Beyond Numeracy: Ruminations of a Numbers Man
by John Allen Paulos
![Beyond Numeracy: Ruminations of a Numbers Man]()
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List Price: $22.00
Our Price: $3.21
Your Save: $ 18.79 ( 85% )
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Manufacturer: Knopf
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Average Customer Rating:  
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Binding: Hardcover
Dewey Decimal Number: 510.3
EAN: 9780394586403
ISBN: 0394586409
Label: Knopf
Number Of Pages: 285
Publication Date: 1991-04-23
Publisher: Knopf
Release Date: 1991-04-23
Studio: Knopf
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Spotlight customer reviews:
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Customer Rating: 
Summary: Encyclopedic knowledge on mathematical topics
Comment: The book consists of short articles on key mathematical topics. The best articles are the ones really focused on mathematical or geometrical topics, especially the ones where he went down to the explanation or demonstration. Other topics like Goedel's theorem are more difficult and although one can try to understand the very broad idea behind, I could not say I have even come close to an understanding.
The articles about the philosophical detours of a mathematician were also difficult to follow. I have the impression (just a metaphor) that when we perceive a formula or mathematical or logical proposition, our brain circuitry recognizes it as such and the signals travel through a special mathematical processor that is difficult to access in regular circumstances, this would explain our fear of formulas, since these neurological pathways are not the common route. Mathematicians seem to use this path as the standard route, so they talk about everyday situations in mathematical constructions leaving us lay persons wondering: "What is he talking about?"
His mathematical account of the perfect democracy offered me new insights of which I had not thought of and I believe the implications of these are very important.
Since each article has no relation with the next, it is not a book that you cannot drop, you can read one chapter every now and then. The author chose an alphabetical order for his articles rather than a chronological one. This makes you jump from Aristotle and Euclid to Goedel's theorem, over Pascal's triangle and back to Pi and Pitagoras. In the end I appreciated this approach, since I did not have the impression that the more I read, the more incomprehensible or difficult it would get, I was rather glad that I could return to known terrain like Pitagoras.
All in all this is a highly recommendable book, I just would have liked some topics explained in a little more detail.
Customer Rating:
Summary: A good starter on some of the more esoteric topics of math
Comment: But you can save your money by only buying a used version of this book.
But how many people do you think are going to be interested in what are quadratic equations if they happen to have missed them in high school? If they haven't seen them by that time, they are not likely inclined enough toward mathematics to pick up this book on their own volition.
The writing was good and clear, but two questions immediately come to mind:
1. At whom is this aimed?
2. Some of the topics were whittled down to bare bones arguments. For the things that he discussed that I did understand, I could see that he left out a lot in the interest of keeping the reader entertained. But the question is: For things that I don't know, how much was left out for the same reasons and how much better could it have been understood if he had bothered to throw in one or two examples with the mathematics worked out.
One particularly good example of this was the "Arrow's Impossibility Theorem." I would very much like to have seen enough logic discussed to be able to follow the proof.
Customer Rating:
Summary: GREAT INTRO REFERENCE TO SIMPLE AND COMPLEX MATH
Comment: This is almost a sequel to Innumeracy in which Paulos goes beyond the simple exposition of people's difficulties with math to teach, in a very readable fashion, to main concepts of mathematics, be it simple high school, college, or even the complex research mathematics.
The nice thing about this book is that you can read it bit by bit, since each chapter that deals with a topic is about 3-5 pages long, so you won't get bored and if you don't understand one topic you can move on to the next one. The topics are not really connected, so one can just move on to somehting one finds more interesting.
Overall, I believe I now know what many of the complex topics like chaos theory are about. Enough for a cocktail conversation with a mathematician at least.
Customer Rating:
Summary: one of the few great mathematics books.
Comment: I was captured entirely by "innumaracy", so i dwelve deeper into John Allen Paulo works, his website and other books, and i manage to buy several of the books.
I particularly like beyond numeracy. It is not as easily read as innumeracy, but it is deeper and more insightful.
It is written in loose shorter essays focusing on special mathematic things. I love the explanation of "infinity", "chaos theory", "pi", "probability" etc. I think people interested slightly in mathematics will be enchanted and enjoying the book.
Some of the essays are only sweet writing words, some contain heavy formula that needs digestions and basic math understanding.
There are about 70 short essays in all that can be read independently at leasure. I found out i strted to get dizzy after reading 10 essays in a straight reading.
John proved that you can make dry stuff interesting, and if you read some of the materials and use if for conversation, it will makes you look like a whiz with great taste! that is one additional benefit of reading! and you will do it without the usual pain. ;-)
Customer Rating:
Summary: Fascinating dictionary
Comment: These short essays, arranged alphabetically present a peek into mathematical topics, some I've long forgotten (differentials) and others new (non-Euclidian geometry). Paulos writes directly, usually without formulas, and if a particular essay doesn't click for you, keep turning, there's a new one in a few pages. Although the essays are mostly independent, there are some interesting connections. In light of the California governors voting recall, the section on voting systems seems clairvoyant, but he warns against the "Jean Dixon" effect in an earlier essay. The essays present mathematics as a dynamic field, and something as basic as variables, was just invented in the 16th century. Even since this book first came out, Fermat's last theorem has been proved, and there is even a larger prime number.
For those working with computers, there is a reminder of some of the mathematical background such as Al-Khwarizmi in Baghdad inventing the "Algorithm", the Turing Test, and sorting.
