The next Public Theater play has an appropriately enigmatic title, "A Number."

What number?

That's one of its questions, as you'd expect of mercurial, masterful playwright, Caryl Churchill.

"A Number" is a taut, 65-minute face-off between two men, a father and son -- or rather two sons, or maybe more, the product of cloning. Father and sons were played in London by Michael Gambon and Daniel Craig and in New York by Sam Shepard and Dallas Roberts, so you know they're juicy parts. In Pittsburgh they're being played by Sam Tsoutsouvas, a crusty, vigorous actor of great integrity who has appeared here at Public, City and PICT, and Craig Baldwin, who like Tsoutsouvas has many classical credits.

The director is Jesse Berger, back for his third mainstage Public assignment, following "I Am My Own Wife" and "Life X 3," which marks him as Ted Pappas' current favorite to direct the edgier contemporary works in the Public spectrum.

But like his actors, Berger has a taste for classic plays and their demanding language. He is the founding artistic director of the Red Bull Theater, an off-off-Broadway company for which he has directed difficult plays by Shakespeare, Middleton and Marlowe. So it seems fitting that he calls "A Number," "in some ways the first classic play of the 21st century."

Berger's first Public assignment, in 2002, was to direct "The Laramie Project" for its Young Company. Then, the Post-Gazette preview quoted Hamlet's lines about how actors are "the abstracts and brief chronicles of the time" and how plays "hold, as 'twere, the mirror up to nature, to show virtue her own feature, scorn her own image, and the very age and body of the time [its] form and pressure."

That certainly fits the spare, disquieting "A Number." But we might cite another famous Hamlet line, "What a piece of work is a man! ... And yet, to me, what is this quintessence of dust?"

That's what "A Number" asks. But it does so with a shrewd and engrossing parable that is part chilling mystery, part black comedy, part family tragedy -- and a challenge for actors and audience. It's such a challenge, in fact, that the New York production left the basic plot somewhat obscure.

Berger intends otherwise, promising a "conscious effort to make it clear without being obvious." He says that's his job as a director and he relishes the challenge:

"This is a play I wanted to direct -- fascinating, heart-breaking, funny, strange. Caryl Churchill is so attractive to grapple with, her language is so specific, not a word wasted. ... It leaves so much to the director, actor and designers [as it] reaches toward the big questions of human existence."

Previous productions have used very minimal sets, practically blank spaces. But the Public's designs by Beowulf Boritt, Scott Zielinski and Zach Moore will be more elaborate, reflecting the content of the play, Berger hopes, without providing more information than Churchill, with great care, doles out to the audience slowly, to increase tension and discovery.

This basically small play turns out to be "remarkably rewarding the deeper you go into it." It confronts the enigma of identity and issues of ethics, responsibility, nature-nurture, predestination-free will, guilt and the face-off between science and morality.

In London, "A Number" was clearly English in characters and place. But here, it will be clearly American, because Berger is using the New York text, for which Churchill Americanized perhaps a dozen specifically British words or phrases. And although in London it seemed to be set in the near future, Berger says his production could well be taking place right now, possibly even in Pittsburgh.

One of the dozen or so best playwrights currently working in the English language, Churchill has been represented on Pittsburgh stages in the past decade or so by "Vinegar Tom," "Serious Money," "Top Girls," "The Skriker" and "Cloud Nine." Her only previous play at the Public was one of its all-time edgy bests, "Mad Forest" in 1993.

Although born in New York, Berger was raised in Oregon, giving him what he calls the "bi-coastal psychology of city folks transplanted to the woods." He fell in love with theater at the Oregon Shakespeare Festival and knew he wanted to be a director ever since his teacher let him take over his fifth grade classroom during recess to put on skits.

He went to college at Southern Utah University, which means he started his training at the Tony-winning Utah Shakespearean Festival, then had choice directing internships at the Guthrie Theatre in Minneapolis and Shakespeare's Globe in London. After three years as assistant director under Michael Kahn at the Shakespeare Theatre in Washington, D.C., he went freelance.

Now, he thinks of the Public as "an artistic home -- each time I come back it's more of a home." And it's a home where he can do plays he doesn't yet get to do in New York.

For a key to "A Number," Berger suggests another, simpler quotation from "Hamlet" -- the play's modest opening lines:

"Who's there?"

"Nay, answer me; stand, and unfold yourself."

Ay, there's the rub. "Unfold yourself" indeed!