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"In the late 19th century, a brilliant mathematician languished in an asylum. His greatest accomplishment, the result of a series of leaps of insight, was his pioneering understanding of the nature of infinity. This is the story of Georg Cantor: how he came to his theories and the reverberations of his work, the consequences of which shape our world." "Cantor's theory of the infinite is famous for its many seeming contradictions: for example, we can prove there are as many points on a line one inch long as on a line one mile long; we can also prove that in all time there are as many years as there are days. According to Cantor, infinite sets are equal." "The mind-twisting, deeply philosophical work of Cantor has its roots in ancient Greek mathematics and Jewish numerology as found in the mystical work known as the Kabbalah. Cantor used the term aleph - the first letter of the Hebrew alphabet, with all its attendant divine associations - to refer to the mysterious number which is the sum of positive integers. It is not the last positive number, because ... there is no last. It is the ultimate number that is always being approached: just as, for example, there is no last fraction before the number 1"--Jacket.… (more)
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Mystery of the Aleph
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.
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.