When you think mathematician, you may picture geeky guys with broken eyeglass frames and mismatched clothes. Not so if you’re talking about the characters in David Auburn’s math-heavy drama “Proof,” now at Acadia Repertory Theatre in Somesville.

First of all, the central mathematician in the story is Catherine, a 30-year-old depressed woman who has spent much of her life caring for her father, an unstable math genius. The man who courts her is an ambitious math professor who also has a rock band. And her sister Claire is quick enough on her feet to put two and two together and come out with something far more meaningful than four.

That’s not to say that “Proof” doesn’t address the tricky balance popular culture sometimes formulates between math and insanity. (Think: “A Beautiful Mind” and “Pi.”) But Auburn’s 2001 Pulitzer Prize- and Tony Award-winning play allows us to relate to these particular math whizzes in an unconventional way because “Proof” really isn’t about math at all. It’s about algebraic family relations and calculations about love.

To underscore the domestic quality of the play, Auburn sets it entirely on a back porch in Chicago near to the university where Catherine’s father has been a departmental star. It’s always dangerous in Maine summer stock to cast a porch as a “character”; it runs the risk of invoking “On Golden Pond.” But Ken Stack, Acadia Rep’s artistic director, does not allow that to happen. He gives the set an urban neighborhood feel – a couple of outdoor chairs and one from the house, a tray of liquor, the combination of wood siding and faux brick. You can just imagine kids on a basketball court down the street.

What’s really pivotal in this show, however, is casting the right person to play Catherine. On Broadway, Mary Louise Parker shaped the leading lady into a quirky, slightly whiny underachiever whose real work is to keep her “bughouse” father out of a nursing home. Both Anne Heche and Jennifer Jason Leigh stepped into the role, which is undoubtedly one of the most substantial roles written for thirtysomething women in a long time.

Acadia Rep’s Jenny O’Sullivan knows she is in pig heaven on this one, and while she looks slightly older than one might expect for Catherine, she somehow still suggests a teenage quality important to the character. Catherine knows herself. She has shouldered responsibility. But she hasn’t quite grown up, and O’Sullivan finds that resource within herself.

She is surrounded by a cast of winners, including Stack as her father, David Blais as the professor and Liz Robbins as her sister from New York. And because O’Sullivan’s father, longtime “guest” artist Wayne Loui is the director, the show has an even deeper poignancy.

“Proof” is in production at summer stock houses nationwide this year. It is sure to be one of the most popular and thought-provoking shows that Acadia Rep offers this season, too. But don’t worry. It’s not a wonky script. It’s funny and sad, and adds up to an intimate and insightful piece of theater.

Acadia Repertory Theatre will present “Proof” 8:15 p.m. Tuesday-Sunday through July 12 and 2 p.m. July 13 at the Masonic Hall in Somesville. No show on July 4. For reservations, call 244-7260.