In Andy Griffith’s Mayberry, the familial porch is an idyllic haven; a place for pickin’ and grinnin’, sharing fatherly wisdom with Opie, courting Miss Crump on the old porch swing, indulging in grateful repose after Aunt Bee’s fine cooking. On the face of it, that Mayberry porch is light years away from the broken down Chicago porch where David Auburn’s Proof unfolds, yet these are both homely places, where important family business gets done.

The family business in Proof is mathematics, a business which has left its mark on the entire clan beginning with Robert (Bill Terranova), whose legacy includes an enviable clutch of brilliant mathematical proofs and two infinitely more complicated daughters, Catherine (Charley Boyd) and Claire (Tara Denton).

Auburn’s exhilarating drama centers on the authorship of a remarkable new mathematical proof, a mystery which steadily exposes each character’s tolerance for uncertainty. It’s fertile soil for exploring the intersection of genius and psychological instability, but we also see, in full bloom, the garden varieties of madness: greed, ambition, love. And hovering over it all like a threatening cloud is the notion that once the imaginative breakthroughs of youth are past, the incandescent mind steadily retreats into a dimly remembered glow. “At 28,” says grad student Hal (Joshua Keller), “you may as well be teaching high school.”

In fact, we learn that all of Robert’s exceptional achievements — proofs and daughters — occurred in his 20s, after which his life gradually tumbled into the spiral of another sort of math: bad, crazy days outnumbering the good. In the final years of her father’s life, Catherine alone has acted as caretaker and confidante of this genius beset by mental illness, forfeiting in the process her academic career and much of her self-esteem. Significantly, we first meet Catherine on the eve of her father’s funeral — and her own 25th birthday.

If Catherine finds herself tormented amid the sudden isolation of an empty house, the arrival of her sister, full of breathlessly delivered plans, merely adds to her pain and uncertainty. Catherine is her father’s daughter in mathematical prowess and emotional disarray. Claire, however, suffers none of her father and sister’s cognitive fuzziness — or their intuitive imagination. A currency trader in New York City, Claire’s principal obsession is timing. Her father’s death, she says, “happened at a good time.” Her upcoming marriage is the logical product of good timing in the career-life equation. Hyper-efficient and linear, Denton’s Claire is the sort who could spot microbial dust bunnies clinging to the underside of an Indy car while remaining apathetic to the thrill of the race.

Catherine is a compelling jumble: an emotional mess with a razor-sharp tongue, an intellectual thoroughbred who gets most of her exercise sprinting 10 yards ahead of a conversation and blurting out precisely whichever uncomfortable truth is being left unsaid, by turns intimidating those around her and noisily crumpling into her own insecurities, Boyd’s Catherine is a young woman everyone wants to rescue but who desperately needs to find her own salvation. To date, her life hasn’t opened many doors for that kind of self discovery. In flashbacks, we see Robert struggling with Catherine’s desire for freedom. Terranova makes a compelling case for the power of Robert’s love for his daughter: fighting for her potential in the face of his own deterioration while showing us how difficult it can be to pass the torch.

Stepping into the fray as Catherine’s erstwhile love interest, Keller’s Hal comes across as the most ambitious character of the lot. Grad student and worshipper at the temple of Robert, looking for the life equivalent of mathematical elegance and beauty, his indecision and dithering nearly cost him everything. Keller accurately renders his character’s hesitant, if steadfast, affection for Catherine and his conflicted loyalties.

Boyd’s Catherine and Denton’s Claire match up beautifully and their scenes are among the most gripping. While Boyd’s role demands the greatest emotional range, Denton’s sharp edges provide just the right amount of provocation to sell the audience on the sibling’s long, complex history. They are a joy to watch.

Midtown/Sheri Grace Productions’s Proof is a taut blend of psychological thriller and family drama. Director Jo Ellen Aspinwall maintains a pace which allows the drama to pull off this delicate balance while never denying her cast the time they need to build the emotional force upon which all this depends. As a result, this porch turns out to be a great place to spend some time.