The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity: Mathematics, the Kabbalah, and the Human Mind [Englisch] [Gebundene Ausgabe]

The search for infinity, that sublime and barely comprehensible mystery, has exercised both mathematicians and theologians over many generations: Jewish mystics in particular laboured 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 Shakespeare 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, the 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 at which science and religion meet. --Gregory McNamee

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

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
Copyright © American Library Association. All rights reserved

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

Copyright 2001 Cahners Business Information, Inc.

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.

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.