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Mystery of the Aleph

3.85  ·  Rating details ·  579 Ratings  ·  43 Reviews
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 ...more
Audio, 5 pages
Published September 4th 2001 by Random House Audio (first published 2000)
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Jul 31, 2015 rated it did not like it  ·  review of another edition
Some of the errors in this book baffle me. They are not of the innocent kind. Some major offences:
Both the continuum hypothesis and its converse are true. And both the continuum hypothesis and its converse are not true. The continuum hypothesis is undecidable within our realm of mathematics.

By 'our realm of mathematics' Aczel means the ZFC theory. By 'undecidable' he means 'independent' (fair enough, apparently the two are used as synonyms in some contexts). What he means by 'converse' is not cl
Nov 27, 2011 rated it it was amazing  ·  review of another edition
Shelves: my-audio-books
A wonderful history of mankind's grappling with the concept of infinity where mathematics, philosophy and religion intersect in amazing ways. This is a relatively short book but it is packed with fascinating stories about ancient Greek philosophers, kabalists, Galileo, Descartes, Georg Cantor, Kurt Gödel and many others. An excellent read. I'll be sure to read all the other books by Amir D. Aczel.
K.D. Rose
This wouldnt seem to be a book that would go under cross-cultural spirituality. It is.
It depends on how much you are trying to understand. Ultimately, deep study takes you to almost every discipline and science, hard and soft.
Nov 05, 2012 rated it it was amazing  ·  review of another edition
This is the third time I've read this book in the last 18 months. It has given me much to ponder on and reflect about in life and our search for the infinite and what that is.
Not a bad little book, detailing briefly the history of transfinite numbers, the lives of Cantor and Gödel, and their theories. Delved a little bit too deeply into religious speculation, and not too much at all in the mathematical implications of the work produced. Recommended, but only as a primer and with additional research.
Nov 28, 2012 rated it really liked it  ·  review of another edition
Shelves: math, kabbalah
This book feels cut from the same mold as Darren Aronofsky's movie "Pi" though being more of a history of the mathematical pursuit of infinity than a story of one just one person's encounter with it. The author discusses the specific mystery cults and important researchers from the Pythagoras to winner of the Fields Medal, Paul Cohen, chronicling the development of our understanding of the irrational. He spends most of the book discussing the key contributions of mathematicians Georg Cantor and ...more
Dennis Littrell
Sep 28, 2015 rated it really liked it  ·  review of another edition
A somewhat flawed, magical, fascinating read

Aczel's fascinating book is a short narrative history of the concept of infinity (the aleph) with a concentration on its mathematical development, especially through Galileo, Cantor, Gödel, Paul Cohen and others, meshed with some very interesting material from the ancient Greeks and the Kabbalists who associated infinity with their ideas of God. He includes some material on how strikingly difficult it was for Cantor and others to go against established
Feb 22, 2009 rated it really liked it  ·  review of another edition
This is an interesting book about the mathematics of infinite sets in general, and about Gregory Cantor and some other mathematicians who have studied this field in particular. Before one blanches at the phrase "mathematics of infinite sets", be advised that this book is written for a public audience and is really quite readable. This is because several of the basic facts about infinite sets, for instance that there are as many even integers as integers, and as many rational numbers as integers, ...more
Phil Scovis

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
Jun 11, 2009 rated it did not like it  ·  review of another edition
Nothing is worse, in my view, than coming across an error or inconsistency near the beginning of a book, especially one that I am reading in order to add to my understanding of a subject. In his discussion of the Kabbalah in chapter three Dr. Aczel states that there are ten permutations of the letters YHVH, which represent the name of God. Now I might have breezed right past this had a previous reader not drawn my attention to the error. The word 'ten' was crossed out and replaced with 'twelve', ...more
Matthew Daniels
Feb 07, 2011 rated it really liked it  ·  review of another edition
Recommends it for: Casual readers interested in history about the infinite
This book was a captivating read... but not exactly what I was looking for when I read it. Though flavorful -- and I can appreciate that this is book is written for a specific audience that I might not be a part of -- I felt that Aczel could have dared to present a little more mathematics in a few places. There were about two or three pages devoted to silhouetting Cantor's diagonal proofs for the countability of the integers and reals, but besides occasionally inserting a statement of the contin ...more
Mar 13, 2009 rated it really liked it  ·  review of another edition
Shelves: audiobooks
This books gives a history of thinking about Infinity, both in a mathematical as in a philosophical and religious meaning. It is also a biography of George Cantor, a mathematician who developed many of the ideas of infinity in mathematics. It is an interesting story about the work of mathematicians.

No Math knowledge is needed to understand this book, but if you know a bit about classical analysis it gives a view of the people behind the theorems.

