I DON'T think Jesse Eisenberg and I will be friends on Facebook. This is a shame. It would be meta to chat to the man who played Mark Zuckerberg in The Social Network on said social network, but, well, he was tricksy. A great, wired actor, one of the best of his generation, but an exhausting interviewee, as if every exchange is a battle he has to win.

After our time, I'm in the lunchroom when he bumps into a colleague of his, who asks if he is in character. "I'm playing the character of myself," he replies. "It's a part I was born for, but it's still sapping." It seems he even tires himself out, like a hamster on a wheel.

It's early May in New Orleans. Outside, the weather is terrible. Local kids are tweeting about hurricanes and tourists scream with every crack of thunder. I meet Eisenberg in the late morning, on the top floor of a chintzy hotel just outside the city's gorgeous, bustling French Quarter. There's an indeterminate bang. "Whoa," he yelps, before sitting down and sticking a toothpick in his mouth. His hair is long and curly. He's wearing jeans and a long-sleeved dark green T-shirt, one arm rolled up, one down.

I tell him I have flown in from London. "Congratulations." I say I saw his new film, Now You See Me, that morning, and am watching The Great Gatsby later on. "At least you're enjoying the city, rather than sitting in a movie theatre all day."

Talking to him is like sparring with a man who speaks as fast and smart in life as he does on screen. Blend his Oscar-nominated turn as the awkward billionaire Zuckerberg - "Did I adequately answer your condescending question?" - with the attitude he has as a magician in his new role - "First rule of magic: always be the smartest person in the room" - and you have the actual man.

His is a delivery whirring to keep up with his thoughts. "I have a good joke, but I can't think of an appropriate reference," he says when I tell him a Louisiana cabbie mistook me for Daniel Radcliffe. There follows an exchange about "cultural perception", Namibia and Hulk Hogan, which peters out when he thinks I haven't understood.

Now You See Me is fun. It's the glossiest, slickest, biggest movie he has been in ("Sure"), a movie for people who want to watch a superb cast practising big-stage magic in a plot written with sleight of hand. The story is Robin Hood, set in post-Katrina New Orleans. Top of the bill is Eisenberg, as "the greatest magician in the world", J. Daniel Atlas, part of a glitzy team that also fields a mind-reader (Woody Harrelson), an escapologist (Isla Fisher) and a boy who bends spoons (Dave Franco). Mark Ruffalo, Michael Caine, Morgan Freeman and Melanie Laurent fill out the pack.

He says the cast attracted him to the film by Louis Leterrier, director of the Clash of the Titans remake. They make it a success. Sometimes, he says, acting can get lost in all the "long days and complicated camera shots". Not here. The leads have 15 Oscar nominations between them, and even the support - such as character actor Michael Kelly - grabs attention. He was in House of Cards, David Fincher's political thriller for Netflix. Fincher directed The Social Network. Eisenberg looks interested when I mention this. He's enthusiastic. "How's that show?" he asks. Great, I reply, saying I watched it all in one weekend. "Sounds like an exciting few hours."

Eisenberg was born in New York in October 1983, a brother between two sisters. His mother was a clown and his father became a professor. He still lives in the city with his girlfriend, Anna, whom he has been dating since "before I was in any movie". The surname comes from eastern Europe, which his family left during World War I to join his great-grandfather Sam, who fled in 1915 to avoid being drafted into the Polish army and ended up working at the Streit's matzo factory, on Manhattan's Lower East Side.

"Which is where we filmed some of this movie," says the great-grandson, of the place where they made Passover bread. "Which was strange because I felt I was getting paid a lot of money to be in a movie in the room where my great-grandfather was probably working for a terrible wage to bring his family over from Poland."

