FATHER-DAUGHTER TIES: Catherine (Kristen Bush) and her father Robert (Michael Siberry) struggle with problems of mathematics, insanity, and affection in McCarter Theatre’s production of David Auburn’s 2001 Pulitzer Prize-winning “Proof,” running at McCarter’s Berlind Theatre, 91 University Place through October 6. (Photo by Richard — Termine)

How do you make a play about mathematicians and a mathematical proof comprehensible and interesting to a general audience? Ask David Auburn the playwright and Emily Mann the director of McCarter Theatre’s exhilarating current production of Mr. Auburn’s 2001 Pulitzer and Tony winner, Proof.

The “proof’ of the title refers most directly to an apparent groundbreaking proof of a mathematical theorem, and that proof is discovered near the end of the first of two acts. But the meaning of the title expands to the question of whether the young protagonist Catherine, inheritor of her father Robert’s genius as well as his mental instability, can prove that she, not her deceased father, actually devised and wrote that proof.

At the same time, Catherine is seeking proof of the affections of Hal, young math professor and protégé of her father; proof of her sister’s questionable intentions; and proof of her own ability to overcome her depression, doubts and fears, so she can move beyond her father’s death.

So, despite initial appearances, Proof, turns out to be more about human relationships than about mathematics, and the engrossing dialogue, even when mathematicians are talking about mathematics, is accessible and engaging.

This intellectual drama, seasoned with a rich dose of warm, entertaining humor, may provoke thought and discussion about frighteningly close connections between genius and insanity, and it may instigate further provocative commentary on the scarcity of women at the higher levels of mathematics. But the most important issues of this play, the ones that lay claim most dynamically to the audience’s attention and emotional engagement, focus on the 25-year-old Catherine — her relationship with her recently deceased father, her growing affection for Hal, and her bitter clashes with her successful, domineering, sister Claire.

Proof, originally at the Manhattan Theatre Club for five months in 2000, then on Broadway for more than two years, with Mary-Louise Parker and Larry Bryggman in the starring roles, before becoming a 2005 movie with Gwyneth Paltrow and Anthony Hopkins, is most essentially the story of Catherine’s coming of age.

Played here with great sensitivity, fragility, and charm by Kristen Bush, Catherine battles with depression, deepened by the death of her father, whose caretaker she has been during his long period of mental instability. She becomes edgy, defensive, even paranoid, alternately angry, suspicious, distraught, then loving and hopeful. Her body language speaks volumes as she wraps herself in her father’s too-large sweater or folds herself up, hunched over in a large chair. Her face glows with love and sadness as she confronts and comforts her father. Her eyes sparkle with laughter and hope as she emerges from her cocoon in connecting with Hal. She bristles with bitter sarcasm in her rancorous quarrels with her sister. The dialogue is spot-on credible, and the characters are richly sympathetic, believable, and appealing.

The action of the play spans a period of about one week, starting from the night before the funeral of Catherine’s father (Michael Siberry), but in nine scenes the play skillfully interweaves the present-day narrative with episodes involving Catherine and her father from the past and from Catherine’s imagination. The play itself is artfully, carefully crafted to make the most of each secret that is revealed, each revelation and twist in the plot, and Ms. Mann’s direction perfectly complements the high-suspense plotting and the fascinating development of characters and relationships. The result is a moving, memorable human drama — funny, touching, and powerful in its impact, especially perhaps for mathematicians, but also for anyone who can reflect on a relationship with father, daughter, lover, or sibling.

The plot here does seem thin, but the suspense is genuine and gripping. Hal (Michael Braun), with dual motivations, encroaches on Catherine’s world. He hopes to find valuable work in the 103 notebooks that Robert left behind and also he is starting to fall in love with Catherine.

Catherine’s older sister Claire (Jessica Dickey) has flown in for the funeral from New York, where she works as a Wall Street currency analyst. A pragmatist and successful businesswoman, she is a striking contrast to her late father and sister. Claire wastes no time in announcing that she’s selling the house and proposing her plans for her troubled sister to move to New York and seek psychiatric help.

As the romance between Catherine and Hal develops, along with conflict between the two sisters, Catherine directs Hal to the notebook containing the historic, earth-shattering proof. The handwriting looks like Robert’s, but he had done no new creative work since his 20s, when the creative spark faded and the madness began to set in. Suspense rises, as the mystery deepens and, in a stunning act-one curtain line, Catherine claims that she wrote the brilliant, barrier-breaking proof.

Mr. Siberry is consistently convincing as the rumpled, white-haired University of Chicago genius mathematics professor. He is funny in his irascible impatience and eccentricity; endearing and sympathetic in his loss of contact with reality and his deeply loving relationship with his self-sacrificing mathematician daughter.

Mr. Braun, the source of many of the witty math jokes in the play, is credible, both as a young, earnest mathematician, with a winning humility and self-awareness, and also as a viable love interest for Catherine.

As the antagonist sister, interloper from another world, trying, it seems, to do the right thing, Ms. Dickey provides a strong voice of “normality” and a formidable obstacle for Catherine to battle as she strives to shape her own life.

Eugene Lee’s inspired set design combines realism with surrealism: a beautifully specific, large, realistic Chicago back porch in early fall is surrounded on the upstage wall by a huge blackboard full of advanced mathematical problems and equations. Thoroughly in-character costumes by Jennifer von Mayrhauser and nuanced lighting by Stephen Strawbridge enhance the realistic effect and help to fully create the world of this play, while Mark Bennett’s creative sound design highlights the drama and supports the varied tone of the proceedings.

Ms. Mann, whose own father was a University of Chicago professor, has directed with loving care, attention to detail, and uncanny ability to highlight the most important moments in the relationships of these four characters and to bring out the rich humanity in this entertaining and emotionally satisfying tale of mathematicians, madness and love.