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27 March 2009

Book Review: The Mystery of the Aleph

I am a sucker for a good math book. No, not the calculus book you had to buy in college--I'm not referring to that. I suppose I might more properly say that I'm a sucker for a good book about math history. My first exposure to this genre came in high school when I read Asimov on Numbers. I was not aware then that Asimov wrote non-fiction, but at that point (I was 17, a senior) I barely had time to be aware of the mandatory reading assignments I was given (thank you, Milton, Ibsen and Faulkner).

So it started, and I've read a great number of math books since. A few weeks ago I picked up The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity by Amir D. Aczel. It is about the mathematicians who have studied infinity and the continuum. Infinity is one of those mathematical concepts that, as a beginner, one thinks he has his head around until he is taught a few advanced concepts. And then, of course, one realizes he knows almost nothing and it is difficult to trust what you already think you know.

The book focuses mostly on work done by Georg Cantor and Kurt Gödel, and explains how each lost his sanity during the course of trying to prove different properties related to the continuum hypothesis. While never able to prove or disprove the continuum hypothesis, each man ended up making valuable contributions to mathematics. Other disciplines too: as a computer science major I remember learning about how Gödel was able to prove that some problems are not solvable in a given system.

For the most part, I enjoyed this book. The math, when presented is covered in terms most non-math types can understand. There are helpful diagrams that serve to illustrate and clarify difficult points and concepts. I've read other works by the author and this book is about what I expected.

Something I didn't care for was the tendency to bring religion into the story where it didn't really fit. I couldn't see the point of dwelling on Cantors Jewish heritage. It didn't help the story and almost made me wonder if the author was trying to say "look, Jews have made important contributions to mathematics!" Big deal. The only group of people who haven't made important contributions to mathematics are the eskimos, and they're too busy to care.

So, if you want to learn about how our perception of infinity has changed over the years, go read this book. It's not bad.

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