David Auburn’s “Proof” has been a crowd-pleaser for several seasons, with good reason. The play, set in Chicago, has received a sterling production by Emily Mann at McCarter Theatre in Princeton.

It seems that Robert is a retired and respected mathematics professor at the University of Chicago. His daughter, Catherine, has apparently inherited some of his brilliance. But now, she is at home with her father, caring for him during the last stages of Alzheimer’s.

The tables are turned when her sister, Claire, arrives for their father’s funeral. She pressures Catherine to move to New York and give up the family home. A former student of Robert’s, Hal, has been sorting through notebooks and papers in Robert’s study. When he stumbles across a notebook with amazing calculations and “proof” of a brilliant mathematical solution, the plot takes on another dimension. Hal is caught up in this revelation and fascinated by the implications for his fellow mathematicians.

To a degree, the plot goes back and forth in time, but those shifts help explain the current status. It’s quite intriguing that the mother is never mentioned.

The cast is superb in this taut, funny and very human story of family angst. Kristen Bush as Catherine perfectly projects the guarded, protective younger sister, very much a loner but still craving some sort of relationship.  Jessica Dickey as her older sister, Claire, takes on the know-it-all, controlling role, even though she was never there for their father. (She was too busy with her career in New York.) Hal, played by Michael Braun, has been in awe of his college professor and hopes to gain new insights through befriending Catherine. Michael Siberry plays Robert with a certain bravura that covers up his slipping sense of reality.

There are plenty of amusing lines to offset the grim reality of these changing lives. Robert’s riffs on pasta versus spaghetti are especially entertaining. Catherine has little use for her older sister’s plans, especially when she’s pressured to move to New York,  and you can see the tension build between the two of them.

Eugene Lee has designed a comfortable, shabby back porch of their house on Chicago South Side, not far from the university. On the walls are scattered all kinds of mathematical equations and numbers, further distilling Robert’s obsession. Mark Bennett’s sound design interjects mood music at just the right places and Stephen Strawbridge’s lighting helps us feel that we’re living in this old, decaying house.

There’s much to ponder, and much to enjoy, in this study of family dynamics and relationships. “Proof” continues through Oct. 6. For tickets, call (609) 258-8787 or visit mccarter.org.