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At 27, Catherine is already worried about turning into her parents. “I think I’m like my dad,” she says. “I’m afraid I’m like my dad.” She’s not talking about a tendency to be critical or scavenge the refrigerator late at night, though: Her father, a brilliant mathematician at the University of Chicago, is also mentally ill.

In Proof’s opening scene, Dad—aka Robert (Anthony Hopkins)—reassures Catherine (Gwyneth Paltrow) that she’s just fine. “Crazy people don’t sit around asking if they’re nuts,” he says. Catherine buys this for a minute—it’s her birthday, after all, and her father and his bottle of cheap champagne constitute her midnight celebration. But then she points out that it’s not a sound argument, because Robert is sitting around discussing the topic despite the fact that’s he’s clearly certifiable himself. He concedes to her logic, then counters, “Yes, but I’m also dead.”

At this, Catherine’s face falls, and already Paltrow is doing a better job playing a woman on the verge than she did in 2003’s Sylvia. Perhaps it was the pressure of representing a beloved literary giant, because whereas Paltrow’s Sylvia Plath was stiff and ridiculous, her Catherine is petulant, defensive, desperate, and generally cracked. And when she gets a little love—and relief from the family and professors who also doubt her prospects—she’s radiant.

The fact that Paltrow had experience playing Catherine onstage in London couldn’t have hurt. Proof, directed by Shakespeare in Love’s John Madden, is an adaptation of the Pulitzer Prize– and Tony Award– winning 2000 play by David Auburn. He co-wrote the screenplay with Rebecca Miller (The Ballad of Jack and Rose), and the engrossing story about trust and love and family remains the same: Catherine’s been her father’s caretaker for the past five years. After his death, she must contend with a former student, Hal (Jake Gyllenhaal), who wants to dig through Robert’s 103 notebooks of nonsense in the hope of finding something publishable, as well as with her sister, Claire (Hope Davis), a well-put-together sort who’s come in from New York to sell the house and drag the surely batty Catherine back with her.

The opening scene’s not the last we see of Robert. Madden relies on flashbacks to illustrate the way Catherine became so angry (at the people who show up for his funeral but were never around when he was sick) and so uncertain (of her own mind and abilities, provoked by her dad’s frequent reminders that he’d done his best work by her age). Woven through these scenes are hints about Proof’s central question, unresolved until the end: After Catherine decides to trust Hal, she gives him the key to a desk drawer that holds what he was looking for—a remarkable proof that will rock the math world. Hal’s beside himself, as is Claire, but they’re really thrown for a loop when Catherine tells them that Robert didn’t write it—she did. Neither believes her, and it’d be difficult to prove the authorship either way.

Paltrow’s impressive performance is matched by those of her co-stars. Davis is friendly but crisp as Claire, appropriately straddling the responsible/irritating caretaker line even though, as written, her character veers toward a knee-jerk assessment of Catherine as completely delusional. Gyllenhaal has standout moments, notably his pained expression during an impromptu eulogy by Catherine and the tricky way Hal, in love with Catherine, agrees with Claire that she couldn’t have written the proof but keeps backpedaling in an attempt to preserve his personal interest. Hopkins, too, gives a sprightly performance, his Robert energized by talk of work and numbers even though he’s no longer as sharp as he thinks he is.

Auburn and Miller’s script is, of course, full of sadness and angst. But there’s cheerfulness—and humor—here, as well. Nerds will love the way Catherine, Hal, and Robert convivially approach nearly every conversation with cold logic instead of meaningless small talk, and the really nerdy nerds will snort at math jokes such as a song called “i,” during which Hal’s band stands silent for three minutes. (The imaginary performance, naturally, represents the imaginary number of the song’s title.) And Catherine keeps up her sarcasm throughout, especially when everyone around her is failing to point out the obvious. It’s one indication that although she may be damaged, she’ll probably be all right. Even if Catherine doesn’t quite believe it, Paltrow makes sure we do.

Moviegoers who prefer sheer wackiness to math jokes should have a fine old time with Everything Is Illuminated, writer-director Liev Schreiber’s adaptation of Jonathan Safran Foer’s best-selling novel about a young man researching his family’s past. At least until its second half, when the film turns solemn with whiplash abruptness.

But I suppose that’s what happens when you try to meld humor with the Holocaust. Foer’s ballyhooed debut, heralded by some while pronounced unreadable by others, juggles stories-within-a-story. But Schreiber extracted only the main plot, which focuses on an American Jew, also cutely named Jonathan Safran Foer, who visits the Ukraine in an attempt to locate a woman who appears in an old picture with his grandfather, whose life she might have saved. Jonathan (Elijah Wood) retains the services of Heritage Tours for his trip, an agency that turns out to be Alex (Eugene Hutz), a bling- and track-suit-wearing college kid who’s obsessed with American culture, and his grandfather (Boris Leskin), a cranky codger who thinks he’s blind and therefore has a—sigh—“seeing-eye bitch” named Sammy Davis Jr. Jr. Grandpa drives.

Schreiber packs his film with as much tired affectedness as Foer’s book, if not more. Klezmer plays incessantly, and Alex’s thickly accented, “comically” malapropian English (“Girls want to get carnal with me, because I’m such a premium dancer”) serves as irksome narration. There’s also a giant, mean waitress who appears when the tourist attempts to order vegetarian food, and, of course, several cuts to Sammy Davis Jr. Jr., who for the entirety of the trip is actually outfitted with a shirt announcing the dog’s status as a—ugh, don’t make me say it again.

Amid all the yuk-a-minute daffiness, Jonathan is as impassive as wallpaper. Always in a black suit, Wood wears big, heavy-framed glasses thick enough to grotesquely magnify his eyes, and his skin is pale and pancake-smooth. Jonathan barely reacts to his sometimes-boorish traveling companions, timidly submitting to their company even though he’s terrified of dogs. In short, he’s infuriating. And after a while, he’s even more infuriating than Alex: It seems an impossible feat, but Hutz, leader of a “gypsy punk band,” eventually transforms his character from a caricature to someone with goofy warm-heartedness and good intentions. He may kinda mean it when he tells the waitress, “Please, this American is deranged” as he tries to order a potato for Jonathan, but his pleading works. Even his cracked English is funny once in a while, though Schreiber ruins one of Alex and Jonathan’s livelier conversations—“I’ve heard of this John Holmes. He has a premium penis!”—with a shot of the damn dog.

Once the trio find the shtetl where Jonathan’s grandfather once lived, the klezmer turns poignant and the car rides get quiet. But from that point, very little is illuminated, really, especially not to an audience unfamiliar with the book. There are flashbacks to executions, sometimes through Alex’s grandfather’s eyes. A lovely elderly woman (Laryssa Lauret) figures into the finale, and there’s a curious but interesting hint of the magical realism that’s more prominent in the book. There are some revelations, and everyone is touched. If you can survive wacky-foreigner jokes, dog jokes, old-man jokes, Sammy Davis Jr. jokes, klezmer, and the Holocaust, you might be, too.CP