Infinity: Beyond the Beyond the Beyond
By Lillian R. Lieber
* Publisher: Paul Dry Books
* Number Of Pages: 359
* Publication Date: 2007-11-01
* ISBN-10 / ASIN: 1589880366
* ISBN-13 / EAN: 9781589880368
* Binding: Paperback
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.
Summary: Infinity analyzed
Rating: 5
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, 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.
Summary: Beware! Beware!
Rating: 5
Beware! This is not Lillian Lieber's original work. It has been abridged. Approximately one third of the original text and presumably the drawings have disappeared. In the forward, Barry Mazur, states plainly that he zapped Lillian's preface, chapter 1, one half of chapter 17, and all of chapters 18 through to 24. Gone is Lillian's introduction to SAM, Lillian's spirit creature of Science, Art, and Mathematics. Why did Mazur do this? He thought the Liebers digressed too much. He wanted them to stay on track with the main subject, transfinite mathematics. He thought that some of their worldly concerns speak less to a modern audience than they did to their readers in 1953. However we have to take Dr. Mazur's word for it, as the sections are deleted and you can no longer judge for yourself. Despite my misgivings I give a 5 star rating as what is left is still beautiful. However you may wish to try the used book market to get the original version.
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