21 April 2010

Logicomix

Logicomix by Apostolos Doxiadis and Christos Papadimitriou is a beautiful graphic novel about math history.

Yes, you read that correctly. Comic book about math.

The story centers around Bertrand Russell's experiences around the turn of the last century, as he and other thinkers tried to formalize all of mathematics— to identify a self-consistent foundation of axioms on top of which all of the rest of mathematics could be derived.

Frege, Hilbert, Wittgenstein, Gödel, and other famous names make appearances in the book. I found the auxiliary characters to be somewhat unmemorable, and the retelling of their stories has been greatly subject to poetic license anyway. What I enjoyed about this book is the fact that it painted such a vivid picture of the early 20th century mathematical zeitgeist. (The graphic novel is an excellent medium for this.) Hilbert and others had great optimism that mathematics could be formalized in such a way that it was consistent, complete, and decidable. In such a world, every well-defined statement about mathematics could be decided one way or the other in a mechanical way. That idea, and its natural extensions— that there could be an arbiter of truth for all factual statements, or even moral statements— were tantalizing to many. (Too tantalizing, apparently, as many of the mathematicians working on this problem really went unhinged.)

Yet, that hope was smashed when Kurt Gödel published his incompleteness theorems, in which he showed, among other things, that there would always be statements that could never be resolved (either proven, or their logical negations proven) within arithmetic or any extension of it. These fundamental limitations on the power of mathematics came as a shock to many. Von Neumann reportedly said, "it's all over," when he learned of Gödel's result. It was the death of a long-standing dream.

The authors manage to tell this whole story with a minimum of jargon, and they even turn the depressing conclusion around with a cute moral. All told this is no small feat.

Logicomix is not a math textbook but a drama. It has limited depth (justifiably so). But it's a neat idea and well executed. It is a worthwhile read (especially considering how short it is).

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