This history inspires him. I tell him about my own Jewish grandfather, who fled Vienna in 1939. "I'm sorry to hear that, Jesus," he says, and conversation flows well, moving to holding on to your heritage, then The Revisionist, the off-Broadway play he wrote and starred in. It's about a young sci-fi novelist (him) who travels to Poland to stay with his second cousin (Vanessa Redgrave). I say my colleague saw it - "OK, yeah" - that she liked it - "That's good" - and that it must have been a hit because it's transferring to Broadway. "It was a good play," he says, one leg now resting on a spare chair. "I knew it would be good. I wrote it six years ago and have been trying to get it on, and I knew when Vanessa signed on to it we would be doing it in the right way."

He thinks his writing is better suited to the stage, laughing at his own work on The Revisionist and how its characters "have opposing goals ... which is good for Drama 101". It's simple, and he plans to do a play a year.

I ask if he has idols: Woody Allen, perhaps, for whom he played a younger version of the director in the veteran's latest effort, To Rome with Love. Is Allen's acting-writing-directing something to emulate? "Maybe at some point," Eisenberg says. "But every time I sit down to write, I write stories that take place in one room, with 3 1/2 spoons, so it's not enough for a movie." It's cheap, though, I suggest. "Unless the spoons are gilded," he replies, looking at the floor, "in which case it's the same price."

Eisenberg's great skill lies in playing the outsider, antagonised or irritated, solemn and often subdued. It is as if there's his clever character, in a T-shirt, then there's the big wide world trying to lessen him. In his excellent, Noah Baumbach-directed breakthrough The Squid and the Whale (2005), it was him and his parents' divorce. Then, in the charming Adventureland (2009), his bookish teen battled his own virginity. In the better-than-it-sounds Zombieland, he fought zombies. It's not that he plays the same role again and again. Rather, he has his talent, his thing, and he tweaks it, subtly. An eyebrow here, a quickened sentence there. Like an edgier Michael Cera or a less confident Robert Downey Jr.

I tell him I'm about to wheel out one of his old quotes. "One of my famous quotes," he repeats drily. "Which one?" One about how, unsettled at school, he started acting in plays during his teens so he could hide behind a character. "You didn't get the exact wording," he says with a shrug, "and I'll send you the T-shirt. But yeah, I mean, acting gives you a prescribed set of behaviours, and that can be really comforting because the rest of the world is chaotic and unpredictable."

With fame, though, he has to strike a balance. There's the "rich emotional inner life" when not performing, then the times "strangers are talking to you on the street". But he acknowledges: "I guess it could be worse."

We talk about David Blaine. I tell him many Brits think the magician is an insufferably pretentious berk. "I don't think anybody thinks he's anything other than really interesting," comes the protest. But in London, he just sat in a box. "We're still excited by things like that here in America." Sitting in a box? "Especially sitting in a box." We do a to-and-fro. "Listen, we are a few hundred years old," he finishes. "We still have reverence."

A few weeks after we met, blogger Romina Puga released a short video of her interview with Eisenberg and I was reminded of our Blaine conversation. "So, I was just humiliated by Jesse Eisenberg," she wrote; he is sarcastic throughout. When asked to say Puga's name as if calling to her in a crowded place, he does so quietly, saying, "The thing is, I didn't want to find you." But then, on the David Letterman chat show about the same time, he is humble, as if his cockiness is directly related to how much he respects other people in the room.

He tells me he has "trouble committing emotionally if I don't think it's the greatest thing in the world".

In 2011, he sued Lionsgate after the studio used his face - in the wake of The Social Network - to flog a horror film he appeared in for mere minutes. It was, the complaint read, "false advertising".

Time's up. The rain has stopped, and there's a city - or a cinema - to see after lunch. He says of the horror film that there was a settlement, and that he "gave all the money to a charity". That sort of action from him makes sense. He cares about what he does and how he is perceived on screen, and denies that the bigger films - such as his blue macaw in the cartoons Rio and Rio 2 - are just done to fund his plays. He voiced the parrot on his day off from The Revisionist because, he says with a smile, it was "the most fun thing to do on a Monday ... to go and improvise as this bird, which is such a sweet character".

We end on a joke of his about buying a ticket for The Great Gatsby in 2-D, which peters out as he heads into the bathroom.

The Sunday Times

Now You See Me is released on August 8.