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(proof)

Assistant professor Matt Foss succeeds on both counts with Proof, David Auburn’s quietly seismic exploration of mental health, family dysfunction, and mathematics, here paced like a Tennessee Williams pageant with its thick reservoir of yearning.

Auburn’s deftly constructed play pivots between the present and past in its setting on the back porch of a ramshackle Chicago home. Catherine (Aneesah S. Taalib-Deen) awaits the arrival of her big sister Claire (Sarena Jackson), a New York currency trader. They will bury their father the next day, and go through the motions of sisterly affection, each wary of the other’s end game.

As the play opens Catherine is celebrating her 25th birthday with the ghost of her late father, Robert (Bill Quinlan). He was a brilliant mathematician whom she nursed through the final five years of his life when dementia was his closest companion.

We learn that Catherine left school to care for her father, but Robert’s ghost — alternately charming and insufferable — insists she now pick up his unfinished work. She was always good with numbers.

It’s Robert’s work that propels the plot forward, as his gawky graduate assistant Hal (Austin T. Rambo) arrives, determined to find some lost gem among his professor’s notebooks. Catherine is suspicious of his every move, yet lonely enough to avail herself to the possibilities his presence suggests.

That, of course, is the drawing room aspect of things, but playwright Auburn is after larger truths here than whether love can spring from unexpected places. Claire’s arrival signals a tonal shift, as she attempts to take control of her father’s legacy and Catherine’s life. It’s the big sister syndrome, fueled by the guilt of having fled Chicago to build her own successful career.

The play takes its title from the document in which mathematicians lay out the formula by which they solve a complicated problem. The right proof can shake up the entire field.

And entire lives, as this compelling drama frames it, since Catherine has not only inherited her father’s brilliance, but quite possibly his mental illness. Claire wants to usher her little sister east to a bevy of doctors. Hal wants Catherine to stay and become the woman her father imagined.

A play about math and love may sound odd, but it works precisely because both have a propensity for rational and irrational traits. The key development arrives at the end of the first act with the discovery of a notebook filled with a brilliant equation. How could Robert have written this revelatory material in his condition — and when?

The first 10 minutes of this production unfold a bit tepidly, but there’s much to admire in what follows, starting with Daniel Thobias’ compact, minimalist set and Ryan Peters-Hieber sound design. Both transport us without being intrusive.