BY MATTHEW HERBERT

In the early 20th century, the philosopher Bertrand Russell upended the niche of mathematics known as set theory when he came up with the idea of “non-normal sets.” Non-normal sets include themselves as members. Normal sets do not. For example, the set of all integers does not include itself as a member; it only includes integers. It’s a normal set.

But what about the set of all sets that don’t include themselves? Or, more picturesquely, barbers who only shave men who do not shave themselves? A barber meeting this description would indeed shave himself, but only because he does not shave himself, which is the criterion of belonging to his set. You can probably think up your own versions of this idea, which has come to be known as the Russell Paradox.

In 36 Arguments for the Existence of God, an intellectually lively novel by Rebecca Newberger Goldstein, one of the characters is a mathematical child prodigy who, at the age of six, reconstructs Euclid’s proof that there is no largest prime number. He is also plagued by a Russell Paradox in real life.

Azarya is a Hasidic Jew set to inherit the mantle of Rabbi from his father. His sect of a few thousand mystics in upstate New York is blindly and utterly counting on him to be their leader when he reaches adulthood.

But then something happens to the boy as he hits adolescence. With trepidation, he leaves the confines of his closed-off community one week to visit MIT. A professor there with connections to his family has noticed the boy’s genius and wants to show him the woundrous, Platonic realm of pure math that awaits his contemplation if he leaves his sect, which studies only Torah and Talmud.

During the visit to MIT, the boy becomes aware of his own genius and begins to long for the unchained life of the mind he could lead if he would move to Boston. He doesn’t even believe the doctrines that send his kinsmen into swaying, chanting religious reveries are true. His intellect tells him to leave it all behind.

But there is a catch. The people of his sect draw their entire sense of identity from the spark of the divine they believe their Rabbi shines forth. Without the boy as their next guide, the community will collapse. Azarya’s grandfather led this sect, Moses-like, to escape the Holocaust by the skin of their teeth. Can Azarya callously commit them to oblivion by choosing MIT and the pure truths of mathematics?

So what happens when an intellectual is convicted by his genius that he must abandon a life of individual genius? There’s the rub. I won’t tell you how Goldstein resolves it, but I will say this problem spells out the ethos of her novel–the idea that religious doctrines, although plagued by illogic and outright falsehoods, remain a fraught and sometimes even beautiful part of who we are.

Azarya, the troubled genius, is actually only a secondary character in the novel. Goldstein’s protagonist is Cass Seltzer, a professor of psychology who has penned a surprise runaway bestseller The Varieties of Religious Illusion and is about to claim his role as an intellectual celebrity by accepting a position at Harvard.

Seltzer is known, even among his critics, as the atheist with a soul. This is because, despite his official atheism (he does not buy any of the tradtional “evidence” for God’s existence) he understands quite well humankind’s impulse for supernatural thinking and the cognitive illusions that make its artifacts seem plausible. As he befriends Azarya, Goldstein lets us believe Cass may even come to see religious illusion as worthy of trumping the truth in certain circumstances.

On balance, 36 Arguments is a worthy novel. It is not an excellent novel, though. Goldstein gives Cass two paper-thin love interests, who, the reader will see from miles away,  are mere props, destined to give way to a third, a finely developed character who owns Cass’s heart with earthiness, bravado and gusto.

Cass’s towering intellectual mentor is also novelistic failure. A buffoon-scholar who absurdly forces together Schopenauer’s weight and Beethoven’s Sturm und Drang, he is a cutout figure who confirms all the vulgar stereotypes of an over-wrought, risibly self-important nutty professor. Goldstein, who has spent her life among real academics, could have done much better than this. Instead she plays to the crowd.

One area where Goldstein does not play to the crowd is in actually taking a real-life position on the main argument that trundles through her book. Like her protagonist Cass with his book, Goldstein allows herself to append an annex that delivers her real message in short form. It’s all very humane to allow people their religious convictions on liberal grounds, she seems to says in the course of her story, but the cold, hard limits of logic say the arguments adduced for the existence of God are all flawed. Goldstein’s annex is a summary knock-down of the traditional (and some not so traditional) arguments for theism.

Although it does not much bother me that Goldstein’s device is one that lets her have her cake and eat it too, because I take her side in the debate about God, I suspect her critics will not like it. Overall, 36 Arguments is a good novel for those already predisposed to enjoy its subject matter, but I doubt it would engage those who stand to benefit most from its message.