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The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity

amir d. aczel

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From Simon & Schuster, The Mystery of the Aleph is Amir D. Aczel's compelling narrative that blends a story of infinity with the tragic tale of a tormented and brilliant mathematician.

From the Pythagoreans, the Greek cult of mathematics, to the mystical Jewish numerology found in the Kabbalah, The Mystery Of The Aleph follows the search for an answer that may never truly be trusted.

258 pages, Paperback

First published January 1,2000

This edition

Format
258 pages, Paperback
Published
September 1, 2001 by Atria Books
ISBN
9780743422994
ASIN
0743422996
Language
English

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amir d. aczel

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Rating(4 / 5.0, 73 votes)
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73 reviews All reviews
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poirotto
★ ★ ★ ★ ★
April 17,2025
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A deep dive into the search for infinity—both mathematical and philosophical. Still not sure if chasing infinity drives people mad or if you have to be a little mad to truly grasp it. Either way, it’s a fascinating read.
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Derenor
★ ★ ★ ★ ★
April 17,2025
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A book about infinity and the man who in modern times did most to advance its study, Georg Cantor. Cantor died in a mental asylum, having been driven there, in a sense, by the maddening complexities of his work. Anyone with a mathematical bent or a certain kind of philosophical inclination who enjoyed mind-bending late-night dorm-room discussions will find much to marvel at in this book.

Side note: When I read this, I had already been intrigued by the complexities of Kabbalah as it figured into Umberto Eco's conspiracy novel, Foucault's Pendulum, so I was pretty well prepared to appreciate its role in Cantor's thinking. Such correspondences and linkages are among the pleasures of wide reading.
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DarkRaven804
★ ★ ★ ★ ★
April 17,2025
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The book covers the idealized history of mathematical ideas related to infinity, while telling in parallel the biographies of the various people who were a part of it. More than one of the stories fall into the "tortured genius versus crusty establishment" trope.

The book breezes through fairly advanced topics without much explanation, which is fine if you already have some idea about set theory and related ideas. Yet in another place, he mentions pi and e, parenthetically explaining that 'e' is the base of natural logarithms. That is, the author seems to be a little confused about whom he's writing for: the mathematics student who already knows what is meant by "multiplying two sets" will probably not be unfamiliar with 'e'.

Despite being in the sub-title, there's not much about Kabbalah, and the connection to Transfinite numbers is strained at best. It comes across as another instance of the now cliche practice of trying to link mysticism and hard science. (If you like this kind of thing, Douglas Hofstadter does a much better job in GEB:EGB)

The book implies Some sort of connection between the contemplation of infinity and the insanity of Cantor and Godel. (There are also others who worked in similar fields that suffered similarly.) It should be mentioned that there are ten thousand mathematicians who understand the theories very well and are totally sane. My own suspicion is that the causation is perhaps the reverse: it is the disconnect with convention (or reality) allows the great mathematician to make new advances.

The edition I had was in some bad need of editing and proofreading; in my library copy, a previous borrower had thoughtfully made some corrections in pencil.

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aish_y
★ ★ ★ ★ ★
April 17,2025
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Not a bad book at all. The book itself is just a little too "intro" to mathematics and not very deep the cultural idea of infinity, as implied in the title.
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Spygecko
★ ★ ★ ★ ★
April 17,2025
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One of the most spiritual books out there for me. Lots of mathematical and logical content to enjoy, but also enough history and mysticism (described from our modern perspective) to keep your mind stimulated.
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makurineko
★ ★ ★ ★ ★
April 17,2025
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This was a very interesting read - intriguing glimpses into the lives of mathematicians, some rather inaccessible (but expected) maths, and some hauntingly mindblowing aspects that hint at the nature of "infinity" to exist at the curled edges of our own consciousness, for something to exist outside of what we can humanly conceive of. That's slightly nuts, TBH.

Would suit anyone with an interest in the weirder side of numbers and philosophy - maths background helps, but this isn't about formulae as much as how human concepts get turned into explanations. The 'battle' between real numbers and continuous number lines, for example, is one which is something that most kids will happily puzzle away at.

I will probably list this for sending/swaps, so let me know if you're interested in it.
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JJnie
★ ★ ★ ★ ★
April 17,2025
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There were some 4/5-star moments in this book but I kinda think this coulda been better off as an essay. I like some of the ideas about the connection between studying the continuum and mental illness, and love diving into some math especially now that I'm just doing data science with my brain. But I could feel the author stretching to fill in the story with biographical notes, and getting into word holes just writing about whether findings on infinity make humans closer to God or prove the eternal seperation of our knowledge from that of a God. Like that is all the stuff I cut from my thesis. Ok I never included it in the first place, and I also didn't really cut anything. Basically just turned in a first draft but it got the job done. This book is not overly mathy so it could be a fun pickup if you don't have a big depth of math knowledge but wanna play with some ideas, but there are better stories in that realm. Benji's summer crusade against nonfiction continues.
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Flexicute
★ ★ ★ ★ ★
April 17,2025
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The main thing you need to know is that despite the subtitle, this is pretty much a book about Georg Cantor. There's enough historical treatment of mathematics for Cantor's story to make sense, but there's no actual mathematics. And there's much less kabbalah than the subtitle would encourage you to believe. But it's really a fine book, quite readable and informative. It's main crimes are that a) it's not as good as David Foster Wallace's "Everything and More" with respect to infinity, and b) it's not as good as Joseph Dan's "A Very Short Introduction to Kabbalah" with respect to Kabbalah. But if DFW is too mathy and too context-heavy, and/or if "A Very Short Introduction to Kabbalah" is too long, you can scratch both itches with this book. But I have to say that while the kabbalah/set-theory connection is interesting and romantically appealing, it is insufficiently argued. I haven't done the math, but I suspect that this is because it doesn't actually withstand the additional scrutiny.
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