Craig Wallace as Robert and Dawn Ursula as Catherine in David Auburn’s “Proof,” at Olney Theatre through June 18. (Stan Barouh)

With great love can come great obstinacy. This truth reverberates through a scene in Olney Theatre Center’s luminous staging of “Proof.” Outside in the depth of a Chicago winter, a young woman named Catherine is looking at her father, Robert, a brilliant mathematician who suffers from mental illness. She is dressed for the cold, in scarf, hat and polar-vortex-worthy parka; he has wandered into the garden in a T-shirt and pajama bottoms. As Catherine prepares to coax him inside, her tense body language and look of bottled-up foreboding reveal her determination not to patronize him. Also obvious is her dogged resolve to sacrifice her own needs to his.

Dawn Ursula brings out the self-destructive stubbornness of Catherine in this gripping, funny and heart-rending production of David Auburn’s Pulitzer Prize-winning play. Ursula’s Catherine is fragile, sure: A near recluse, she worries that she has inherited her father’s illness. But her vulnerability is entwined with a tenacity that could be her ruin or — if she turns out to possess mathematical genius like her father’s, as seems possible — her salvation.

Ursula’s performance fits like an elegant puzzle piece into director Timothy Douglas’s staging, which does justice to all of the complementary facets of the 2000 play. “Proof” is, after all, a mystery; a love story; an aching family drama; a tasty brew of intellectual allusions; and a meditation on trust, betrayal and all that is unknowable in life.

From left, Biko Eisen-Martin, Aakhu TuahNera Freeman and Dawn Ursula in Olney’s “Proof.” (Stan Barouh)

In the Olney rendition, it also is a seamless ensemble piece. Craig Wallace is riveting as the now-frail, now-jovial, now-cantankerous Robert, a sometime university professor whose assessment of his own “machinery” (as he terms his cerebral process) is built on quicksand. Biko Eisen-Martin lends the story extra sizzle with his seductive portrait of Hal, an affable, brainy and socially bumbling mathematician who has designs on a set of Robert’s old notebooks. Hal turns out to be among a group of mathematics scholars who moonlight in a rock band. We never glimpse this band, but when Catherine grudgingly admires the group’s song about imaginary numbers, we long to hear it, too.

Rounding out the cast, Aakhu TuahNera Freeman deepens the play’s vision with her turn as Catherine’s better-adjusted sister, Claire. Despite her urge to meddle in Catherine’s life, Claire comes across as a remarkably sympathetic, caring and generous person whose perspective on events could be as valid as her sibling’s. It’s impossible to fault her, for instance, when she frets about a confrontation with the police that Catherine has inadvertently instigated. (The account of this episode, early in the play, arguably acquires an extra layer of tension given that this production of “Proof,” with an all-African American cast, takes place in the aftermath of the police-related incidents that have fueled the Black Lives Matter movement.)

Scenic designer Luciana Stecconi’s simple yet poetic set suggests the precariousness of the life that Catherine and Robert have shared: The furniture on the deck outside their home appears to have rusted, and the boards are weather-beaten. But behind the screen of the porch, scrawled equations cover a wall — a stylized visual conceit underscoring the tantalizing mathematical ideas that entrance most of the play’s characters.

Catherine at one point recalls her father striving to write down “beautiful mathematics . . . proofs like music.” Translate that goal into theatrical terms, and you’d envisage a production much like this one.

Proof, by David Auburn. Directed by Timothy Douglas; costumes, Kendra Rai; lighting, Mike Durst; sound and original music, Matthew M. Nielson. About 2 hours and 20 minutes. Tickets: $50-$70. Through June 18 at the Olney Theatre Center, 2001 Olney-Sandy Spring Rd., Olney. Call 301-924-3400 or visit