God created the integers the mathematical breakthroughs that changed history
God created the integers the mathematical breakthroughs that changed history
manjunath5496/Stephen-Hawking-Books
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README.md
Books:
Properties of Expanding Universes
The Nature of Space and Time
George and the Big Bang
Black Holes and Baby Universes and Other Essays
George’s Cosmic Treasure Hunt
The Large, the Small and the Human Mind
George’s Secret Key to the Universe (Russian Edition)
A Brief History of Time
My Brief History
The Theory of Everything
Three Hundred Years of Gravitation
The Grand Design
The Collected Papers of Stephen Hawking
The Large Scale Structure of Space-Time
The Universe in a Nutshell
A Briefer History of Time
Hawking on the Big Bang and Black Holes
God Created the Integers: The Mathematical Breakthroughs That Changed History
On the Shoulders of Giants: The Great Works of Physics and Astronomy
Brief Answers to the Big Questions
Lectures:
About
God Created the Integers: The Mathematical Breakthroughs That Changed History
1160 pages, Hardcover
First published October 4, 2005
About the author
Stephen Hawking
Stephen William Hawking was born on 8 January 1942 in Oxford, England. His parents’ house was in north London, but during the second world war Oxford was considered a safer place to have babies. When he was eight, his family moved to St Albans, a town about 20 miles north of London. At eleven Stephen went to St Albans School, and then on to University College, Oxford, his father’s old college. Stephen wanted to do Mathematics, although his father would have preferred medicine. Mathematics was not available at University College, so he did Physics instead. After three years and not very much work he was awarded a first class honours degree in Natural Science.
Stephen then went on to Cambridge to do research in Cosmology, there being no-one working in that area in Oxford at the time. His supervisor was Denis Sciama, although he had hoped to get Fred Hoyle who was working in Cambridge. After gaining his Ph.D. he became first a Research Fellow, and later on a Professorial Fellow at Gonville and Caius College. After leaving the Institute of Astronomy in 1973 Stephen came to the Department of Applied Mathematics and Theoretical Physics, and since 1979 has held the post of Lucasian Professor of Mathematics. The chair was founded in 1663 with money left in the will of the Reverend Henry Lucas, who had been the Member of Parliament for the University. It was first held by Isaac Barrow, and then in 1669 by Isaac Newton.
Stephen Hawking worked on the basic laws which govern the universe. With Roger Penrose he showed that Einstein’s General Theory of Relativity implied space and time would have a beginning in the Big Bang and an end in black holes. These results indicated it was necessary to unify General Relativity with Quantum Theory, the other great Scientific development of the first half of the 20th Century. One consequence of such a unification that he discovered was that black holes should not be completely black, but should emit radiation and eventually evaporate and disappear. Another conjecture is that the universe has no edge or boundary in imaginary time. This would imply that the way the universe began was completely determined by the laws of science.
His many publications include The Large Scale Structure of Spacetime with G.F.R. Ellis, General Relativity: An Einstein Centenary Survey, with W. Israel, and 300 Years of Gravity, with W. Israel. Stephen Hawking has three popular books published; his best seller A Brief History of Time, Black Holes and Baby Universes and Other Essays and most recently in 2001, The Universe in a Nutshell.
Professor Hawking received twelve honorary degrees, was awarded the CBE in 1982, and was made a Companion of Honour in 1989. He was the recipient of many awards, medals and prizes and is a Fellow of The Royal Society and a Member of the US National Academy of Sciences.
God Created the Integers: Mathematical Breakthroughs that Changed History
This book is evidently conceived as a companion to the author’s previous work, On the Shoulders of Giants (2003). Both share the same format. Selections from the works of great mathematicians (in the volume under review) or physicists (in the previous volume) are preceded by brief biographies written by Hawking. While only five physicists appear in Giants (Copernicus, Galileo, Kepler, Newton, and Einstein), each quoted extensively, the current volume includes chapters on seventeen mathematicians: Euclid, Archimedes, Diophantus, Descartes, Newton, Laplace, Fourier, Gauss, Cauchy, Boole, Riemann, Weierstrass, Dedekind, Cantor, Lebesgue, Gödel, and Turing, and is slightly shorter in length so the excerpts are shorter. Only Newton appears in both.
