Customer Reviews

God Created the Integers: The Mathematical Breakthroughs That Changed History

5 star:		(9)
4 star:		(11)
3 star:		(11)
2 star:		(3)
1 star:		(0)

 

 

First, I loved the idea of this book--a compendum of the more significant mathematical breakthroughs in all their detail, as written by their creators. The text is refreshing in that it is not a watered down version of someone's results. I have a math background and all the details are appreciated. There's something about reading the original text, straight from the minds of these great men.

This book could be useful, for example, for someone who likes math and wants a 'sampler' of different areas of study. It could also be useful for someone reading up on the history of mathematics who wants to dig deeper into certain areas and see the original works.

All that said, I have to agree with another reviewer about the editing. It's awful (yes, awful) that such typographical errors could exist in a math book. The first section I looked at in this book, Riemann's original paper on the zeta function, had four typos ON THE SAME PAGE. This is disasterous to someone trying to learn the material for the first time, or someone trying to follow a tight line of argument. If this was a college text book, I'd probably burn it, because learning math is difficult enough, without having to contend with typos. To the editors of this book: COME ON GUYS, YOU CAN DO BETTER THAN THIS. YOU SHOULD BE ASHAMED (YES, ASHAMED) OF YOURSELVES (you're just COPYING something someone else wrote--and yet you managed to mess that up)! At least put an errata page somewhere online.

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.

I really want to give this book at least 4 stars as I love the idea of encapsulating those great mathematical breakthroughs in one book and giving each a proper account instead of over simplistic summaries like many other math readings do.
HOWEVER, the errors contained in this book is intolerable. It doesn't make sense anymore to give those mathematical details as you can hardly follow them due to the errors.
For example, on page 5 it prints:
If (2^n - 1) is a prime number then 2^(n-1)*(2^(n-1)-1) is a perfect number and that even perfect numbers must have this form.
it obveriously should be 2^(n-1)*(2^n - 1) instead of what has been printed. As other readers have suggested, you would expect more similar errors along the way.
Don't buy this book and wait for the 2nd edition if the publisher ever want to make an effort to make this book readable. I'm so very disappointed.

This book contains surprisingly many grammatical and spelling errors, as well as errors in the equations. If these occurred only in the editor's prologue to each paper, it might be overlooked. But the errors also pervade the papers themselves. These errors are extremely distracting, and often obfuscating.

To evaluate my comments, I think you should know who I am and why I bought this book: I'm a former technical editor and writer. As a girl, I was discouraged from studying math, because at the time (the Fifties and Sixties) they thought girls couldn't understand it.

Recently I've tried to fill in the gaps in my math and science education. I thought the idea of Hawkings choosing landmark math texts and commenting on them was fantastic. After spending three days trying to understand the Euclidian proof of the Pythagorean theorem, and concluding I was just too dumb, I turned the page and discovered that according to the commentary the proof was for an isosceles right triangle, while the illustration was not isosceles.

Other reviewers have commented on the egregious errors and typos. I'd like to add that the whole publication is a typographical horror. The publisher should be ashamed. The font size is miniscule. The illustrations are often misleading. Hawkings may have chosen the texts, but the publisher apparently selected the editions based not on quality of translation but whether the copyright had expired: most appear to be nineteenth-century and to include outdated commentaries. At first I thought the commentaries were by Hawkings, but they aren't, and this was not only a disappointment but also a source of my confusion at several points where I couldn't understand them.

I would be surprised if even ten percent of the book is authored by Hawkings. Given this, the ghastly page layout, inaccurate reprints of outdated texts, and amateurish copyediting, this book is overpriced.

IF YOU'RE MATHEMATICALLY LITERATE, you will likely find Hawkings' material a joy to read. Even I -- with my limited background -- am able to appreciate some of it. But the minute after I want to shout for joy when I understand something beautiful in the book, I want to throw it across the room for something like spelling Leonardo da Vinci "Lionardo" or typos like "Archimedes's asked." With glaringly obvious typos like those, I can only assume there are less obvious typos where it really counts, in the math. It's not that I think typos out-weigh the value of Hawkings' insights, by any means. It's that mathematicians have to be precise in their formulas and proofs if they want to convince anyone they're right. God is also in the details.

Addendum: The more I read, the more disappointed I am in this book. I'm beginning to question whether Hawkings wrote even the introductions to the excerpts. Many of them are nothing but poorly written biographies of the mathematicians anthologized. The intro to Newton asserts that Newton falsely claimed priority over Leibniz for devising calculus, for example, but the book doesn't include anything written by Leibniz. The book excerpts Euler, but only mentions the constant e in one sentence in the Euler intro. I'm going to look for a good history of mathematics and give up on this volume. And when I'm ready, I'll look for good translations of the original texts.

I do not regret spending $30 on this text, but I feel it is not worth the money.

There are a few fundamental problems with the book.

First, Someone is only going to buy a book this nerdy if they are really into the subject. If they're really into the subject, they will probably want the full texts, not highlighted excerpts. Highlighted excerpts are handy as a reference, but since there is no index, this cannot be considered a reference book.

Second - it's nice that these works have Hawking's Seal of Approval, but the fact that Hawking has is name on this seems like nothing more than a marketing ploy. Most people buy Hawking's books because he makes a difficult subject easy. This being a collection of others' work makes me think that the publishers used Hawking's reputation to move copies.

Third - no index. That's ridiculous for a book like this.

Overall, I'm happy with the book, but I think it fails because it hovers between a reference book and a historical collection.

If you're serious about studying the subjects covered, I would suggest spending your money on the Dover edition of what you're looking for. Buy this book if you're an enthusiast and want some stimulating reading.

Math enables human society to function - but that areas of math make modern wonders possible, and what problem made each theory's first inventor become involved in a puzzle? While GOD CREATED THE INTEGERS: THE MATHEMATICAL BREAKTHROUGHS THAT CHANGED HISTORY is a follow-up to ON THE SHOULDERS OF GIANTS, it stands well alone as a history of thirty-one landmark cases of mathematical problem-solving, from geometry to calculus. Also included are biographies of each mathematician, the full proof of work reproduced from the original publication, and newly translated results; three of which appear in English for the first time. Recommended as a pick for college-level collections strong in mathematics.

Diane C. Donovan
California Bookwatch

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.

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.

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 Gödel. I don't know that his perspective on Gödel's philosophical views or expectations, as regards this Incompleteness Theorems, or Gödel's relationship with the Vienna Circle, is portrayed accurately. Witnesses and other biographers have convincingly portrayed the story otherwise. Gödel's famous proofs may have surprised and disappointed the Positivists, but it seems they neither disappointed nor surprised [the Platonist] Gödel (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 Gödel and his work that are available for the interested reader. A very nice exposition focused mainly on the philosophical import of Gödel'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 Gödel's famous paper, rather than the whole paper).

Staying with Hawking's presentation of Gödel, I also note that, in his introduction (xii), Hawking writes "Kurt Gödel 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, Gödel would quickly protest, "yes, no (!), and yes": True, Gödel's result troubled certain philosophers -- most especially Wittgenstein! (Wittgenstein is said to have, in frustration, resolved to "ignore" Gödel's result; Gödel, for his part, considered Wittgenstein to be not only a poor judge of mathematical thought, but also a poor philosopher generally.) What Gödel 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 Gödel'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 Gödel 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.