Catherine isn’t very nice. She’s snarky, contemptuous, volatile and bitingly sarcastic. She’s not very happy, either. Here she is, on her 25th birthday, drinking alone. Well, not exactly alone. Her father is keeping her company. Her father, a mathematician whose early genius was overtaken by insanity. And who died last week.

That’s why Catherine’s bossy sister, Claire, is coming back to Chicago from New York for the funeral. And that’s why Hal, a former student of their father’s, is in the study upstairs, searching for any sparks of brilliance in the gibberish-filled notebooks he left behind.

Catherine has inherited her father’s gift for math and perhaps, she fears, his insanity. That’s part of the reason people won’t take her seriously as a mathematician—that, and her lack of academic credentials, since she abandoned her education and put her life on hold to care for her crazy dad.

The title of David Auburn’s Proof, now playing at the Majestic Theater, has a double meaning. One is the riddle at the center of the plot, the formal proof of a mathematical theorem that may or may not have been written by Catherine’s father in a rare period of lucidity. But although the play’s second half revolves around that authorship question, its main thrust is the daughter’s struggle to prove herself—her sanity, her independence and her intellectual bona fides.

Proof is a play of ideas—ideas about truth and trust, feeling and knowing. There are moments of high emotion, but the real action takes place within subtly pointed dialogues. In Danny Eaton’s understated production, there’s a physical stillness that belies and underscores the conflict and tension. The mood is enhanced by Greg Trochlil’s setting, the back porch of an old house with glimpses into the interior (like the play itself), Daniel D. Rist’s evocative lighting that dapples the house with the shadows of autumn leaves, and Mitch Chakour’s elegiac incidental music.

Eaton’s quartet of actors also serve the production well; or should I say, the actors in the three supporting roles ably serve the incandescent center of the drama, Amy Prothero as Catherine. A welcome newcomer to the Valley theater, Prothero is almost never offstage and is mesmerizing every second she’s on. Like her Shakespearean namesake, Catherine’s primary weapon is her acid tongue. But Prothero embodies the character’s protean moods in every inch of her wiry frame—now sprawled loose-limbed and insolent in a wicker armchair, now hunched and hunted, a tangle of auburn hair falling across her face, now rigid and wild-eyed with indignation.

The characters of Claire and Hal are essentially foils for Catherine—Claire the self-possessed, officious opposite of her messy sister, Hal an amiable rebuttal of the math-geek stereotype but an academic nonetheless, who dismisses Catherine’s intellectual capacity because of the absence of letters after her name. Dustin Sleight is a convincing Hal, rumpled and self-mocking, a man who recognizes his own limitations in a rarefied field, and Lea Oppedisano is effective, if rather one-note, as stiff, steely Claire. Keith Langsdale gives the scenes with Catherine’s father—two flashbacks in addition to the opening fantasy—a deceptively casual feel wrapped in dry wit.

Proof: The Theater Project at the Majestic Theater, 131 Elm Street, West Springfield, through Feb. 13. 747-7797, www.majestictheater.com.