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To Infinity and Beyond: A Cultural History of the Infinite Paperback – July 9, 1991

ISBN-13: 978-0691025117 ISBN-10: 0691025118

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To Infinity and Beyond:  A Cultural History of the Infinite + e: The Story of a Number (Princeton Science Library) + An Imaginary Tale: The Story of [the Square Root of Minus One] (Princeton Science Library)
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Product Details

  • Paperback: 304 pages
  • Publisher: Princeton University Press (July 9, 1991)
  • Language: English
  • ISBN-10: 0691025118
  • ISBN-13: 978-0691025117
  • Product Dimensions: 0.6 x 6.3 x 9.4 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #215,181 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times

"Fascinating and enjoyable . . . [P]laces the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

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Customer Reviews

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Clearly this is a book that has appeal for both the professional mathematician and the layperson alike.
Dennis Littrell
Indeed, this is one of the things I like about Maor best - he's written a book that is fun to read, even if you already know most of the stuff.
Duwayne Anderson
Interspersed with the historical narrative, but easily separable, it contains good solid mathematics in a clear and concise fashion.
Not a Clue

Most Helpful Customer Reviews

29 of 30 people found the following review helpful By J. Grupp on June 1, 2001
Format: Paperback
Maor titles his book "a cultural study," but the cultural work domainates the second half of the book. The first half--which is more interesting than the second half--is a truly amazing analysis of just what the infinite is. Maor goes into detailed discussion of the nature of infinity in prime numbers, irrationals, rationals, and so on. The patterns, surprises, and mysteries of number fields are discussed with perfect clarity. Other issues involving infinity are mapped with equal precision and clarity for the beginner. The second half of the book involves studying the infinite in Escher's art, in geometric systems before and after Euclid, and in art, theology, science, singularities, and etc. Overall, for those interested in the mecahnics of nature, this book is not to be passed up!!! But be cautioned, this book is for beginners, for those only interested in grasping basic concepts of mathematics, not intense formulas that lead to singularities, for example. I am a graduate student in philosophy, so it served my purposes to the maximum level.
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46 of 52 people found the following review helpful By Timothy J. Spencer on December 27, 1999
Format: Paperback Verified Purchase
Maor is thoroughly at home in the realm of mathematics, its history and the frequent detours into the lives of the men who have brought its secrets to light. To Infinity and Beyond is a lighter read than either e, the Story of a Number or Trignometric Delights (his two previous titles). However, this work is infinitely enlightening and exponentially chocked full of "aha's". Maor enriches the reader's understanding not only of mathematics but the culture in which it has flourished. An absorbing read.
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17 of 19 people found the following review helpful By Duwayne Anderson on November 8, 2004
Format: Paperback
Maor has written a book for both mathematicians and poets. Since he is a mathematician himself there is, to be sure, plenty of math in Maor's book. But the book should also appeal to the aesthetic side of many readers (me included) by exploring human perspectives of infinity, such as how we try to relate to the concept at a personal level, and how different people have tried to capture the notion in art and prose.

The book is arranged in four parts, dealing with the mathematical concept of infinity (how it shows up in algebra, etc.), geometrical infinity, aesthetic infinity (both art and poetry) and cosmological infinity.

The section on mathematical infinity has the typical assortment of historical examples, beginning with examples like the runner's paradox made famous by Zeno. There are also examples of infinite series that converge, including examples of how ancient mathematicians invented infinite series for transcendental numbers like pi. There's a plethora of little tidbits found throughout this section in little mini chapters that are short essays, only a few pages long, that give surprisingly succinct, tantalizing, and often delicious examples of mathematical infinity. Reading this book I was struck by what good reading it makes for any student preparing to take a class in calculus.

Some of the author's most interesting material is the author's discussions about infinite series. I particularly enjoyed his examples how the associative property doesn't hold for infinite series (a non-intuitive fact that often comes as a surprise to many new students). Ordinarily, if you have a string of numbers that are connected by addition (x1+x2+x3+..+xn) for example, you can rearrange their order and get the same result.
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13 of 15 people found the following review helpful By Not a Clue on August 4, 2001
Format: Paperback
I have read other books by Eli Maor. After "June 8, 2004", I had doubts about this one, but I wanted to clarify some Cantorian issues. Once I started this one, I could not put it down. It also answered my questions.
Most, if not all of the material should be accessible to a motivated high school senior. It presents the history of infinity in a manner as fascinating as a mystery or adventure story (a true one, better than fiction); it reminds me of "Terrible Lizards" in that sense. Interspersed with the historical narrative, but easily separable, it contains good solid mathematics in a clear and concise fashion. Only the section on Bertrand Russell's paradoxes failed to satisfy.
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6 of 7 people found the following review helpful By Dennis Littrell HALL OF FAMETOP 1000 REVIEWERVINE VOICE on December 28, 2007
Format: Paperback
Israeli mathematician Eli Maor's beautiful book came out in 1987 and has remained in print ever since. The reason is simple: it is authoritative yet accessible. There are numerous graphs, drawings and equations; but the focus, as the subtitle expresses it, is on the cultural history of the infinite.

The book is divided into four parts for four types of infinity: mathematical, geometric, aesthetic, and cosmological. The highlight of mathematic infinity has to be Georg Cantor's discovery and demonstration in the 19th century that there are hierarchies of infinity--that is, that some infinities are larger than others! Cantor's proof is most amazing and indeed one of the great triumphs of mathematics. What I found fascinating about geometric infinity is tessellation, which is the art and science of laying geometric patterns on a surface, such as squares, triangles, circles, etc. Probably the best known and most delightful expression of aesthetic infinity is in the work of M. C. Escher. Maor includes a number of Escher's drawings and paintings including five pages of color plates in the middle of the book. As for cosmological infinity, well, physicists and cosmologists shy away from infinity, of course, but it is impossible to think about the cosmos without having our notions tinged with the infinite. After all, it is hard to escape from the idea that the universe came from nothing or has always been. If it's always been, then that is infinity; and if there was once nothing, for how long was there nothing?

Maor adorns the text with numerous quotes about the infinite from scientists, mathematicians, artists, and others.
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