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.

This was an interesting biography of Cantor and introduction to the concept of transfinite numbers, though I feel that Aczel never made a clear enough connection between Kabbalah and Cantor's work: in particular, it's not clear from anything in the book that Cantor was even aware of Kabbalah, little say of Kabbalah's idea's about infinity.

Aczel weaves together an introduction to kabbalah and transfinite numbers. Largely this is done with the biographies of Georg Cantor and Kurt Gödel. There's a Jewish connection. A God connection. Both pondered infinities into mental instability, it seems. So, this is a safer way to consider the innumerable, the uncountable, and the continuum hypothesis.

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.

The mathematician's stories that are told in the book make it worth the read. It can go a bit too deep into the maths and religion aspect but it was interesting.

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.

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 the math in the book, but I did grasp enough to get the gist of set theory and infinities. I like the idea of some infinities being larger than others. Poor Cantor did spend a lot of time in mental hospitals, but I agree with Jenna Levin, there probably are many factors related to his illness, besides his work. Overall, the whole idea of infinity is a slippery concept.

This book was DEEP, a little above my paygrade! A fascinating premise that math and religion can explore the same topics (e.g. the infinity of God also contains nothingness vs. Set theory/math: an infinite set also contains the empty set.). I really enjoyed the brief side story, synopsis of Gödel's contributions and narratives about his relationship with Einstein. *His logic to the extreme discovered a loophole in the US constitution to allow for a dictator!? Anyways good survey of the history of math & interesting subject.

A finite history of infinities.

From Pythagoreans, the Kabbalah, Galileo, Bolzano, Gauss, Riemann, Weierstrass, to Cantor. From Cantor to Gödel, Zermelo, and the eugenist Bertrand Russel.

Philosophers and mathematicians, some of them utterly entranced by the concept, like moths to the flame. Some of them completely oblivious a world war was tempestuously unravelling around them — that someone is Gödel, who was no longer a part of this dimension, narrowly escaping being drafted in some army, having to cross Siberia to arrive to the US. Like Cantor before him, his mental and physical health were quickly deteriorating, along with his trust for people around him. This is also one of my criticisms, the author goes at length to put an equal sign between studying set theory and developing mental health issues, which only serves to create stigma(s).

The book also talks about the axiom of choice — the statement that a Cartesian product of a collection of non-empty sets is non-empty. Set theory. Any collection of sets, from each containing at least one element it's possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite.

Like infinity(-ies), this book doesn't really know what it is, it doesn't have a linear progression, it doesn't feel planned. It feels like a patchwork, but overall a good patchwork, and I hope people are inspired to read other books as they encounter all the tangents.

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.

This book shows why so many mathematicians went insane trying to explain infinity because it's too complex to wrap one's mind around. Whether contemplating numbers that go on forever or the infinity of numbers between zero and one I don't think the human brain can grasp it.

Just getting into it. Story of mathematician that was crazy--- or was he?