But can you prove it?

Proof. Proof of a mathematical hypothesis. Proof of love. Proof that you are what you appear to be. Proof that what you say is straightforward. Proof that what you say is not straightforward but ironic/sarcastic. Proof that intuitive forces exist. Proof that you are mad. Proof that you are sane.

These are the things that David Auburn’s Proof, masterfully directed by Cynthia Lammel and opening this week at Chico State’s Harlen Adams Theater, is about. It’s a tough, challenging play (especially in a large hall). Like a tight, psychological drama by Henrik Ibsen, Proof is actor-intense, with only four characters: Robert, an aging, formerly brilliant University of Chicago mathematician (played by Joel Rogers), his psychologically fragile daughter Catherine (played by Hannah Knight), Catherine’s bitchy, shallowly self-important sister Claire (played by Denice Burbach) and Robert’s former student and Catherine’s would-be lover Hal (played by Rich Matli).

For characters like these, caught up in a series of intense confrontations, the actors must—to borrow one of the play’s frequently used terms—be good. And they are. Joel Rogers plays the somewhat addled father to perfection, while Denise Burbach does just fine with the less intelligent of the two sisters trying to defend her dignity and choices. The other two roles are more difficult because they are more complex. Rich Matli’s Hal is at once a failed mathematician (mathematicians are over the hill by 25), a stumbling lover, a likable geek and a not-very-likable doubter (of himself, of others). But Matli, who at first seems a bit young, grows into his role and does just fine.

The linchpin, of course, is Catherine, who is a psychological mess—guilty about her relationship with her father, ambivalent about her sister and her boyfriend, intellectually brilliant but too quick-witted for her own good, torn between the behaviors the world seems to expect and her own deeper intuitions. Displaying all these different personalities lies in Hannah Knight’s able hands, and she delivers quite splendidly. Watching these actors work is the chief joy of the production.

The set, designed by Jaye Beetem, is also splendid—an open, typically Chicago middle-class brick house like many I (a Chicago lover) have visited over the years.

And, again, Proof employs other Ibsen tricks. Every scene is a confrontation between two people, each of whom enters the confrontation determined to win the argument. Watching these verbal confrontations and seeing who really does win (and at what cost) is intriguing stuff. And then there’s that final Ibsen device of ending a scene with a sudden revelation. “Oh my God!” you say, and the stage goes dark.

Perhaps, following the mathematical nature of Proof, the most central of these revelations can be put in the form of a simple equation. A : B :: B : C. That is to say, A is to B as B is to C. Or character A is to character B as character B is to Character C. Or the Killer is to the Psychologically Vulnerable as the Psychologically Vulnerable-turned-Killer is to another Psychologically Vulnerable. Or Claire (whom we recognize as a killer from the start) is to Catherine as Catherine (whom we fail to recognize as the killer she considers herself to be) is to her mentally unbalanced father Robert.

This revelation is held off until late in the play, and it deepens Proof's insights into human relationships immensely. Go see it. Test its hypotheses. See if it offers what its title promises—proof.