"Amir D. Aczel … serves as an expert guide on Cantor's voyages to the far reaches of abstraction. Aczel's story is a poignant one.…" — The Sciences

"… In assessing Cantor's achievement as the first to probe infinity with mathematical rigor, Aczel demonstrates the same gift for interpeting complex concepts which he previously demonstrated in God's Equation, about Einstein's pioneering work in cosmology. And as in his book on Einstein, Aczel penetrates to the human mind behind the formulas, detailing the personal frustrations and professional conflicts that drove Cantor into mental collapse. Aczel also uncovers the uncanny ways in which Cantor's life foreshadowed that of his more famous successor, Godel, who was attracted to the same problems and doomed to the same descent into madness. An indispensable book for anyone interested in the darker side of intellectual progress." — Booklist (starred review)

"Compact and fascinating.… [Aczel's] biographical armatures, his clean prose and his asides about Jewish mysticism keep his book reader-friendly. It's a good introduction to an amazing and sometimes baffling set of problems, suited to readers interested in math — even, or especially, if they lack training." — Publishers Weekly (8/21/00)

Towards the end of the 19th century, one of the most brilliant mathematicians in history languished in an asylum. His greatest accomplishment, the result of a series of extraordinary leaps of insight, was his pioneering understanding of the nature of infinity.

The Mystery of the Aleph is the story of Georg Cantor, who died in the Halle Nervenklinik in 1918: how he came to his theories and the reverberations of his pioneering work, the consequences of which will shape our world for the foreseeable future. While the inspiration for Cantor's genius lies in the very origins of mathematics, its meaning is still being interpreted. Only in 1947 did Kurt Godel prove that Cantor's Continuum Hypothesis is independent of the rest of mathematics — and that the foundations of mathematics itself are therefore shaky.

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 mindtwisting, 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.

Amir D. Aczel, Ph.D., is the author of God's Equation: Einstein, Relativity and the Expanding Universe, Fermat's Last Theorem, and several other books. His work has been translated into Turkish, Hebrew, French, German, Italian, Chinese, and Spanish. A Visiting Professor at Brandeis University, he lives in Massachusetts.