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 enlarge | Author: Stephen Hawking
Publisher: Running Press
Category: Book
List Price: $22.95
Buy New: $3.80
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Rating:  25 reviews
Sales Rank: 153848
Media: Paperback
Pages: 1376
Number Of Items: 1
Shipping Weight (lbs): 2.9
Dimensions (in): 9 x 5.8 x 2.1
ISBN: 0762430044
Dewey Decimal Number: 510
EAN: 9780762430048
Publication Date: October 8, 2007
Availability: Usually ships in 1-2 business days
Condition: Oversized paperback. Great condition. Minor shelf wear, unused. Ships quickly
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| Customer Reviews:
 A great mathematics source book March 31, 2007
Vic Dannon
0 out of 19 found this review helpful
I follow the excellent translation of Riemann's 1859 zeta paper
in my book "Riemann's Zeta paper: The Product Formula Error"
 A Browsers Delight But With One Important Defect November 2, 2005
R. E. Little
156 out of 163 found this review helpful
It's not for everyone, but if you have a couple of years of college-level math, you can find your way through most of the material. Open to a random page, see what's going on, if it grabs you, find the beginning of the presentation and plow right in. Hawking's biographical/historical pieces are a delight and worth buying the book for even if you don't do the math. How come I graded one of the greatest minds of our time only 80% (4 stars)? The damn book has no index and it drives me crazy. Because of this defect, it's a pain to try to tie the work of the great mathematicians together. You miss out on an entire layer of interest that could be developed so much more easily had their been an index.
17 people discover 17 new continents October 16, 2005
Dr. Lee D. Carlson (Saint Louis, Missouri USA)
113 out of 172 found this review helpful
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.
A great idea well executed (with a caveat). June 26, 2007
Wesley L. Janssen (San Diego, CA USA)
13 out of 14 found this review helpful
Hawking here puts his name as editor to an outstanding collection of the writings, theorems and proofs of several of history's most influential mathematicians. He also contributes historical and biographical context commentaries. The choice of title, and implicit subtitle due to Leopold Kronecker, is itself interesting in its metamathematical posture, alluding to both the platonic (real but 'immaterial') mathematical Given, i.e., "God Created the Integers", and the concept of mathematics as human 'invention', i.e., "all the rest is the work of man". In his popular writings, Hawking has long identified with positivism, a philosophy claimed by relatively many in the natural sciences but by very few practitioners of mathematics (likely all the men profiled here would consider themselves Platonists, believing that mathematical truths are discovered as opposed to contrived/invented). I find it slightly fascinating that one can be so assertive in his scientific positivism while also frequently conceding a weak mathematical Platonism/realism.
While all of the 'chapters' are worthy of attention, I was particularly interested in Hawking's presentation of the life, work and thought of Kurt Goedel. I don't know that his perspective on Goedel's philosophical views or expectations, as regards this Incompleteness Theorems, or Goedel's relationship with the Vienna Circle, is portrayed accurately. Witnesses and other biographers have convincingly portrayed the story otherwise. Goedel's famous proofs may have surprised and disappointed the Positivists, but it seems they neither disappointed nor surprised [the Platonist] Goedel (although he calls his result "surprising," it seems he is speaking to how they must be received by Hilbert, Wittgenstein, and the positivists, rather than to his own view). There are several popular sources [books] on Goedel and his work that are available for the interested reader. A very nice exposition focused mainly on the philosophical import of Goedel's result is "Incompleteness: The Proof and Paradox of Kurt Godel" by Rebecca Goldstein (although, unlike Hawking's book, Goldstein presents only a good summary explanation of Goedel's famous paper, rather than the whole paper).
Staying with Hawking's presentation of Goedel, I also note that, in his introduction (xii), Hawking writes "Kurt Goedel proved a theorem troubling to many philosophers, as well as anyone else believing in absolute truth: that in any sufficiently complex logical system (such as arithmetic) there must exist statements that can neither be proven nor disproven." Dividing Hawking's statement into those segments defined by the sentence's punctuation, Goedel would quickly protest, "yes, no (!), and yes": True, Goedel's result troubled certain philosophers -- most especially Wittgenstein! (Wittgenstein is said to have, in frustration, resolved to "ignore" Goedel's result; Goedel, for his part, considered Wittgenstein to be not only a poor judge of mathematical thought, but also a poor philosopher generally.) What Goedel would categorically deny of Hawking's summation, is the idea that his result in any real way questioned the ontology of 'absolute truth.' In fact, he inferred exactly the opposite. His result addressed the decidability of propositions and not the existence of truths! Hawking obviously understands this, but has taken some license in assailing 'truth' anyway, perhaps subconsciously attempting a kind of Wittgensteinian proxy revenge; but Goedel's result addresses the limits of formal logic, NOT any constraint on 'truth' itself. (Sorry if this seems like a lengthy digression, but as Kurt Goedel isn't around to defend the philosophical meaning of his work from positivistic spin-doctoring, other mathematical Platonists must.)
One indicator of this volume's uniqueness is the fact that some of these texts had not previously been published in English. The book is a great idea well executed, and is definitely recommended to anyone with an interest in the history of mathematics or in familiarizing themselves with great (and often quirky) mathematicians. Read it front to back or in any manner you wish, although there is an obvious 'building' through the book, the segments on the life and work of each mathematician will be of interest in their own right.
Special, but Missing Some January 29, 2006
J. L. Thoreen (Fort Walton Beach, Florida, USA)
10 out of 11 found this review helpful
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.
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