Daniel Libeskind gets into the office at 9am. “But sometimes it’s 7am,” says Thierry Debaille, his scheduling director. Yes, scheduling director. This is Manhattan, and this is the world’s most famous architect. Libeskind’s day is so tight that his schedule says things such as “Journey time: 2 hours 16 minutes”.

Libeskind has already hit the gym in his Hudson Street apartment. “A good hour on the treadmill,” Nina, his wife and business partner, says. “If he didn’t, he’d never get through the day.” Striding away on the walking machine he watches the History Channel and memorises poetry — Shakespearean sonnets.

Libeskind is most famous for designing the masterplan for the building that will eventually emerge from the crater of Ground Zero. Top-dog architects have to be showmen, but it can be an awkward marriage: his angular, challenging architecture, such as Berlin’s Jewish Museum, sits uneasily with appearing on Oprah. Their bond? Emoting: he wants his buildings to stir your heart.

Today, apart from me, he has TV cameras pirouetting round him for a BBC Two documentary. “Since we arrived in New York, it’s been relentless,” says Debaille. “Like a pop star. Girls ask Daniel to sign their chests. People are passionate, though it can get a little odd.” The death threats, which have followed Libeskind since he built the Jewish Museum in Berlin, continue.

First, to Ground Zero for the groundbreaking ceremony of Santiago Calatrava’s Transportation Hub. Hillary’s there, New York mayor Michael Bloomberg too. Libeskind is not speaking but has to be there. It must be odd for him. His once-grand plan for the site has long been superseded by the architect David Childs’s more conservative design. There have been reports of disagreements with Larry Silverstein, the developer who holds the lease on the World Trade Centre. Whatever, the Freedom Tower is not Libeskind’s project any more, but still he looms over it. He smilingly insists ad infinitum, “compromise, negotiation is the reality of architecture”. He sees himself as watchdog of the site’s integrity: “You write the score, you have to make sure it gets played right.”

Studio Libeskind takes up the 19th floor of a Gotham-era skyscraper near Ground Zero itself. Inside it’s like any architect’s office: industrial style, hushed youngsters glued to computers, vast menageries of angular models (I spot the stillborn “Spiral” extension project for the V&A gathering dust). “Daniel keeps everything,” Debaille says. You can feel Libeskind and Nina return. An advance guard of staff whisk back to their desks. “Grab him,” Thierry tells one. “He’s got two hours.”

“It was like an oven down there!” shrieks Nina, out of the lift. “Like 80 degrees. Water was pouring down your back, Daniel.” Libeskind, always in black even in 80 degrees, disappears, mopping himself furiously. He’s back in an instant. “I showered in the sink,” he laughs. The man is like a spinning top. He wheels between staff, inspecting details. “How are you? Anything to see?” There’s a new balustrade for a 9/11 memorial in Padua, Italy: a salvaged World Trade Centre fragment in a zig-zagged open book. “How’s it fixed?” “Welded.” “It would have to be welded. Can we do it in time?” It opens the following week. Warsaw: he gets a scalpel and hacks away at a skyscraper model. He likes models: “I can barely use a computer.” Next, Denver: an art museum and its landscape. He scribbles felt-pen curves over a plan on greaseproof kitchen paper. Good absorbency, apparently. “Curve it, at a very precise angle. Casual, but elegant, you know? A knot! That’s it. Or a loop.” Since Ground Zero work has increased exponentially — skyscrapers, shopping malls, offices, from Eastern Europe to the Far East. His challenge, he says, is to maintain the intellectual rigour that’s made his name. So he keeps his staff small.

He likes to be face-to-face with everyone, not just project leaders, which is rare for an architect of his stature. He likes back-slapping, shoulder-squeezing and always, always that Cheshire-cat smile.

“Architecture is about communication,” he insists. “The building has to communicate to an incredible range of people, and you have to communicate to an incredible range of people to get it built. If people saw the unimaginable lengths you go to to get the simplest thing built, they’d be shocked. At Ground Zero we argue over inches!

“But it’s all architecture. It’s like cinema. If you slowed the film down you’d see how it’s made. But you don’t. You enjoy the film. And, in the end, you enjoy the building. All the arguments that made it fade away.”

It’s 4.30pm. I haven’t seen him eat lunch. Next, a two and a half hour drive to give a lecture, a book signing, a radio interview. He gets home at midnight. “We managed to slip him a sandwich,” says Nina.

“I love the adrenalin,” says Libeskind. “This isn’t a job. It’s life. I could never do nine to five. Thierry sometimes writes in the schedule: ‘2.15-2.18: relax.’ I say: ‘Thierry, it has never yet happened!’ ”