When I took a course on the study of the Kabbalah back in college, this book was one of the required reading materials. At the time, we only covered parts of it, but I loved the entire connection between the Kabbalah and mathematics, and hoped to read through the whole thing at some point.

Unfortunately, my perspective towards math has become much more favorable since then. I say "unfortunate" because although this book helped me become less intimidated and more interested with the field of mathematics, it didn't wow me as much as it did in the past. Moreover, the Kabbalah connection is very loosely connected -- not only is it not mentioned much more in the book after the first couple of chapters, but it's based upon a conjecture on the depths of Cantor's heritage. It might just be my own perception, but it doesn't seem like the theme holds together very well, and at points the timeframe of when important people are described seems to jump all over the place.

What I disliked the most, however, was Aczel's occasional insinuation that the pursuit of infinity "caused" the decline in mental health of several key figures. This bothers me because it makes it sound like there were no other root causes. While Aczel does note other things (particularly Cantor's antagonists, who made efforts to discredit his views), and while I understand how it's impossible to get into neurochemistry and psychopathology considering how the figures are historical, it becomes annoying when there is no other theories presented about how a person with mental illness might have been so motivated to research these concepts.

Still, maybe time will again make me look at this book in a different light. The subjects that aren't relating to mathematics (history, psychology, philosophy, religion) are all there but don't come together. What does come together is what kept me reading this book: the math (which was easy for me back then to understand) and the passion behind mathematics. So I can't recommend this book to everyone, but if you grew up thinking math was boring or difficult or intimidating (not that the concept of infinity is NOT difficult or intimidating)... maybe this will help you fall in love, just like it happened with me. ( )

This is my third book by Aczel, preceded (in reading order) by The Riddle of the Compass and Pendulum. I found this one to be the weakest of the three, which is odd since Aczel has multiple degrees in mathematics and has lectured on the subject at several top universities.

Mystery of the Aleph traces the concept of infinity from its first stirrings in Greek antiquity, through early efforts at defining it both as a mathematical concept and as a metaphor for God (the Kabbalah connection), and into the life of Georg Cantor and his successors who turned the study of infinity into a concrete mathematical exercise.

I think that perhaps Aczel, being a mathematician, was too close to the subject matter and I found many of the mathematical explanations a bit sparse. I also did not care for the over-emphasis on the descent into madness of both Cantor and Gödel while working on transfinite set theory. It reminded me of similar stories surrounding thermodynamics and the depression of Boltzmann and others. Repeat after me: sometimes people with bipolar disorder, schizophrenia, or other mental illnesses have jobs in math or science, but the study of hard or esoteric math problems does not cause or trigger mental illness. ( )

18 February 2001
The Mystery of the Aleph
Amir D. Aczel

This is largely a discussion of Georg Cantor and infinite set theory. There is a brief introductory chapter on the Kabala, with some notion to link the mystical and meditative texts with the discovery of the infinite God through meditation. Meditation on the infinite, the Ein Sof of the Kabbalah, was reputed to be dangerous, and could not be safely done by everyone. The mathematical concept of infinity was extended by Cantor in the 19th century, and the author implies that this mathematician's struggles with the concept was the cause of his depression and madness. Cantor was in and out of a Nervenklinik for the last 30 years of his life, and developed an obsession that Francis Bacon wrote Shakespeare's plays, while studying the continuum problem, the problem of how much greater the infinity of the continuum is than the inifinity of countable numbers. The author makes much the same mystical claim to explain Kurt Godel's later madness as well, since Gödel also worked on problems of infinite dimension ( )

If you're looking for much connection to Kabbalah, you won't find it. According to Aczel, Cantor was a Frankist. However, Aczel's book is like low-hanging entertainment fruit for us nerdy types....and we like him for that. ( )

A quite readable history of the transfinite numbers. Appropriately emphasizes Georg Cantor and the Continuum Hypothesis (which claims there is no infinite cardinal between the number of integers and the number of reals). Mischievously suggests that anyone (e.g. Cantor, Gödel) who thinks too hard about the CH is bound to go mad.