Since winning the Pulitzer Prize in 2001, “Proof” by David Auburn has enjoyed numerous revivals. The desperation of the characters and their dicey relationships make the play a challenge to stage. But the production now running at Act II Playhouse turns Auburn’s script into a gripping show.

“Proof” is an exotic family drama that draws you into the arcane world of creative mathematics. Robert, the family father, was an eminent mathematics genius until mental illness eclipsed his career. Now in old age, he struggles to deny his condition. Played by Scott Langdon, the flickering gleam in Robert’s eyes captures your attention as his manic passions wax and wane.

After Robert’s death, a second tension comes center stage. Hal, a University of Chicago doctoral candidate, discovers an original proof of prime numbers among Robert’s notebooks. Hal refuses to believe Robert’s young daughter, Catherine, could have created this work. The focus shifts, and the word proof takes on a double meaning.

Auburn’s script dramatizes key moments in Catherine’s life to develop a rounded image of her predicament. With this portrayal, Jenna Kuerzi will probably add to her growing list of Barrymore nominations. Catherine is a treacherous role to pull off, because the character is so alienated that she threatens to alienate you. In caring for a doomed father and sacrificing her dreams, Catherine is worn out. She is also wearing.

How can you like someone who greets everyone with snide remarks and exhausted indifference? And yet, Kuerzi pulls it off. The glimpse of radiant joy in Catherine’s brief moments of hopefulness gives sympathetic insight into the character’s standoffish insolence. And, slowly, you come to understand how much Catherine fears she has inherited her father’s insanity along with his talent.

Adam Riggar’s set design is atmospheric. The back porch of a brick house in Chicago with soiled window sills tells you this family has seen better days. And the costume design of Katherine Fritz accents shifts in the characters’ mood and situation. But director Kate Brennan’s cast drives the show.

Adam Howard’s Hal is more than a bland plot necessity. In awe of Robert’s genius, Hal recognizes that he lacks that special spark of creativity. He struggles to accept his fate. Hal thinks he loves Catherine, but he loves mathematics just as much, and Howard makes you feel the character’s tortured earnestness.

Claire, Catherine’s sister, flies in from New York to attend the father’s funeral. Claire wants to help her sister, but does not understand that she feeds into Catherine’s fears of insanity. Claire is potentially an officious nag, but in Megan McDermott’s hands, Claire, too, is likable. You sense she has always suffered from knowing that Catherine was her father’s favorite. When Catherine brutally rebuffs her, Claire leaves in a huff, saying, “You’re the genius, you figure it out.”

Although the play is nonlinear, Auburn’s drama is reminiscent of the 19th-century “Well Made Play” sensibility, in that dramatic segments are cleverly interconnected as they build to a climax. In this approach, if one segment is implausible, the play feels “put together” or, to borrow Catherine’s word for inelegant mathematics, “lumpy.” And you sense you are being gamed.

That has been the fate of some “Proof” revivals. But not here. Director Brennan makes the most of each dramatic opportunity. The production is not dependent on a meticulous plot because the cast brings authenticity and depth to each character. No one is weak or dishonorable. The true nemesis in “Proof” is fate, and you feel the decency of each character’s yearning.

Act II Players is located at 56 E. Butler Pike in Ambler. “Proof” will run through March 1. Tickets are available at 215-654-0200 or online at act2.org.