“Proof,” David Auburn’s second full-length play, began its journey in a workshop production at Manhattan Theatre Club. Soon after, it made its way to Broadway, where it became the longest running straight play in 20 years. Auburn garnered much acclaim for his torturous tale, winning both the Tony Award and Pulitzer Prize.

That being said, director Wendy Goldberg and her cast had their work cut out for them to shed fresh light on the already well-received play. To do so, Goldberg engaged in discourse with the playwright to explore the inner workings of his complicated mind.

“Proof” follows approximately a week in the life of a young woman named Catherine who has just lost her mathematically brilliant but mentally ill father. Having spent the formative years of her life caring for him until his death, Catherine finds herself at a crossroads on her 25th birthday.

“She has the enormous burden of having potentially inherited her father’s illness as well as his talent, and of not knowing if the two are inextricable or not,” Auburn has said about Catherine. This pressure is compounded with the addition of a well-intentioned but overbearing sister and a developing relationship with one of her father’s prot?g?s.

“Proof” is not the first show to tackle the illusive topic of insanity, being preceded by plays such as “One Flew Over the Cuckoo’s Nest,” “‘Night Mother,” and “A Streetcar Named Desire.” However, Auburn is quite innovative in his approach to the correlation between brilliance and insanity. His play is riddled with misleading dialogue that causes the viewer to question the reliability of the speakers, namely Catherine and her father, Robert. But it is not all smoke and mirrors. The meat of the play is found in the time-reliant banter and dry wit distinctive to each of the four characters.

It became clear that the production team was trying something new when I saw the cover of the program had bypassed the traditional portrait of Catherine’s face for a more Picasso-like visage, and the distinctions don’t end there.

Michael Brown’s set design pairs the original production’s back porch setting with a collage of overtly “meaningful” images. The beauty of Auburn’s play is in its subtlety, so the prime numbers rimming the proscenium and lighted box of strewn composition books only serve as a distraction. Perhaps commenting on the intelligence of the Arena Stage audience, Goldberg and Brown have made strong efforts to clearly portray Catherine as a confused individual.

In a conversation with Auburn, printed in the play’s Performance Journal, Goldberg makes it clear that she understands the idiosyncrasies of the playwright’s script. But Goldberg’s vision is a bit overstated, a common problem among young, zealous directors. I found myself longing to put the pieces together myself, instead of having them assembled for me.

Such direction shows up again in Keira Naughton’s portrayal of the enigmatic Catherine. Though her line delivery is well timed and her intense moments are well acted, Naughton fails to perceive the subtle variety of Catherine’s different moods. Faced with so much pressure, the character responds with a dry, often sedated wit. This is intended to build to an emotional meltdown, but Naughton’s performance techniques foreshadow this conclusion from the beginning.

Next to Naughton’s high level of nervous intensity, Barnaby Carpenter’s Hal is a sigh of relief, proving to be the most endearing of characters. Hal takes on the role of Robert’s 28-year-old student-turned-math professor who fears his best work is in the past.

Another strong presence on the stage is that of Michael Rudko as Robert. In one of the play’s crucial flashback scenes, Rudko masterfully navigates the varying levels of a man whose mind is slowly deteriorating. As Catherine reads Robert’s nonsensical proof, the audience feels the painful transition from pride to realization and, eventually, to complete despair.

Susan Lynskey, as Catherine’s pushy sister Claire, gets off to a slow start. Lynskey’s interpretation of her character is at first more of a caricature, but eventually she becomes comfortable in the part. Though the audience is arguably expected to sympathize with Catherine, by the time Claire storms out for the final time, Lynskey has truly established the frustration and suffering of financially supporting a family from 700 miles away.

“Proof” is so dangerously complex and well written that neither the actors nor the director could ever upstage it. In the end, the audience members’ minds are left reeling over Catherine’s plight.