Paulos always touches on the human aspects of math, such as the fractal nature of human consciousness or mathematics in ethics.
QED - a great read
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Editorial Reviews:
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Customer Rating:
Summary: Encyclopedic knowledge on mathematical topics
Comment: The book consists of short articles on key mathematical topics. The best articles are the ones really focused on mathematical or geometrical topics, especially the ones where he went down to the explanation or demonstration. Other topics like Goedel's theorem are more difficult and although one can try to understand the very broad idea behind, I could not say I have even come close to an understanding.
The articles about the philosophical detours of a mathematician were also difficult to follow. I have the impression (just a metaphor) that when we perceive a formula or mathematical or logical proposition, our brain circuitry recognizes it as such and the signals travel through a special mathematical processor that is difficult to access in regular circumstances, this would explain our fear of formulas, since these neurological pathways are not the common route. Mathematicians seem to use this path as the standard route, so they talk about everyday situations in mathematical constructions leaving us lay persons wondering: "What is he talking about?"
His mathematical account of the perfect democracy offered me new insights of which I had not thought of and I believe the implications of these are very important.
Since each article has no relation with the next, it is not a book that you cannot drop, you can read one chapter every now and then. The author chose an alphabetical order for his articles rather than a chronological one. This makes you jump from Aristotle and Euclid to Goedel's theorem, over Pascal's triangle and back to Pi and Pitagoras. In the end I appreciated this approach, since I did not have the impression that the more I read, the more incomprehensible or difficult it would get, I was rather glad that I could return to known terrain like Pitagoras.
All in all this is a highly recommendable book, I just would have liked some topics explained in a little more detail.
Customer Rating:
Summary: A good starter on some of the more esoteric topics of math
Comment: But you can save your money by only buying a used version of this book.
But how many people do you think are going to be interested in what are quadratic equations if they happen to have missed them in high school? If they haven't seen them by that time, they are not likely inclined enough toward mathematics to pick up this book on their own volition.
The writing was good and clear, but two questions immediately come to mind:
1. At whom is this aimed?
2. Some of the topics were whittled down to bare bones arguments. For the things that he discussed that I did understand, I could see that he left out a lot in the interest of keeping the reader entertained. But the question is: For things that I don't know, how much was left out for the same reasons and how much better could it have been understood if he had bothered to throw in one or two examples with the mathematics worked out.
One particularly good example of this was the "Arrow's Impossibility Theorem." I would very much like to have seen enough logic discussed to be able to follow the proof.
Customer Rating:
Summary: GREAT INTRO REFERENCE TO SIMPLE AND COMPLEX MATH
Comment: This is almost a sequel to Innumeracy in which Paulos goes beyond the simple exposition of people's difficulties with math to teach, in a very readable fashion, to main concepts of mathematics, be it simple high school, college, or even the complex research mathematics.
The nice thing about this book is that you can read it bit by bit, since each chapter that deals with a topic is about 3-5 pages long, so you won't get bored and if you don't understand one topic you can move on to the next one. The topics are not really connected, so one can just move on to somehting one finds more interesting.
Overall, I believe I now know what many of the complex topics like chaos theory are about. Enough for a cocktail conversation with a mathematician at least.
Customer Rating:
Summary: one of the few great mathematics books.
Comment: I was captured entirely by "innumaracy", so i dwelve deeper into John Allen Paulo works, his website and other books, and i manage to buy several of the books.
I particularly like beyond numeracy. It is not as easily read as innumeracy, but it is deeper and more insightful.
It is written in loose shorter essays focusing on special mathematic things. I love the explanation of "infinity", "chaos theory", "pi", "probability" etc. I think people interested slightly in mathematics will be enchanted and enjoying the book.
Some of the essays are only sweet writing words, some contain heavy formula that needs digestions and basic math understanding.
There are about 70 short essays in all that can be read independently at leasure. I found out i strted to get dizzy after reading 10 essays in a straight reading.
John proved that you can make dry stuff interesting, and if you read some of the materials and use if for conversation, it will makes you look like a whiz with great taste! that is one additional benefit of reading! and you will do it without the usual pain. ;-)
Customer Rating:
Summary: Fascinating dictionary
Comment: These short essays, arranged alphabetically present a peek into mathematical topics, some I've long forgotten (differentials) and others new (non-Euclidian geometry). Paulos writes directly, usually without formulas, and if a particular essay doesn't click for you, keep turning, there's a new one in a few pages. Although the essays are mostly independent, there are some interesting connections. In light of the California governors voting recall, the section on voting systems seems clairvoyant, but he warns against the "Jean Dixon" effect in an earlier essay. The essays present mathematics as a dynamic field, and something as basic as variables, was just invented in the 16th century. Even since this book first came out, Fermat's last theorem has been proved, and there is even a larger prime number.
For those working with computers, there is a reminder of some of the mathematical background such as Al-Khwarizmi in Baghdad inventing the "Algorithm", the Turing Test, and sorting.
Paulos always touches on the human aspects of math, such as the fractal nature of human consciousness or mathematics in ethics.
QED - a great read
From the author of the national bestseller Innumeracy, a delightful exploration and explanation of mathematical concepts from algebra to zero in easily accessible alphabetical entries. "Paulos . . . does for mathematics what The Joy of Sex did for the boudoir. . . ."--Washington Post Book World. First time in paperback.
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