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Eli Maor
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To Infinity and Beyond: A Cultural History of the Infinite

by Eli Maor (Author, Foreword)
4.4 4.4 out of 5 stars 54 ratings
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Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "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 "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

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  1. ISBN-10
    9780691025117
  2. ISBN-13
    978-0691025117
  3. Publisher
    Princeton University Press
  4. Publication date
    July 9, 1991
  5. Language
    English
  6. Dimensions
    6.75 x 0.75 x 9.75 inches
  7. Print length
    304 pages
  8. See all details
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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

Product details

  • ASIN ‏ : ‎ 0691025118
  • Publisher ‏ : ‎ Princeton University Press (July 9, 1991)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 304 pages
  • ISBN-10 ‏ : ‎ 9780691025117
  • ISBN-13 ‏ : ‎ 978-0691025117
  • Item Weight ‏ : ‎ 1.2 pounds
  • Dimensions ‏ : ‎ 6.75 x 0.75 x 9.75 inches
  • Customer Reviews:
    4.4 4.4 out of 5 stars 54 ratings

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Eli Maor

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4.4 out of 5 stars
4.4 out of 5
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54 global ratings

Top reviews from the United States

H. Sedaghat
5.0 out of 5 stars An enjoyable introduction to the infinity for non-mathematicians
Reviewed in the United States on August 29, 2018
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I bought this book both for its content discussing the infinity in an unusual historical context and for its author Eli Maor who has a fine reputation as a mathematics expositor. The book discusses the infinity from a few different points of view, ranging from mathematical to the aesthetic. He discusses the infinity of positive integers, the concepts of convergence and limits, the intrigue of infinite series (including Zeno's paradoxes), the strangeness of irrational numbers and more. He also discusses some aesthetic aspects of the infinite including the work of he Dutch artist M.C. Escher which is illustrated using both black and white and color pictures. The appendix supplies additional details for those interested in understanding the topics at a greater depth. Maor's style of writing is relaxed and his prose is full of historical remarks and lively comments about ideas and the bright people who thought them up. The reader with a with rather negligible mathematical background gets a non-trivial and enjoyable understanding of the infinity from reading this book. This is a more fulfilling read than the average layman level expositions to the topic of infinity that often tend to be too light and airy.
2 people found this helpful
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Vassilios A.
5.0 out of 5 stars Excellent subject for all the people who wander about things.
Reviewed in the United States on August 20, 2016
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I bought this book just to remind myself a few lessons I had learned about 45- 55 years ago. Now I am ready to answer my grandson's question, what is infinity and how do I get there?
This is a fantastic book for anyone who has had some extensive Math and Calculus training in his/her past. I highly recommend it to anyone who wants to open their mind and learn something beautiful with ease.
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Paul Aizley
4.0 out of 5 stars Four Stars
Reviewed in the United States on April 1, 2018
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It’s more cultural than scientific and I am looking for mathematical treatments of infinity.
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Mead C. Whorton Jr.
5.0 out of 5 stars Fast Service!
Reviewed in the United States on June 14, 2023
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Excellent buy. Low price. Book as described and arrived promptly. Use this vendor!
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Timothy J. Spencer
5.0 out of 5 stars What do Nothingness and Infinity have in common?
Reviewed in the United States on December 28, 1999
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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.
47 people found this helpful
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5.0 out of 5 stars Easy to read.
Reviewed in the United States on March 14, 2022
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Humorous. Well explained math at the foundations of Calculus. Beyond that as well.
Highly recommended for anyone interested in modern thought
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N. Wallach
3.0 out of 5 stars Math and its influence on culture
Reviewed in the United States on March 29, 2007
This 235 page book attempts to place the concept of Infinity within the cultural realm. To accomplish this, the author has to first establish what infinity means and then to show how it was used in such divers arenas as art and astronomy. Therefore, the book is divided into sections. In the first section, therefore, we focus on the arithmetic meaning of infinity. This is an excellent explanation of the concept and with the stretching of the information in to Calculus serves as a good way of introducing people to why Calculus was developed. Certainly this is a more informative way of looking at it than what is typically taught in the normal high school math curricula!

From arithmetic we move to geometry and there are introduced to the way that the concept of inifinity allows the mathematician to create interesting geometrical constructs including such things as non-euclidean geomtries (plural!!!). This part of the book can be a bit dense and even the inclusion of a practical example of the creation of Mercator projections of the world's map do not help much.

Next we move to the realm of art. Here the author expresses his admiration for the work of the Dutch artist Escher and uses several of his prints as examples. These prints are great and fun illustrations of how one moves from infinity to center stage and back to infinity and as an admirer of Escher's works myself, it's fun to read about it in such glowing terms. However, since Escher himself claimed to not understand any of the mathematics behind his inventions, it is somewhat puzzling why the two are interpolated here.

Finally, we move on to deal with astronomy. Since astronomy is the science that deals with very large numbers and concepts, I suppose that is appropriate. But, at this point the book moves away from the mathematics and becomes a somewhat straight-forward recounting of astronomical history. This is interesting but it is not clear to me how the concept of inifinity really applied despite the somewhat tortuous attempts the author makes.

