As the book progresses, however, Mr. Paulos’s writing becomes increasingly technical and increasingly jokey, and his reasoning becomes more and more difficult for the nonmathematician to follow. His repudiation of the ontological argument for the existence of God, for instance, is based on a reductive, paper-tiger summation of the argument itself: God is “the greatest and most perfect possible being;” this “most perfect being must possess all characteristics of perfection”; and “since it’s better to exist than not to exist, existence is a characteristic of perfection.” Hence, “God exists by definition.”

Similarly, Mr. Paulos’s argument that “doubt that God exists is almost banal in comparison to the more radical doubt” that people “exist, at least as anything more than nominal, marginally integrated entities having convenient labels like Myrtle and Oscar” is hardly persuasive. After all, how many readers who aren’t college students having stoned, late-night conversations want to debate whether or not they exist themselves?

As for Mr. Paulos’s discussion of the contradictions involved in a deity being both omnipotent and benevolent, it consists of little more than regurgitation of the Epicurus aphorism to the effect that if God is willing to prevent evil but unable to, then he is not omnipotent; that if he is able to but unwilling, then he is malevolent; and that if he is both able and willing to prevent evil, then there is no explanation for evil’s continued existence.

Although Mr. Paulos begins “Irreligion” by promising that he will not use any hard-to-follow scientific formulas to make his case, he soon leads the reader deep into the mathematical wilderness by talking about things like the “Boolean satisfiability problem” and “combinatorial identities” and posing annoying paradoxes that do little but remind the reader of the ordeal of taking SATs. (“What is the smallest number of guests who need be present so that it will be certain that at least three of them will know each other or at least three of them will be strangers to each other?”)

In the course of this volume Mr. Paulos does provide some interesting asides about the so-called “confirmation bias, a psychological tendency to seek confirmation rather than disconfirmation of any hypothesis we’ve adopted, however tentatively” (which would seem to have applications to the Bush administration’s use of intelligence in the prelude to the Iraq war). And he also does an entertaining job of applying probability theory to people’s talk about miracles and amazing coincidences, which they’ve taken as evidence of the existence of God.

Still, there is something perfunctory and hurried about all of Mr. Paulos’s arguments, which will be shrugged off by anyone who has made the leap of faith into belief, and which will seem obvious to anyone who is already a proud heathen. Indeed, the reader finishes this volume with the suspicion that it was a rushed and cursory project, turned out quickly in an effort to catch the coattails of Messrs. Hitchens, Dawkins and Harris.