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### Summary

### Summary

From the end of the 19th century until his death, one of history's most brilliant mathematicians languished in an asylum. The Mystery of the Aleph tells the story of Georg Cantor (1845-1918), a Russian-born German who created set theory, the concept of infinite numbers, and the "continuum hypothesis," which challenged the very foundations of mathematics. His ideas brought expected denunciation from established corners - he was called a "corruptor of youth" not only for his work in mathematics, but for his larger attempts to meld spirituality and science.

### Author Notes

Amir D. Aczel was born in Haifa, Israel on November 6, 1950. He received bachelor's and master's degrees in mathematics from the University of California, Berkeley and a doctorate in decision sciences from the business school at the University of Oregon. He taught at several universities during his lifetime including the University of Alaska and Bentley College.

His first book, Complete Business Statistics, was published in 1989 and went through eight editions. His other books include How to Beat the I.R.S. at Its Own Game: Strategies to Avoid - and Fight - an Audit; Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem; The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity; The Riddle of the Compass: The Invention That Changed the World; Entanglement: The Greatest Mystery in Physics; and Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers. He died from cancer on November 26, 2015 at the age of 65.

(Bowker Author Biography)

### Reviews 4

### Booklist Review

If, as G. K. Chesterton once proposed, insanity constitutes the modern form of heresy, then Georg Cantor deserves recognition as one of modernity's supreme heretics, one who lost his sanity in challenging the limits of mathematical rationality. In this engrossing story of a man and of an idea, Aczel elevates Cantor out of obscurity into his proper place in cultural history, while confronting readers with the intellectual riddle that unhinged Cantor's powerful mind: the riddle of infinity. Discovered as a potent geometrical tool by the ancient Greeks, contemplated as a divine mystery by the medieval Kabbalists, infinity remained a mere potentiality for Newton and Leibniz, but it loomed above Cantor as a terrifying yet irresistible reality. In assessing Cantor's achievement as the first to probe infinity with mathematical rigor, Aczel demonstrates the same gift for interpreting complex concepts that he previously demonstrated in God's Equation [BKL S 15 99], about Einstein's pioneering work in cosmology. And as in his book on Einstein, Aczel penetrates to the human drama behind the formulas, detailing the personal frustrations and professional conflicts that drove Cantor into mental collapse. Aczel also uncovers the uncanny ways in which Cantor's life foreshadowed that of his more famous successor, Godel, who was attracted to the same problems and doomed to the same descent into madness. An indispensable book for anyone interested in the darker side of intellectual progress. --Bryce Christensen

### Publisher's Weekly Review

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 infinityÄof 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 mathÄcalled set theoryÄ"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 mathÄeven, 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. (Sept.) (c) Copyright PWxyz, LLC. All rights reserved

### School Library Journal Review

Adult/High School-Aczel tells of mathematicians struggling with absolute infinity and some of its mind-bending ramifications. The crown jewel of this struggle was conceived more than a century ago by Georg Cantor and remains an enigma to mathematicians. Cantor spent his life going back and forth between trying to prove and disprove his continuum hypothesis. In the Kabbalah, the aleph "represents the infinite nature, and the oneness, of God." Cantor deliberately picked this symbol for use in his equations: to him, trying to understand the absolute infinite was like trying to touch the face of God. About 50 years after his death, another mathematician definitively showed that the continuum hypothesis cannot be proven valid or invalid by any known means. Aczel provides a good history leading up to and past Cantor's work. Personal stories of people such as Pythagoras, Galileo, Newton, and G?del are mixed in with well-put explanations of the concepts they pondered. A brief history of the Kabbalah and highlights of some of its concepts help readers understand Cantor's work. The author writes cleanly and clearly on a complex subject, and readers don't have to be good at math to enjoy this book. It's perfect for analytically minded students who love to ponder big questions. Those who enjoyed the popular cosmology books by Stephen Hawking are likely to devour this one as well.-Sheila Shoup, Fairfax County Public Library, VA (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.

### Choice Review

Mystery of the Aleph is a riveting tale of Georg Cantor and his quest for a theory of transfinite cardinal and ordinal numbers. Aczel (Brandeis Univ.) has managed to combine into one work an intellectual history of the concept of infinity, a sociopolitical study of the mathematics community of the mid- and early 20th century, and an in-depth biographical sketch of one of the most important figures in the foundations of mathematics. The level of mathematics presented is suited for general readers, while the historical content will inform and entertain both the novice and professional. Readers with a taste for greater mathematical depth may prefer the more formal and scholarly work by Joseph W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (CH, Sep'79; reprint, 1990). Highly recommended for undergraduates, general readers, and anyone interested in the history of mathematics. R. L. Pour; Emory and Henry College