The Monty Hall Problem by Jason Rosenhouse

Since I saw this book was mentioned on Jason Kottke's blog I anxiously awaited its release. Having majored in math in college, I always enjoy books that are for the general public with mathematical themes. This one is about one of the most contentious math problems in recent history.

The problem goes like this: you are on a game show faced with three doors, one of which contains a car. You choose a door, the host (Monty Hall) opens one of the other doors to reveal that it is empty. At this point in the game, should you stick with your original choice or should you switch to the other closed door? The answer (you should switch) is not intuitive, and as Parade Magazine's Marilyn vos Savant found out after writing a column on the topic in 1990, has caused many heated arguments among the top mathematicians.

Rosenhouse's book traces the history of this problem, covering the earliest known mention of it, several variations on it whose solutions are equally non-intuitive, and including various mathematical proofs for how to solve it. While the reviews claim that it has very little math in it, I think that's misleading - I enjoyed the math, but it was hardcore. Having just attended a reunion for a math-oriented summer program I attended 20+ years ago, I was jonesing for some math, but for the average reader this might be too much.

However, there was plenty of reading that was not focused on math - Rosenhouse also spends several chapters surveying the literature on cognitive and philosophical ideas around the problem. Cognitive scientists seek to figure out why it is so unintuitive - after seeing the Bayesian proof for the answer I was struck by the same question. Studies have been done that indicate that this lack of intuition crosses cultural and linguistic borders. Rosenhouse even spends a few pages on quantum mechanics, suggesting how this problem might help us understand those concepts better.

My only disappointment with this book was that there was some lackadaisical editing - a few of the math sections had inconsistencies that I found distracting though they didn't impact the math. That aside, I really enjoyed reading it and hope Rosenhouse chooses to address some other math problems with similar books in the future.