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A review by mateitudor
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity by Amir D. Aczel
4.0
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.
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.