The selections are offered in chronological order so that reading the whole book spans two and a half millennia of mathematics history. The majority of the text discusses events subsequent to the sixteenth century. One could contest the particular choice of mathematicians included but 2500 years is a long time and some choices had to be made. The complete volume presents a reasonable survey for the period of history covered.
Disappointingly, it is difficult to recognize the book’s intended audience. Certainly, it is not written for the mathematics historian. The biographical sketches contain nothing that is not well known to even the most casual reader in the history of mathematics. Indeed, where the mathematician under consideration appears in both, there is almost nothing of a biographical nature that cannot also be found in E. T. Bell’s Men of Mathematics (Bell’s known errors notwithstanding). Few of the excerpts are complete and most are available from other sources. The dust cover blurb states that three of them are translated into English for the first time in this volume. While this is a positive addition to the literature, I have been unable to ascertain precisely which three.
God Created the Integers is not for the curious layman or the average mathematics student. The overwhelming bulk of the text is devoted to excerpts from the published works of the mathematicians under consideration. Probably few laymen will benefit from reading Gödel’s “On Formally Undecidable Propositions of Mathematics”, Gauss’ “Disquisitiones Arithmeticae”, or even Newton’s “Principia” unless the entries are extensively footnoted, which they are not.
On the other hand, a student taking a course in Number Theory, for example, might just enjoy reading Gauss’ exposition of the topic, which suggests that this text might be useful as a resource for a course on the history of mathematics. This is what I was hoping for when I agreed to do this review and it is possible, given the right circumstances.
If I were teaching a two semester course in the history of mathematics I would seriously consider this text as the primary resource for the second semester. The mathematicians and excerpts beginning with Descartes and ending with Gödel and Turing provide a good overview of the progress and sweep of Western mathematics from the sixteenth century forward. Supplementary materials would be required, of course, but this book provides a workable central core. Alas, the course I teach confines the entire history of mathematics to a single semester so I, personally, cannot use it.
Eugene Boman, Associate Professor of Mathematics, The Pennsylvania State University, Middletown,PA.
See also the MAA Review by Fernando Q. Gouvêa.
Eugene Boman, reviewer, «God Created the Integers: Mathematical Breakthroughs that Changed History,» Convergence (July 2007)
God Created the Integers: The Mathematical Breakthroughs that Changed History
Historians of mathematics are always looking for sourcebooks, especially for use in class. Finding translated versions of many classical texts is quite difficult. When they exist, they turn out to have been published twenty years ago in very small print runs and are long out of print. So a book that brings together a selection of historically significant works is very useful. Several such sourcebooks already exist, so Stephen Hawking’s God Created the Integers enters into a crowded field. The main question for a reviewer, then, is whether Hawking’s collection offers something new.
First of all, there is Hawking’s brief introduction and the commentaries on each of the authors included. These strike me as rather perfunctory at the beginning, then better when the material comes closer to modern science. They tend to be mostly biographical. Hawking is not a historian; inevitably, there are annoying mistakes in these introductions. Many of these amount to the repetition of «folklore,» but some are more serious.
Then we come to the selections themselves, and things get more idiosyncratic. The book opens with selections from Euclid. They are all from Heath’s translation of the Elements, and they include Heath’s copious notes (in very very small print). The beginning of book I is included: definitions, postulates, and common notions. Then (without much warning to the reader) we are suddenly at Proposition 47, the Pythagorean theorem. This all fits on three pages. There follow 15 pages of notes by Heath. This is very weird: one could almost fit all of book I in those 15 pages. Wouldn’t that serve the reader better?
And so it goes. For Euclid, we then get all of book V (Eudoxus’ theory of proportions), all of book VII, and little bits of books IX and X. Next comes Archimedes (in Heath’s paraphrased translation), with both parts of «The Sphere and the Cylinder», «Measurement of a Circle», «The Sand Reckoner», and the «Method». To finish off Greek mathematics, we get selections from Heath’s book on Diophantus, which of course does not even claim to be a translation.
After this obligatory nod to the ancient Greeks, we take a flying leap to early modern times, and get selections from Descartes, Newton, Laplace, Fourier, Gauss, Cauchy. (No, nothing from Euler!) At this point, we’re well into modern mathematics, and the book concludes with selections from Boole, Riemann, Weierstrass, Dedekind, Cantor, Lebesgue, Gödel, and Turing. Most of these (and some of the earlier material too) will be inaccessible to most non-mathematician readers.
