无论是对无穷的坚信还是对整数的迷恋，其实数学家们对于自己信念所保持的执着大概与修道院中埋首经书的修士们无异。我想他们的信念大约来自某种超验，但当他们试图用逻辑证明这种不知其来处的信仰时，有时会成功，有时大概只会被自己的执着拖入癫狂吧。不过全书卡巴拉的部分不多，数学内容的翻译不够好，希望有更好的版本吧。

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', with the added marginalia "but only 10 are used because.....?" Not one to take the word of an unknown commentator I did the math. To find the number of permutations of a word take the factorial of n, denoted by n!, where n is the number of letters in the word; in this case 4! = 24. In the case of duplicate letters (there are two of the letter H), which would result in duplicate permutations, divide the permutation by the factorial of the number of letters that are identical. 4! / 2! = 12 is the correct answer! The previous reader's question is a good one. Dr. Aczel makes much of the importance of the number ten and indeed the Sefirot, the subject at hand, is composed of ten Sefira or divine qualities. Either he misunderstood the relationship between the permutations of YHVH and the Sefirot or there is none. I was left puzzled. Mysticism is a difficult enough subject for one who prefers reason over the supernatural.

Nice to read some intelligent thoughts on the relation between science and mysticism.

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.

The misleading subtitle probably is largely responsible for the poor reviews, though the early chapters that jump around quite a bit do it no favors. Overall, I enjoyed it as a easy-reading history of mathematics with specific focus on infinity and set theory, and brief biographies of Georg Cantor and Kurt Godel. To fully realize the promise of the the subtitle, it would've needed far more content exploring the historical intersection of mysticism and mathematics.

This book is challenging to read. It begins innocuously enough with a discussion of Pythagoras before branching out to the Jewish mysticism of the Kabbalah. Significant attention is devoted to the distinction between the Sefirot and the notion of the (infinite) n  Ein Sof n that lies behind them.

The book then proceeds to present the lives and interests of many great scientists (Galileo, Riemann, Cantor, Gödel, and others) who have explored the notion of infinity. A huge amount of attention is given to the life of Georg Cantor, whose job and sanity were both negatively impacted by his work on differing degrees of infinity(s). It is interesting to note that Gödel also suffered challenges to his mental health while working on infinity.

The latter part of the book is difficult to follow. It is fairly easy to conceptualize the idea of a 'countable' number of points along a line, but the idea that the infinity of 'countable' points in the both dimensions of a plane is of the same order as that of a line gets difficult indeed. The mathematics of this section gets pretty challenging. Understanding the Continuum Hypothesis and why and how it matters is a challenge as well!

One thing I find interesting are the parallels between the Sefiroth and Ein Sof and the Ten Thousand Things and the Tao of Chinese mysticism. The universality and unapproach-ability of the Ein Sof and the Tao as radiant sources of God or the Mother are very much aligned.

In general this is a book about people who have glimpsed the infinite. Specifically it's about Gregor Cantor.
The most exciting part to me was explicitly linking Gregor Cantor to his Jewish roots and from thence to the Kabbalah and the study of the infinite.
The book also explored the connection between the study of the infinite and mental health. Both Cantor and Kurt godel were plagued with mental health problems especially in their later life after they had studied the Continuum problem extensively.

This was the third time I've read this book, and I thoroughly enjoyed it once again. Set theory was my favorite class while I was studying computing science at the Eindhoven University of Technology many years ago, and it's great to revisit this subject every now and then. The relationship between formal mathematical set theory and Jewish esoterism is not worked out well in this book, though. It should either have been scrapped, or given more attention, supported by deeper research. I found it intriguing to be reminded that Georg Cantor is one of several authors who believe that Francis Bacon is the real author of the works of Shakespeare. I would love to find out more about his involvement in this. I have a small volume by Manly P. Hall called Francis Bacon: The Concealed Poet in my library, which tries to demonstrate the same proposition.

Georg Cantor, a Jewish mathematician, drove himself mad attempting to understand infinity. However, in doing so, he developed a new branch of mathematics we know as Set theory.

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 )

Excellent!

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.