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119th out of 166 books
—
98 voters
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity
In the late nineteenth century, an extraordinary mathematician languished in an asylum. His life's work on "the continuum problem" would bring us closer than any mathematician before him in helping us understand the nature of infinity. This is the story of Georg Cantor.
Cantor's work, though brilliant, seemed to move in half-steps. The closer he came to the answers he sough
...morePaperback, 258 pages
Published
August 28th 2001
by Washington Square Press
(first published 2000)
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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
Feb 07, 2011
Matthew Daniels
rated it
4 of 5 stars
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
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
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...more
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...more
In The Mystery of the Aleph, Aczel explores the concept of infinity from Pythagoras to Cantor. I wish I could understand all...more
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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 U...more
Side note: When I read this, I had already been intrigued by the complexities of Kabbalah as it figured into U...more
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
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
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...more
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...more
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
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
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.
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.
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.
Jun 13, 2012
K.D. Rose
rated it
5 of 5 stars
Shelves:
cross-cultural-spirituality,
math-that-matters
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.
It depends on how much you are trying to understand. Ultimately, deep study takes you to almost every discipline and science, hard and soft.
Nice to read some intelligent thoughts on the relation between science and mysticism.
It is Aczel what else needs to be said. This is a good book that is a fun read.
Feb 26, 2009
Jason
is currently reading it
Just getting into it. Story of mathematician that was crazy--- or was he?
Impressive, well-researched, easy to follow. Good explanations of the math.
Georg Cantor is worthwhile to learn about; the rest of the book, not so much.
Didn't quite get all of this, but now I understand why ' infinities ' are a problem when the show up ( and the difference between potential and actual infinity )
A surprisingly quick read! I would have liked a little more in-depth info on all the mathy stuff, but I can understand where that might not have been possible. Interesting stuff.
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.
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.
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.
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.
a wonderful book about the search for infinity. Historical, entertaining, and most of all, filled with more math than you can shake a stick at.
The odds of hitting a rational number between 0 and 1 by throwing a dart at the number line are zero.
SV
SV
Aug 28, 2009
Benjamin
rated it
3 of 5 stars
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....more
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....more
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