Children, cover your ears. John Allen Paulos's latest book, A Mathematician Plays the Stock Market, tells the sorry tale of a normally hardheaded, hard-science kind of guy slithering down the road to perdition after "falling disastrously in love." Paulos confesses to being the love slave not of a sultry siren, but of a sizzling stock. His "illicit affair" with WorldCom ran from early 2000 until the spring of 2002.

It's a misery-loves-company saga for anyone burned by the tech bubble. Before he was smitten, Paulos, a professor at Temple University in Philadelphia, mostly stuck with index funds because he believed "stock movements were entirely random and that trying to outsmart dice was a fool's errand." He sent himself on that errand when he bought WorldCom at $47. He then "averaged down," buying more as the price declined, even when it dipped below $5. He bought on margin to magnify his position; he bought call options in hopes of making up for earlier losses. He warns wittily about the psychological foibles that bedevil investors, including "confirmation bias," which had him searching for any crumb of good news about WorldCom (even in seamy Internet chat rooms).

While Paulos's financial bath runs throughout the text, this is largely a vehicle for his exploration of "the basic conceptual mathematics of the market." Paulos dissects different approaches to stock picking and offers his take on each: "If the movement of stock prices is random or near-random, then the tools of technical analysis are nothing more than comforting blather."

Below average? Paulos is at his best when explaining that although numbers may not lie, they can easily mislead. Assume, for example, that half of all initial public offerings (IPOs) increase in value 80% during their first week of trading, and the other half fall 60%. Buying and selling an IPO each week would result in an average gain of 10% a week and would turn a $10,000 investment into $1.4 million in one year.

But, the good professor explains, half the investors trying this strategy would wind up with less than $1.95 at the end of the year. The average return is skewed high by the lucky few. It's not evened out by the unlucky many because while they can lose everything, they can't lose more than $10,000 each. That's why a majority of investors receive worse-than-average returns.

Paulos is a fine writer, but this book isn't easy going. How could it be? He's trying to explain how Nobel prize- winners and lesser souls try to use betas, Sharpe ratios and even fractals to get a leg up on the market. Paulos offers plenty of explanations to bring you along, as well as the occasional brainteaser. Consider the three businessmen who pay $30 for a booth at a convention. When the manager realizes he's overcharged them, he asks a bellhop to return $5. Unable to evenly divide the five-spot, the bellhop gives each man a buck and pockets $2 for himself. Later he wonders, if each man has $9 and he has $2, what happened to the extra dollar?

If you are for an instant bamboozled by the question, Paulos asks, how on earth do you hope to understand the accounting intricacies that go into judging the true value of a stock?

Paulos learned the hard way that it's hard to beat the market. His book uses wit and humor--and a lot of numbers--to show just how hard it is.