicht in den Band aufgenommen wurde, abgeleitet ist: „Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk..“

Während im humanistischen Bereich, das Studium von Originalarbeiten unabdingbar ist, werden wohl nur wenige Mathematikstudenten je eine der Arbeiten dieser Sammlung direkt in den Händen gehalten haben. Das liegt natürlich auch am besonderen Charakter der Mathematik, in der es auf besondere Strömungen und Ansichten kaum ankommt, entscheidend sich exakte Formulierungen und deren Beweise; insofern sind Erkenntnisse, die im Laufe der Geschichte angesammelt wurden, im heutigen Kanon der Mathematik aufgehoben – wenn auch oft in transformierter Form. So ist der Inhalt der Arbeiten dieser Sammlung heute wohlbekannt oder gehört gar zur mathematischen ‘Folklore‘. Aber wie Niels Bohr im Hinblick auf die Quantentheorie sagte, zu einem wahren und tiefen Verständnis der Theorie, jenseits der Anwendung ihrer formalen Regeln, gelangt man erst, wenn man auch die historischen Hintergründe und die Entwicklung ihrer Begriffe und Konzept kennt. Das gilt sicher sinngemäß für alle exakten Wissenschaften. Es ist somit gerade das Faszinierende an diesem Buch, dass es die Entstehung und Entwicklung berühmter Ideen, an Hand ihrer Quellen, nachvollziehbar macht, und das auch für eine Leserschaft, die u.U. nicht ständigen Zugang zu den Monographien und Zeitschriftenbänden einer Universitätsbibliothek hat.

Den Beiträgen vorangestellt sind jeweils ein kurze Einführungen zum Leben und Werk ihrer Autoren. Das Buch steht damit in der Tradition von “On the shoulders of giants“ (2002) (dt.: Die Klassiker der Physik (2004)), das Auszügen aus bahnbrechenden Arbeiten von fünf Physikern und Astronomen wieder aufgelegt hatte.

Da der Verfasser des ‚Life and Work‘- Abschnitts zu Newton, erwähnt, dass er, wie einst Newton, Inhaber des Lucasischen Lehrstuhls in Cambridge ist, wird klar, dass dieser biographische Abriss Teil der Kommentare ist, die Hawking beigesteuert hat. Leider geht nicht hervor, ob sich dass auf alle anderen solcher Texte bezieht, da die Herausgeber nirgends namentlich erscheinen. Da aber das Zusammenstellen solcher historischer Begleittexte eher eine editorische Standardtätigkeit ist, ist nicht anzunehmen, dass sich Hawking diese 2006 aufgebürdet hat. Es handelt sich wohl eher um ein Produkt der “Hawking Book Factory“, das der Verleger unter dem Namen von Stephen Hawking herausgebracht hat – nach dem Welterfolg von ‘A Brief History of Time‘, sicher ein Verkaufsargument.

Völlig unverständlich ist allerdings die lieblose Ausstattung des Buches. Nicht nur, dass ein, in einem solchen Werk unverzichtbare, Index fehlt, gibt es weder Anmerkungen zum Text, noch eine Bibliographie, abgesehen von den minimalen ‘text and pricture credits‘.

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Aloke B.

Great but only if you understand mathematics..not a no formula book..

Reviewed in India on October 12, 2020

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Not for people who suddenly come to know about the book after reading Theory of Everything and think them to be similar reads.
A compilation of great works by Mathematicians through History. You need to understand basic mathematical terms and notations before buying this..like limits and summation...series and geometry and algebra. Overall..great book...a little inconvenient font size but that is kind of obvious.

3 people found this helpful

OLIVER

Extraordinario

Reviewed in Mexico on February 25, 2018

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Es un libro que te permite conocer la filosofía de las matematicas....creo que leerlo para aquellos que dicen no ser de su agrado esta ciencia seria de mucha utilidad.

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Cliente Amazon

Libro muy bueno

Reviewed in Spain on June 2, 2018

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Me parece un libro muy interesante para todos aquellos a los que nos gustan las matemáticas. Aunque considero que para poder entender más allá de las biografías hay que tener ciertos conocimientos matemáticos y estar familiarizado con las demostraciones. Libro muy recomendable.

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Mr. David Williams

Very useful

Reviewed in the United Kingdom on August 8, 2017

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

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