Math is everywhere: medicine, sports, banking, gambling, National Security Agency espionage.

And then there’s science, which has adopted math as the preferred method of description for life, nonlife and the entire physical universe. Math does a decent enough job at this to inspire wonder among physicists about why it works so well. The answer isn’t obvious, but Tegmark thinks he knows: It’s because reality *is* math. In fact, he contends, all mathematical structures are real. The internal reality of human perceptions is merely a pale approximation of the true external reality embodied in one of those mathematical structures.

It’s fascinating speculation, presented engagingly. But it’s unfortunately more than 200 pages into the book before he actually begins to discuss his point. The first half of the book is a semiautobiographical crash course in modern cosmology, of which Tegmark is a prominent practitioner. And the last chapter veers into a rant about ways human civilization could self-destruct, having virtually nothing to do with the rest of the book at all.

Tegmark’s case is not entirely convincing. To believe, you need to accept the “block universe” view of spacetime, in which time and change are illusions because all spacetime already exists, just sitting there. He further requires doing away with infinity, as math with infinities is subject to the Gödel undecidability theorem, which demonstrates that mathematical systems of sufficient complexity cannot be completely consistent. So in some way the “real” underlying mathematical reality must somehow be simpler than most of the math that scientists actually use.

Of course, the math now in use hasn’t succeeded in answering all of science’s big questions either. So perhaps it will turn out that there’s a sense in which Tegmark is right about all this. But if so, he’s a century ahead of his time. Or three or four.

*Knopf, $30*

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