The philosophical angle is the question: what is
Steve Lew
Mar 23, 2013 rated it liked it  ·  review of another edition
Shelves: infinity
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 ...more
Michael Dworaczyk
I was infinitely disappointed with this book. I expected so much more. The biggest problem is that I don't believe Aczel knew what kind of book he wanted to write. The subtitle is “Mathematics, the Kabbalah, and the Search for Infinity.” What the subtitle should have been was, “Study Infinity and Lose your Mind.” Because that's really all he harped on. Cantor studied infinity, and what happened to him? He went crazy. Godel picks up the torch. Result? Crazy. I think a few more mathematicians migh ...more
John Jr.
Dec 04, 2011 rated it liked it  ·  review of another edition
Shelves: mathematics
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 U
Jan 17, 2010 rated it it was amazing  ·  review of another edition
Shelves: science-physics
There is a video in You Tube about “dangerous knowledge”. It is a product of the BBC which examines the lives of three mathematicians Georg Cantor, Ludwig Boltzman and Kurt Godel. The video tries to make the argument because each of these men explored the idea of infinity they went insane. I thought the video to be sensationalistic drivel and didn’t watch the whole thing.
In The Mystery of the Aleph, Aczel explores the concept of infinity from Pythagoras to Cantor. I wish I could understand all
Aug 26, 2009 rated it liked it  ·  review of another edition
Recommends it for: If that title grabs your interest than read the book.
I feel the same way about advanced mathematics and advanced physics.
The concepts and ramifications fascinate me, but I don't want to spend the
time and energy it would take to fully comprehend the details.
The author did an excellent job focusing on the background of the
discussions about infinity, Cantor's life, and a few mathmaticians that followed
in his footsteps. He explained just enough of infinity math so that the layman
could understand the concepts without getting bogged down in the details.
Feb 14, 2016 rated it it was amazing  ·  review of another edition
an interesting book about the history of math, in particular about cardinal numbers (sizes of infinity) as well as logic. i gave it a five not because it is perfect but because it is a good book for someone looking for an introduction to mathematical analysis. the density of Q and R-Q, sets of measure zero, comparing "infinities", completeness and other topics are not necessarily discussed in depth here, but notions are introduced to allow the reader to move into move advanced topics. not a subs ...more
Oct 20, 2014 rated it did not like it  ·  review of another edition
So much promise in the subject, undone by incoherent organization and a lack of focus.

Cantor went insane, seemingly due to pondering infinities. Godel underwent a similar breakdown for similar reasons. Fascinating! But let's sum that up as an oddity in about one paragraph and move on...

The timeline was muddled. Are we following Cantor or not? What year is it again? We linger over the math theory, yet the application of it, the reason why what we're reading matters, eh, let's just take that as gi
Gregory Mcdonald
I confess I didn't hold out much hope for this book when I began to read it,several years after it came into my possession,but I ended up enjoying it despite my reservations. Much of the math,even "dumbed down" to layman levels by Mr. Aczel was still over my head. But the history of the search for an understanding of infinity,and the connections to such mystic disciplines as Kabbalah really held my interest. I'm a sucker for those seeking ultimate truth. Even if in the end they fall a bit short. ...more
Definitely the most philosophical or mystical of his books I've read so far. Loads about the Kabbalah and how contemplating infinity might drive you mad, like poor Georg Cantor who is featured in the book. I've always found the levels of infinity hard to grasp, but Aczel makes them as transparent as possible. Definitely worth trying to wrap your head around from either a mathematical or a religious perspective, but be warned: you might start to question everything!
Apr 21, 2009 rated it liked it  ·  review of another edition
Shelves: non-fiction
3.5. There's really not very much about the Kabbalah in here. There's a decent amount of math, but honestly, I feel like a lot of space was wasted giving the backgrounds of all the mathematicians mentioned. I didn't really care about that -- I wanted more religion and math stuff! B/c that stuff was really interesting and cool.
Michael Schellman
Mar 24, 2015 rated it really liked it  ·  review of another edition
Reading this book was like watching the movie Pi. I think the story of Cantor's mental breakdown in the pursuit of the concept of infinity is the inspiration for Max Cohen's character. Amir Aczel writes about math in a way that can be appreciated by the non-mathematician. He has several other books. He is definitely going in my list of favorite authors.
Kane Faucher
A few small errors, but in all a fairly accessible text on the beginnings and subsequent development of set theory and Cantor's continuum hypothesis. Does point to some key resources for more sustained study. As an introductory text for non-mathematicians, it frames some of the major issues acceptably.
Jan 24, 2014 rated it really liked it  ·  review of another edition
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.
Will Boncher
Mar 16, 2010 rated it really liked it  ·  review of another edition
Shelves: library
Very fun story about the mathematical development of infinity. The introduction to Kabbalah in the beginning was super interesting, I'll have to look into that more deeply. Great mini-biographies of mathematicians associated.
Apr 20, 2010 rated it really liked it  ·  review of another edition
Shelves: non-fiction
a tour de force through mathematical history. totally accessible to the non-mathematician who also is curious about the history of "infinity" and the people who explored this aspect of mathematics.
Dec 22, 2007 rated it really liked it  ·  review of another edition
was a good read although it did not go indepth..."casual" math reading, if you will. i always gravitate towards the mathematics section in the bookstore (math nerd) and this was a good "light" read while i was doped up on vicodin after i got my wisdom teeth out.
Aug 28, 2012 rated it really liked it  ·  review of another edition
Nice to read some intelligent thoughts on the relation between science and mysticism.
Gail Kennon
could not understand much of it but i'm glad i read it.
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