From very large distances we go to the infintesimal when the author spends one, two page chapter on the atom. This is clearly an attempt to be all inclusive and does not work - in my opinion. We are already past the 200 page mark when this happens and one has to ask why other topics deserve such long descriptions, but sub-atomic physics gets only a paragraph or two?

In any case, this was an interesting survey of various topics that seem to be connected through the concept of infinity. It will probably not teach you too much, but will also illuminate some dark recesses of the world's thoughts, so it is probably worth a quick read.
9 people found this helpful
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Amazon Customer
5.0 out of 5 stars Some infinities are smaller than others
Reviewed in the United States on December 23, 2016
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I purchased this for a first year seminar college course and thoroughly enjoyed the read. Maor explores the history of infinity through ancient and modern scientists and philosophers. The book covers infinity in art, science, philosophy, mathematics, space, and conceptualization. This book would be a informational read that isn't too difficult to understand and explains material thoroughly. Will read again in the future.
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G. Parameswaran
4.0 out of 5 stars This book is an absolute gem!
Reviewed in India on January 8, 2023
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I have had the pleasure of reading two books by mathematician Eli Maor. The book currently under discussion is titled "To Infinity and Beyond", a beautiful paradoxical phrase. If one reaches or gets to infinity, then it is no longer infinity (In a physical sense impossible, but mentally getting there and beyond is possible). The part one which describes various challenging concepts of "Mathematical Infinity" is a masterpiece of elegant explanation of various abstract concepts. The concepts of limits, convergence and Cantor's Set Theory are discussed in a manner that a good high school student can understand. The second part which covers the "Geometric Infinity " is also superb and helps in visualizing Non-Euclidean Geometry. The third part called "Aesthetic Infinity" which artistically intriguing is not on the same level as the previous two sections. Mr. Maor concludes the book with a brief introduction to "Cosmological Infinity" and set of Appendices that are a gateway to further study. The overall rating is a four due to the weakness of the third part. This author has also penned another book on the number "e", which is also worth reading.
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堀川
5.0 out of 5 stars 無限からみた数学史
Reviewed in Japan on May 11, 2024
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無限という実体を4種類にわけて、それぞれの簡単な歴史が書かれている。数学的無限と幾何学的無限の他に美的無限と宇宙論的無限が加わっているのが特徴的だと感じた。
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the great amphibian
5.0 out of 5 stars Startlingly good book.
Reviewed in the United Kingdom on December 12, 2003
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It should be noted that this book was written in 1987, several years before Maor's book: "e- the Story of a Number" - [the computer rendered image on the cover may belie the age of the book]. As I write this I am a second year mathematics undergraduate; I read "To Infinity and Beyond" during the summer. I was first introduced to Cantor's levels of infinity in this book, (extending countability and uncountability to aliph values, and that in effect bijective functions could map one set to another providing it has the same aliph value. First learning this principle felt like an eery truth of reality of high subtlety and high information. All of the great ideas have the eery convincingness that overcomes initial non-intuitivity... either non-intuitivity or that people before missed all together that which was sprawled in front of them). There was a rewarding explanation of the conception of non-Euclidean geometry, which to my shock but not to my surprise, was yet another fundamental idea that came from the mind of Gauss. Tragedy is touched upon as the tale of the Italian scientist, (he probably would have been called 'Philosopher' back then), named Bruno was burnt to the stake for his beatiful imagination in conjecturing that the universe is truly infinite and that there are infinitely many other worlds of creatures like us. The final chapter fills the reader with inspiration as Maor explains our place in the universe and ends with the comment, (not verbatim): "Perhaps the greatest question remaining to human enquiry is whether we are alone."
13 people found this helpful
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Sayan Datta
4.0 out of 5 stars One of Maor's best
Reviewed in India on July 31, 2022
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This is probably one of Eli Maor's first. It is good but his other book ' e, the story of a number' goes to greater depth albeit covering, arguably, lesser breadth and is probably his best. These are from a unique genre of math books; their closest parallel that I can think of are Rudy Rucker's books like ' Geometry, Relativity and the 4th dimension '. They are not for every Tom, Dick and Harry. If you are well versed in Math you may breeze through courtesy of these excellent authors; else, significant effort is needed to wade through. And if you are up for it, the authors make the journeys worthwhile with many hidden gems in every nook and cranny of the books. Note to American publishers - Print and paper quality can be significantly improved given the price at which you sell books like these.
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Amazon カスタマー
2.0 out of 5 stars 煙草臭いです。
Reviewed in Japan on March 25, 2017
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商品の状態は「良い」とのことでしたが、１９８９年出版の本で非常に古いので、「良い」ことはないだろうと思って購入しました。この商品の中古本を買うのは３度目ですが、他社の表記と比べると経年劣化からして「可」だと思います。それにしても商品がとても煙草臭い。以前の持ち主が喫煙者だったのだと思いますが、匂いまではさすがにクリーニングできないのでしょうか。ビニール袋から取り出した状態で部屋に置いておきたくはないほどです。おそらくそのまま廃棄すると思います。
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