Proof Positive Sure signs of autumn: The leaves are changing. There's a nip in the air. John Lee Beatty is designing Broadway shows. This year, the set designer kicks off the season with a pair of plays, one from a neophyte and one from the last of the Broadway masters.

First, there's Proof, which opened last May at Manhattan Theatre Club to general acclaim; it transferred to Broadway's Walter Kerr Theatre on October 24. David Auburn's tightly plotted drama centers around Catherine, an eccentric woman in her 20s (Mary-Louise Parker); her father Robert, a famous mathematician with a history of mental illness; Hal, one of Robert's students, and a groundbreaking mathematical proof. To tell more would give away too much; at least twice in Act I, Auburn has arranged dramatic revelations that elicit gasps from the audience. The situation is straight out of The Aspern Papers or The Heiress (the latter memorably designed by Beatty in its Broadway revival); is Hal really attracted Catherine, or is he an academic climber interested in her father's work?

Proof takes place in on the back porch of Robert's house in Chicago; it is, in Beatty's words, "an American porch play" - and he ought to know, having been the king of the genre in his years at Circle Repertory Company, where Lanford Wilson and others specialized in romantic-realism family dramas. "English plays," Beatty says wryly, "are about class. American plays are about real estate."

For this particular piece of theatrical real estate, Beatty exploited the horizontal nature of the MTC stage, creating an extra-wide wooden porch, attached to the rear of a brick house. Parts of the neighboring houses were visible on either side. Also, the kitchen and back hall of Robert's house were visible through the windows. One critic noted that the set's Chicago location was immediately apparent; Beatty agrees, noting that houses there are subject to a "prairie influence. The row houses are built several feet apart, to allow the winds to blow through." Also he says, "They're Chicago bricks." When pressed to identify them, he adds, "You just know them when you see them."

For research, Beatty had a friend photograph various Chicago locations, but adds that, having worked many times at the Goodman Theatre there, he is familiar with the city. However, he says, "The play is a romance," so he removed all extraneous detail (including garbage cans or plastic materials), to give the setting a rather romanticized, almost iconic, look. Because Robert has endured a number of hard times, Beatty says, one major question was, "How rundown should the house be?" adding, "It couldn't be shabby chic." The addition of a layer of autumn leaves on the deck and part of the porch made for an evocative detail, strongly suggesting that Catherine and her father live insulated lives. The rooms behind the windows were heavily dressed - the back hall with its service stairs, he says, was based on similar rooms remembered from his childhood - and helped to suggest the kind of life Catherine and Robert shared there. "There is a private-lives aspect about the play," he notes. Indeed, the audience, like Hal, was left on the outside, peering in, looking for clues to the lives lived there.

Then again, no detail is too minor for Beatty, especially when it comes to supporting the cast. At the request of Mary-Louise Parker, the book containing the mathematical proof is no simple prop - it contains an authentic piece of math theory. (Similarly, this past summer, Beatty designed the Off Broadway drama Spinning Into Butter. The lead character, played by Hope Davis, was a college administrator, and Beatty filled the onstage credenzas with realistic student files.).

Any time a production moves from Manhattan Theatre Club, a designer will be challenged, because there is no other theatre in New York - or in the rest of the world - with similar proportions. The Walter Kerr Theatre has a much taller, shallower stage space, so the set for Proof has been heavily reconfigured. "At the Walter Kerr, you'll see above, to the roof of the house," he says. "You'll see the window of Robert's study, as well. You'll still see houses on either side of the stage, but the set is being rebuilt." What isn't being changed is the set's faintly autumnal quality, its air of sadness that sets the stage for the play's distinctive combination of romance and mystery.

Light years away from the comfortably worn, middle-class world of Proof is The Dinner Party, one of Neil Simon's darker, more probing efforts. The action takes place in the private dining room of a chic Parisian restaurant. Three haute-bourgeois couples - all of them divorced - are mysteriously summoned to a dinner party, then find themselves locked in for the evening. Soon, each relationship is subjected to close examination, revealing a number of unpleasant truths.

Beatty's simple yet stunning design is dominated by a back wall, made up of three panels of Fragonard's Four Seasons of Love, its classical tableaux providing a mocking commentary on the personal disarray of Simon's characters. The designer notes that the play, is "not realistic; it's a little like an Agatha Christie thriller, with its artificially induced encounters." Director John Rando wanted to highlight the play's slightly surreal quality, so Beatty designed a room with no windows, the imposing paintings, a table, chairs, and some additional furniture, and nothing more. The overall look is handsome, airless, and slightly menacing.

More adjustments: The Dinner Party opened at the Mark Taper Forum in Los Angeles, then was restaged at the Kennedy Center in Washington, DC. The former is a circular thrust stage, while the latter is a conventional proscenium house. Thus Beatty says in Los Angeles, he designed "a round room," while for Washington, he compressed his design to fit the shallower space of the Eisenhower Theatre. Now the production is booked into the much deeper Music Box Theatre in New York; he adds, "You could park four cars behind the set."

Although the well-heeled worldlings of The Dinner Party inhabit a world far away from the reclusive intellectuals of Proof, both plays share a certain stylization, and a kind of rueful quality. (In both, characters pick through the past, trying to find out where it all went wrong). For both productions, Beatty has provided designs that, at first glance seem fairly naturalistic, but which, in fact, are carefully calibrated to each play's idiosyncrasies of style.

Proof, which was directed by Daniel Sullivan, opened October 24. It also featured costumes by Jess Goldstein, lighting by Pat Collins, and sound by John Gromada. The original set was designed by Manhattan Theatre Club's scene shop, with the Broadway version featuring additions by Hudson Scenic. The Dinner Party opened October 19. Other designers on the production include Jane Greenwood (costumes), Brian MacDevitt (lighting), and Jon Gottlieb (sound). Scenery was built by F&D Scene Changes, based in Calgary, Alberta.

Typically, Beatty is off and running with a busy season. Next up for him was To Fool the Eye, a new translation of a Jean Anoulih drama, for the Guthrie Theatre, followed by the Alan Ayckbourn fantasy Comic Potential, for Manhattan Theatre Club. In addition, there's Encores!, the annual trio of concert productions of vintage Broadway musicals, at New York's City Center. And, one suspects, there are many more surprises to come before spring is here.