I don’t know if I would classify David Auburn’s play Proof – which had its first production in 2000, and won a Pulitzer Prize in 2001 – a “classic”: it’s a bit young to have earned that distinction. But it is a very well-written drama about family, loyalty, trust, love, and mental fragility (all staples of classic drama), so I suppose it makes sense that a company that calls itself Pittsburgh Classic Players would be drawn to produce it.

The action of the play is set on the back porch of the Chicago home of mathemetician Robert (David Maslow), recently deceased, and his equally mathematically-gifted daughter Catherine (Harper York). Robert had been a genius superstar in his field as a young adult, but fell victim to mental illness in his later years; for the past four years, Catherine has been tending to him full-time while he became increasingly disconnected from reality. Now he’s gone, and she’s not only at loose ends about what comes next, but also fearful that she may have inherited his madness along with his math genius.

Also at the house is the genial Hal (Christopher Cattell), one of Robert’s former students, who is sorting through the 103 identical notebooks filled with nonsensical scribblings that Robert left behind, on the chance that in a lucid moment Robert might have cracked some knotty math problem.

The play’s fourth character is Catherine’s older sister, Claire (Alison Weisgall), in town for their father’s funeral. Less mathematically gifted than Catherine, she is proportionately more socially ept and financially secure. She has her own concerns about Catherine’s psychological well-being, and wants Catherine to move back to New York with her so that she can keep a closer eye on her.

The play is a cross between a family drama, a psychological suspense story, and a romance. The first act traces the conflict between the sisters over Catherine’s future as well as a budding attraction between Hal and Catherine; the second examines the fallout when both Hal and Claire refuse to believe Catherine’s assertion that she is the author of a groundbreaking mathematical proof that Hal finds in one of Robert’s desk drawers (in a notebook identical to the ones Robert used). This betrayal of trust breaks Catherine, sending her into a days-long depressive episode that vindicates Claire’s conviction that she can’t take care of herself.

Much of the play’s impact derives from the subtle way Auburn destabilizes our perception of Catherine’s psychological stability: it’s hard to know whose assessment to trust from moment to moment. We only get brief flashes of Catherine’s fragility, and York’s strong and stable physicality as an actor throws additional doubt on Claire’s characterization of her sister as weak and unstable. Weisgall is excellent at conveying the walking on eggshells apprehension that characterizes being around someone who is “bughouse” (Robert’s name for his illness), and as the action unspools her character looks less and less like Catherine’s antagonist and more and more like the one person who really understands how much support Catherine needs.

Jonathan Visser has directed the production with an actor’s attention to the relationships and conflicts between the characters. The production design is spare but serviceable; an echo-y room makes some of the dialogue difficult to hear, but the story is otherwise crafted with clarity and cogency. The play’s primary themes, revolving around the question of what constitutes “proof” in the realms of love, family, and the inner workings of the mind, ring through with resonance.