Infinity: Beyond the Beyond the Beyond (Paperback)

~ Lillian R. Lieber (Author), Hugh Gray Lieber (Illustrator), Barry Mazur (Foreword)

Editorial Reviews

Product Description

"Another excellent book for the lay reader of mathematics . . . In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."-Library Journal

"The interpolations tying mathematics into human life and thought are brilliantly clear."-Booklist

"Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in The Education of T.C. MITS."-Chicago Sunday Tribune

Infinity, another delightful mathematics book from the creators of The Education of T.C. MITS, offers an entertaining, yet thorough, explanation of the concept of, yes, infinity. Accessible to non-mathematicians, this book also cleverly connects mathematical reasoning to larger issues in society. The new foreword by Harvard mathematics professor Barry Mazur is a tribute to the Liebers' influence on generations of mathematicians.

Lillian Lieber was a professor and head of the Department of Mathematics at Long Island University. She wrote a series of light-hearted (and well-respected) math books, many of them illustrated by her husband.

Barry Mazur is the Gerhard Gade University Professor of Mathematics at Harvard University and is the author of Imagining Numbers.

About the Author

Lillian R. Lieber was Professor and Head of the Department of Mathematics at Long Island University. She wrote a series of light-hearted (and well-respected) math books, many of them illustrated by her husband.

Hugh Gray Lieber was Professor and Head of the Department of Fine Arts at Long Island University.

Barry Mazur does his mathematics at Harvard University and lives in Cambridge, Massachussetts, with the writer Grace Dane Mazur. He is the author of "Imagining Numbers (Particularly the Square Root of Minus Fifteen)" (FSG, 2003). He has won numerous prizes in his field, including the Veblen Prize, Cole Prize, Steele Prize, and Chauvenet Prize.

Product Details

• Paperback: 359 pages
• Publisher: Paul Dry Books; 1st Paul Dry Books Ed edition (November 1, 2007)
• Language: English
• ISBN-10: 1589880366
• ISBN-13: 978-1589880368
• Product Dimensions: 7.8 x 4.9 x 0.8 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (6 customer reviews)
• Amazon.com Sales Rank: #395,094 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 11 people found the following review helpful:

5.0 out of 5 stars A Wonderful Book!, May 30, 2001

By	"maguszero" (Greenville, SC USA) - See all my reviews

This review is from: Infinity: Beyond the Beyond the Beyond (Hardcover)

Lillian Lieber and her husband Hugh created some of the most wonderful books in the fields of mathematics, logic, and relativity. Although some of my fondest childhood memories are the hours I spent trying to fully grasp the meaning in her books, I find these same books to be no less enjoyable today as an adult. I cannot recommend her books highly enough.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Infinity, November 26, 2003

By	Brian Marley (seattle, wa, usa) - See all my reviews

This review is from: Infinity: Beyond the Beyond the Beyond (Hardcover)

This is a great book. I first found it in my high school library. For the uninitiated, who would have thought there were different levels of infinity? This book explains infinity in a readable and entertaining way. It is too bad this book is out of print as I suspect it would still be in high demand. It would make a great title for a book club. Somebody needs to republish it!

6 of 6 people found the following review helpful:

5.0 out of 5 stars Infinity analyzed, August 24, 2008

By	Dawson C. Smith (Stratford, CT) - See all my reviews

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Nobody explains mathematical ideas for the layman as does Lillian R. Lieber. And the fanciful illustrations that always accompany her work, done by Hugh Gray Lieber, are amusing and informative.

Infinity: Beyond the Beyond the Beyond presents an account of how mathematics has learned to deal with the infinite, primarily through the work of Georg Cantor. Controversial in its day, Cantor's set theory and transfinite arithmetic are now part of the foundations of modern mathematics. Perhaps the most startling idea to be had from this book is that infinite sets are not all of the same size.

I have before me a copy of the 1953 original, as well as the 2007 abridgement. Aside from the fact that the older book is a hardcover, the abridgement is the better book. The editor, Barry Mazur, a mathematician at Harvard, has removed the dated, nonmathematical introductory material and the chapters on calculus. This book is now a superb layman's guide to the mathematics of transfinities.

If you would like more biography and less mathematics, you might try The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity, by Amir D. Aczel.

Note: In 1900, David Hilbert put forth a list of the 23 most important unsolved problems in mathematics. At the head of the list was Cantor's continuum hypothesis. The problem was still open when the Liebers wrote their book. In 1963, a mathematician named Paul Cohen proved that the continuum hypothesis is actually independent of the generally accepted axioms of set theory, and earned the Fields medal for it.