Is Gwyneth Paltrow a Genius?

If X is the amount of actual mathematics in a given movie, then X was pretty close to zero in Proof, the Hollywood version of the Pulitzer Prize winning play about mathematical genius, according to three math graduate students who attended its premier Friday in New York City.

Still, the budding mathematicians found conversation fodder in the movie, in which Catherine, played by Gwyneth Paltrow, is the daughter of Robert, a once revolutionary mathematician who just died, leaving Catherine with to-be-determined portions of both his genius and his madness.

After Robert dies, one of his grad students, Hal, played by Jake Gyllenhaal, sets to rummaging through his 103 notebooks to see if anything worth publishing made its way onto paper as Robert descended into insanity. Hal, at 28, is already thoroughly convinced that the window for his own chance of a paradigm-shifting idea closed years ago. "I like teaching," he says, as a form of concession.

"That’s pretty much true” for theoretical math, commented Alex Kontorovich, 25, a fourth-year grad student studying analytic number theory at Columbia University and one of the students who agreed to view and comment on the film for this article. “You can only really change the field when you’re young and still forming your concept of how it looks.” Kontorovich said that, in the past, there has been a saying among math students: “If you get a teaching award before tenure, you’re screwed,” because you’ve actually taken time from research to talk to students.

In the film, we get the idea that Robert was obviously obsessed with his work, but must have reached out enough that Hal “loved” him.

“I meet my adviser once a week for an hour or two, and I’ve been to dinner,” said Sam Stechmann, 24, a third-year studying the applied math of atmospheric science at New York University. Still, he agreed it wouldn’t be all that strange for a student or colleague to sift through papers left behind for quality work. Kontorovich said he definitely knows of students who have developed close relationships with peculiar profs. He recalled a fellow student whose adviser was “pretty eccentric, and never publishes,” he said. One day the student showed up for a meeting, and the adviser had tickets to Argentina in hand for a meeting with another mathematician.

Hal apparently spent enough time at Robert’s place that, with Robert gone, he is ready to pounce not only on his notebooks, all filled with gibberish, but also on his daughter. Hal, who describes himself and his friends as math grad students who “get laid surprisingly often,” doesn’t seem to mind Gwyneth’s Ramen Noodle coiffure.

“That definitely happens,” said Shilpa Khatri, 24, a third-year applied math grad student studying computational fluid dynamics at NYU, referring to the hair, not the romance. “When you have an idea and get excited, you’re like, ‘Oh, I haven’t showered or eaten,’” said Khatri, who also happens to be Stechmann’s girlfriend. All three agreed that the pace of work alluded to in the movie, nil at some points and frantically inspired at others, resembles real life. At one point, inspiration strikes and Catherine’s hand freezes as she reaches for a jar of Mayo, the only food in her refrigerator. “Ideas come at weird times,” Stechmann said. Added Kontorovich, “most of my work, I do on the can.”

Hal is less inspired than Catherine and more entrenched in academic culture. He thinks his own research is lame, and tries to tantalize Catherine with tales of the “partying, drinking, drugs, papers, lectures” that are math conferences. At a conference, “somebody whose work you admire might invite you to their room,” Kontorovich said. “It’s not a raging party, but there are 20 people in there doing random drugs and this old guy who proved a theorem in 1964 hitting on a grad student.”

The allusion to math conferences may have been realistic, but what about Paltrow’s portrayal of a math wunderkind? “It sounded like she mastered several fields,” said Stechmann, an applied math student. “It’s kind of unreal to do that reading books by yourself.” But Kontorovich, a theoretical math student, disagreed. “I don’t think so,” he said. “When you’re entering, you don’t know what’s hard.”

Catherine’s math education came mostly from books and her father, who was proud she went into math, and, in flashbacks in the film, enthusiastically proposes working on problems when Catherine can’t sleep. Kontorovich’s mother and brother are mathematicians. He said his mother didn’t pressure him, but, like Robert, gave the occasional nudge. “When we were driving to Great Adventure she would say, ‘You can go on the Scream Machine if you solve this,’” Kontorovich recalled.

At one point, a glancing allusion is made to the idea that Catherine’s genius might be less likely because she is a woman. “There’s definitely a lack of women in the field,” Khatri said. “There’s a lower bar in the sense that you’re trying to get them into the department. But there’s no prejudice against giving me work,” she added. “And there are women in the field that are just as good as men.”

Beside the fact that math professors in the movie wear ties -- “never,” said Kontorovich  -- and “there are no blackboards,” noted Stechmann – who laughed when Hal called a proof “hip,” – the aspect of the movie the students found strangest was that it centered on an argument over whether Catherine could have done a certain bit of mathematics that she kept secret for years. Kontorovich said keeping work under wraps to stop “the hype from taking over,” is not unexpected, but as to the continued arguing, “Are you retarded?” Kontorovich asked. “It’s a proof. Go through it.” All three students agreed that mathophiles would be more focused on examining the work than debating the author. “Everyone was happy when [ Andrew Wiles] proved Fermat's Last Theorem," even though many had labored unsuccessfully, Kontorovich said. “It was a proof for humanity.” Added Stechmann, “people said, ‘Great, we can stop working on it now.’”

While Kontorovich “was like, ‘Right on,’” when the movie mentioned, “ Siegel Zero,” a term from analytic number theory, don’t expect his life to be imitating this art. One show-stopping moment, literally, came when Hal’s band plays “i,” – for “imaginary number” –  in which they just stand silent. Kontorovich is in a band,  but said he doesn’t plan on covering “i.” “I don’t think we have the chops for that.”