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God Created the Integers: The Mathematical Breakthroughs that Changed History
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Customer Reviews
Rating:  - a great physicist tells about great breakthroughs in math
To see what interests a great physicist is, to me, of great interest.
In God Created the Integers, Stephen Hawking describes not only what he sees as the key mathematical breakthroughs of history, but also the lives of those who made these breakthroughs. Both are of great interest.
In particular, Lebesgue's grounding the integral on "measure" reveals a pattern. Certain things are unmeasurable. Other things measure zero-- but still, they are something (not nothing). And certain collections, although arising from infinite architecural processes, have finite measure. As in the numbers themselves that result from integration, by the enabling component of integration-- measure-- the finite meets the infinite.
Since integration is basic to physics (for example, as the context for the Born equation of quantum mechanics) I guess after reading this book I shouldn't be surprised that Stephen Hawking would tell us about this breakthrough in very human and understandable terms.
Rating:  - Great compendium
Great compendium of (some of) the most important works in math. I would have added some authors but I think the selection is awesome. Clearly explained and original works are well referenced.
Rating: - My son liked his Christmas gift
My son asked for this book for Christmas, so I bought it for him. Looking inside, I saw it was way over my head. But he, being a math and computer genius, loved it.
Rating:  - Shout for joy or toss it?
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.
Rating: - God Created the Integers
This is a beautiful book because it lists the life and work of 16 mathematicians whose work has inspired our civilization. For example Einstein is not included, but Riemann whose analysis of curved space is the foundation of the General Theory of Relativity is rhere. So also are Archimedes and Newton the pillars of mathematical physics.Kurt Godel in 1931 proved that there will always a truth that is outside a set of axioms.Some of the original papers are difficult but I have gained much from the logic of George Boole which also governs computer programmes.
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