The mystery of the Aleph

M a t h e m a t i c s , t h e K a b b a l a h , a n d t h e s e a r c h f o r i n f i n i t y

by Amir D Aczel

Jonathan Allin

This review is a hopefully more digestible spin-off from the rather lengthy and tortuous review of David Deutch’s “The beginning of infinity” in the Rosh HaShanah magazine. In writing the latter I regularly referred to “The mystery of the Aleph”, and so thought it worth discussing. Amir Aczel was an American-Israeli mathematician. Born in Haifa in 1950, he died in Nîmes, France, in 2015. Aczel’s style is straightforward and approachable. He provides an insight into Kabbalah and its history, and the importance of numbers and of the Ein Sof in Kabbalah. The relationship that’s developed between Kabbalah and Georg Cantor’s work on infinity makes the book especially interesting. There’s a good balance between biography and mathematics: as well as a (not too deep) mathematical insight, the book provides an interesting history of our understanding of numbers and of infinity, from Pythagoras, Rabbi Akiva, Isaac the blind, and other Kabbalists, through Augustine, Kepler, Galileo, Reimann, and Cantor, and then Cantor’s successors such as Zermelo, Gödel, and Paul Cohen. Aczel argues that Cantor had strong Jewish traditions. Although Cantor was a committed and practicing Lutheran, he chose ℵ for infinity explicitly because of his Jewish roots. Aczel quotes Adon Olam, “beli reshit, beli tachlit”, with which Cantor would have been familiar. Cantor came to the conclusion that there was an Absolute because of the impossibility of a set that contains everything. Aczel seems comfortable that Gödel and Cantor both came to believe in the Divine: Cantor explicitly believed in a God who can understand the infinite of the continuum, whilst Gödel, having proved that no system can