In one of his routines, Steve Martin notes that there's a convention of plumbers in town, many of whom have come to the show, so he's worked up a joke especially for them, which begins, "This lawn supervisor was out on a sprinkler maintenance job and he started working on a Findlay sprinkler head with a Langstrom 7 gangly wrench."

Why, you're wondering, would I bring this up in a review of Ethan Canin's new novel, "A Doubter's Almanac"?

Because this book is a 550-page immersion in expertise, and it raises the question: How much do you have to know about what a character knows to understand his story?

The expertise in this case is mathematics (not "math," which makes these characters cringe), and everyone of any significance in the book is a mathematical genius or an acolyte at the altar of mathematics.

The first half of the novel is the story of Milo Andret, a brilliant oddball and loner from the Midwest who solves the Malosz conjecture (a made-up problem on par with Fermat's last theorem or the Riemann hypothesis) (I guess), wins the Fields Medal (mathematics' analog to the Nobel Prize) and briefly holds an endowed chair at Princeton University before his tenuous hold on what others might call normal life gives way to drink and a sort of madness that makes mathematical genius look like a personality disorder.

The second part of the book is narrated by Milo's son Hans, who also turns out to have fashioned the third-person first half — and it is about Milo, too, because, well, he's the story: his own, his early lover's, his early lover's lover's, his wife's, his children's, his grandchildren's. He is a quite horrible person, but fascinating — and tormented enough to merit some sympathy, if not nearly as much as everyone accords him.

In his mind, Hans tells us, "all the other academic disciplines — including the physical sciences … were irrevocably tainted by their debt to substance."

And this is where the genius of Ethan Canin's storytelling lies — negotiating that space between pure thought and substance where all of us have to find a way to live.

What we might not get, from mathematics applied or pure, is no small thing, he concedes in a roundabout way, because what's best in the book is far from abstract.

Watching his daughter (next mathematical genius!) admiring the undulating carpet of lily pads on a slow stretch of river, Hans remarks: "The feeling is much like the joy of mathematics itself, the original secret of the guild: that the miracle of the universe can be worshipped without actually witnessing the divine."

But that's not a guild secret, is it?

"Were these plumbers supposed to be here this show?"

Ellen Akins is a writer and book critic in Wisconsin.