As with the previous collection of this type edited by Hawking, On the Shoulders of Giants, one gets the feeling that the selections were determined more by the availability of translations in the public domain than by any other considerations. According to the preface, four of the selections were translated specifically for this volume. (I think they are: a selection from Cauchy’s course on differential calculus, two selections from Riemann, a selection from Weierstrass.) Almost all the others are reproductions of material from various Dover publications, even when, as in the case of Newton, parts of Archimedes, and Laplace, there are better translations available.
In the end, I’m not too impressed. A selection of mathematical texts of historical importance (as in «The Mathematical Breakthroughs that Changed History») that excludes all of Arabic mathematics, all of Medieval and Renaissance mathematics, and that doesn’t include Stevin, Fermat, the Bernoullis, Euler, Lagrange, Abel, Galois, Hilbert, Poincaré. it all seems weirdly lopsided. There is nothing on statistics, and very little that is recent. In fact, the only texts included here that were published after 1920 are by Gödel, and Turing, as if 20th century mathematics were dominated by logic.
I don’t think that the publishers of the other sourcebooks need to worry about the competition from this one.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College and the co-author, with William P. Berlinghoff, of Math through the Ages. He somehow finds time to also be the editor of MAA Reviews.
God Created the Integers: The Mathematical Breakthroughs That Changed History
1160 pages, Hardcover
First published October 4, 2005
About the author
Stephen Hawking
Stephen William Hawking was born on 8 January 1942 in Oxford, England. His parents’ house was in north London, but during the second world war Oxford was considered a safer place to have babies. When he was eight, his family moved to St Albans, a town about 20 miles north of London. At eleven Stephen went to St Albans School, and then on to University College, Oxford, his father’s old college. Stephen wanted to do Mathematics, although his father would have preferred medicine. Mathematics was not available at University College, so he did Physics instead. After three years and not very much work he was awarded a first class honours degree in Natural Science.
Stephen then went on to Cambridge to do research in Cosmology, there being no-one working in that area in Oxford at the time. His supervisor was Denis Sciama, although he had hoped to get Fred Hoyle who was working in Cambridge. After gaining his Ph.D. he became first a Research Fellow, and later on a Professorial Fellow at Gonville and Caius College. After leaving the Institute of Astronomy in 1973 Stephen came to the Department of Applied Mathematics and Theoretical Physics, and since 1979 has held the post of Lucasian Professor of Mathematics. The chair was founded in 1663 with money left in the will of the Reverend Henry Lucas, who had been the Member of Parliament for the University. It was first held by Isaac Barrow, and then in 1669 by Isaac Newton.
Stephen Hawking worked on the basic laws which govern the universe. With Roger Penrose he showed that Einstein’s General Theory of Relativity implied space and time would have a beginning in the Big Bang and an end in black holes. These results indicated it was necessary to unify General Relativity with Quantum Theory, the other great Scientific development of the first half of the 20th Century. One consequence of such a unification that he discovered was that black holes should not be completely black, but should emit radiation and eventually evaporate and disappear. Another conjecture is that the universe has no edge or boundary in imaginary time. This would imply that the way the universe began was completely determined by the laws of science.
His many publications include The Large Scale Structure of Spacetime with G.F.R. Ellis, General Relativity: An Einstein Centenary Survey, with W. Israel, and 300 Years of Gravity, with W. Israel. Stephen Hawking has three popular books published; his best seller A Brief History of Time, Black Holes and Baby Universes and Other Essays and most recently in 2001, The Universe in a Nutshell.
Professor Hawking received twelve honorary degrees, was awarded the CBE in 1982, and was made a Companion of Honour in 1989. He was the recipient of many awards, medals and prizes and is a Fellow of The Royal Society and a Member of the US National Academy of Sciences.
Источники информации:
- http://www.goodreads.com/book/show/2096.God_Created_the_Integers
- http://www.maa.org/press/periodicals/convergence/god-created-the-integers-mathematical-breakthroughs-that-changed-history
- http://www.maa.org/press/maa-reviews/god-created-the-integers-the-mathematical-breakthroughs-that-changed-history
- http://www.goodreads.com/book/show/2096.God_Created_the_Integers?page=2