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The search for infinity, that sublime and barely comprehensible mystery, has exercised both mathematicians and theologians over many generations. Jewish mystics, in particular, labored with elaborate numerological schema to imagine the pure nothingness of infinity, while scientists such as Galileo, the great astronomer, and Georg Cantor, the inventor of modern set theory (as well as a gifted Shakespearean scholar), brought their training to bear on the unimaginable infinitude of numbers and of space, seeking the key to the universe.
In this sometimes technical but always accessible narrative, Amir Aczel, author of the spirited study Fermat's Last Theorem, contemplates such matters as the Greek philosopher Zeno's several paradoxes; the curious careers of defrocked priests, (literal) mad scientists, and sober scholars whose work helped untangle some of those paradoxes; and the conundrums that modern mathematics has substituted for the puzzles of yore. To negotiate some of those enigmas requires a belief not unlike faith, Aczel hints, noting, "We may find it hard to believe that an elegant and seemingly very simple system of numbers and operations such as addition and multiplication--elements so intuitive that children learn them in school--should be fraught with holes and logical hurdles." Hard to believe, indeed. Aczel's book makes for a fine and fun exercise in brain-stretching, while providing a learned survey of the regions where science and religion meet. --Gregory McNamee --This text refers to an out of print or unavailable edition of this title.
Aczel's compact and fascinating work of mathematical popularization uses the life and work of the German mathematician Georg Cantor (1845-1918) to describe the history of infinityAof human thought about boundlessly large numbers, sequences and sets. Aczel begins with the ancient Greeks, who made infinite series a basis for famous puzzles, and Jewish medieval mystics' system of thought (Kabbalah), which used sophisticated ideas to describe the attributes of the one and infinite God. Moving to 19th-century Germany, mathematician Aczel (Fermat's Last Theorem) introduces a cast of supporting characters along with the problems on which they worked. He then brings in Cantor, whose branch of mathAcalled set theoryA"leads invariably to great paradoxes," especially when the sets in question are infinite. Are there as (infinitely) many points on a line as there are inside a square or within a cube? Bizarrely, Cantor discovered, the answer is yes. But (as he also showed) some infinities are bigger than others. To distinguish them, Cantor used the Hebrew letter aleph: the number of whole numbers is aleph-null; the number of irrational numbers, aleph-one. These "transfinite numbers" pose new problems. One, called the continuum hypothesis, vexed Cantor for the rest of his life, through a series of breakdowns and delusions: others who pursued it have also gone mad. This hypothesis turns out to be neither provable, nor disprovable, within the existing foundations of mathematics: Aczel spends his last chapters explaining why. His biographical armatures, his clean prose and his asides about Jewish mysticism keep his book reader friendly. It's a good introduction to an amazing and sometimes baffling set of problems, suited to readers interested in mathAeven, or especially, if they lack training. B&w illustrations not seen by PW. 5-city author tour; $30,000 ad/promo; 30,000 first printing.
Copyright 2000 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.
Not bad. Not great either. Connecting Cantor's work to the Kabbalah is stretching it, but the biographical information is quite interesting. Read morePublished 5 months ago by Dasein
I have read a number of Aczel's works. They're decent in attempting to combine a readable by the layperson history of a mathematical concept with some very heavy mathematical... Read morePublished 16 months ago by Edward J. Barton
Aczel is a great writer. He makes complex things simple. He did a great job explaining Cantor's Diagonal Process on p. 111-116, chapter 8; "the first circle. Read morePublished on September 8, 2013 by Patrick Moore LMT Educator
This book was only okay. I felt like it couldn't decide if it wanted to be a history book, a biography or a math book, so it ended up missing the mark on all three counts. Read morePublished on February 20, 2013 by WanderingReader
By profession, I am an engineer and we tend not to take (or have time for) the pure math courses as we progress through our university eduction. Read morePublished on March 14, 2012 by H. Hall
This book is for set theory and math lovers, or anyone who is unfamiliar but interested. This book is about 200 pages, the first 100 are all history and the second 100 are all... Read morePublished on April 18, 2011 by cerulean city
This is an entertaining read about the life of Georg Cantor, concepts of infinity used in mathematics (especially in set theory) and the Kabbalah. Read morePublished on November 8, 2010 by NC
I read this book because I am intrigued by Cantor's thoughts, concepts and theorems on infinity. When Newton and Leibniz independently invented the modern infinitesimal calculus in... Read morePublished on November 3, 2010 by Arie Pieter Vander Stroom
The book went way over my head. I read it, and have to admit that I didn't understand much of it. I rated this one a five because I stand in admiration of smart people like Dr. Read morePublished on October 6, 2008 by Sam I Am