From Zero to Infinity: What Makes Numbers Interesting [Paperback]

Constance Reid (Author)

Book Description

ISBN-10: 1568812736 | ISBN-13: 978-1568812731 | Publication Date: February 4, 2006 | Edition: 5th

From Zero to Infinity is a combination of number lore, number history, and sparkling descriptions of the simply stated but exceedingly difficult problems posed by the most ordinary numbers that first appeared in 1955 and has been kept in print continuously ever since. With the fifth edition this classic has been updated to report on advances in number theory over the last 50 years, including the proof of Fermat's Last Theorem. Deceptively simple in style and structure, it is a book to which the reader will return again and again, gaining greater understanding and satisfaction with each reading.

Editorial Reviews

Review

" Zero To Infinity is a sequence of rare beauty, a drama built out of nothing but numbers---and imagination."" -Freeman Dyson, Institute for Advanced Study, Princeton, November 2005
""...in a delightful way it... get others interested in the fascinating theory of numbers."" -John Leamy, Mathematics Teacher, March 1993
book singular for its insight into the imagination, relevance and sheer excitement of mathematics."" -Kirkus Bulliten, Kirkus Bulliten , November 2005
""Upon reading this edition anew, I was struck by its superb mathematical taste."" ""I knew I was meant to spend my life loving numbers and working with them; From Zero to Infinity crucially told me that there was a large community of People of Number I could hope to join when I grew up. . . . As I got older, I continued to read From Zero to Infinity and the other influential math books I knew; . . . I was truly fortunate to have run across From Zero to Infinity when I did."" -Bruce Reznick, Notices of the AMS, February 2007
""This book should be in the library of every mathematics teacher, and university faculty who prepare students to teach mathematics should also own this book. "" -Murray H. Siegel, Mathematics Teaching in the Middle School, February 2007
ein Buch nach 50 Jahren in fünften Auflage erscheint, so spricht vieles für seine Qualität. Tatsächlich ist es spannend zu lesen, und über weite Strecken reichen schulische Mathematikkenntnisse aus Der Inhalt wurde inzwishen erweitert und vor allem, was die Suche nach großen Primzahlen betrifft, ergänzt. Es handelt sich um eine geschickt formulierte Mischung aus der Geschichte der Mathematik und einer Einführung in mathematisches Denken. Ein Beispiel genüge: Im Kapitel Eight wird die Zahl 8 als 8 = 2 * 2 * 2 eingeführt und dann auf die Darstellung der Kuben als Summe aufeinanderfolgender ungerader Zahlen hingewiesen, die auf Nikomachos zurüchgeht. Aber letztlich landet man beim Waringschen Problem und seiner Geschichte."" -F. Schweiger, Internationale Mathematische Nachrichten, December 2007
Zero to Infinity is a combination of number lore, number theory, and sparkling descriptions of the simply stated but exceedingly difficult problems posed by the most ordinary numbers, that first appeared in 1955 and has been kept in print continuously ever since. With the fifth edition this classic has been updated to report on advances in number theory over the last 50 years, including the proof of Fermat's Last Theorem. Deceptively simple in style and structure, it is a book to which the reader will return again and again, gaining greater understanding and satisfaction with each reading."" -L'Enseignement Mathématique, January 2006"

About the Author

Although not trained as a mathematician, Constance Reid is well known for her books on mathematicians and mathematics. Following the success of From Zero to Infinity, her first book, Reid went on to write: A Long Way from Euclid; Hilbert; Courant in Gottingen and New York; Neyman; The Search for E.T. Bell; Julia - a Life in Mathematics, among others.

Product Details

• Paperback: 208 pages
• Publisher: A K Peters, Ltd.; 5th edition (February 4, 2006)
• Language: English
• ISBN-10: 1568812736
• ISBN-13: 978-1568812731
• Product Dimensions: 7.9 x 5 x 0.7 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #644,312 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

22 of 22 people found the following review helpful:

4.0 out of 5 stars Numbers being treated with respect, March 14, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: From Zero to Infinity (Spectrum Series) (Paperback)

Few books capture the range and rapture of mathematics like this one. Even though only twelve numbers are discussed, (zero through 9, e and aleph-zero), many of the trials, tribulations and joys of numbers and their admirers comes through. The style cannot merely be described by the word clarity, as this is a work that can be read by virtually anyone, even though a lot of mathematics is presented.
With numbers being touched, almost lovingly fondled, rather than discussed, this book belongs in every library. And it should be read, and read, and read, . . .

Published in Journal of Recreational Mathematics, reprinted with permission.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Old but good writer, July 14, 2007

By 

Wayne Ferrier "Wayne Ferrier" (upstate New York) - See all my reviews
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This review is from: From Zero to Infinity: What Makes Numbers Interesting (Paperback)

Constance Reid is one of those authors where I ended up buying everything she wrote. If you are advanced in mathematics she might be a tad elementary; but if you are an imbecile when it comes to mathematics as I am, you may find her interesting. It is number theory; however Reid's relationship with the little fellows seems to be more personal, more introspective than many number theorists.

1 of 1 people found the following review helpful:

4.0 out of 5 stars Numbers & their encapsulation of our world, December 9, 2011

By 

Souvik Mitra "S!" (Bangalore, India) - See all my reviews
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This review is from: From Zero to Infinity: What Makes Numbers Interesting (Kindle Edition)

For those of us who have passed out of our secondary schools & liked Mathematics - though our yearly transcripts told a different story - this book is a wonderful walk down the memory lane. Without the fear of our scores in Mathematics being a reflection of our worth, number theory is not just interesting - as in a intellectual domain - but also awe inspiring - as in the philosophical domain around what these numbers are telling us by exhibiting all these relationships.

We have gotten more & more efficient at telling if a number is prime, & yet we have no method of generating one. We know the each number can be squared, & both the count of numbers & the corresponding count of their squares are infinite, yet the constructs of equality, congruence & basic mathematical operations are baffling when applied to infinity. In chapters dwelling from 0 to 9 & then going onto 'e' & 'aleph zero' - or infinity of first order cardinality - Reid brings alive the 'easiest to understand intuitively but very difficult to prove Mathematically' relationships, theorems & properties of the entire number system. To be fair, some of it was a little terse & made my head spin & imagination boggle, in Bertie Wooster's words, - but that could just be me - & some of it, was plain riveting.

Most of the chapters, contrary to my initial expectation, were actually about wider concepts than just the numbers themselves. For example, 2 was about the binary number system, 3 about the primes, 4 about squares, 6 about perfect numbers & 8 about cubes. With7, I was plainly baffled, & I have no recall of what that was about - perhaps primes of a different type or something. The chapter on 'aleph-zero' would take me a few rebirths, per the Hindu system, to comprehend.

On an idle Saturday, if you want to revisit what Maths at school was like - read this book. It'll bring joy or make you feel like an worthless nincompoop. I do not know any Maths to tell you which one of the two is more likely - & yes, I have heard of statistical probability & measures of confidence & all that. :)