Since 1994, British designer Thomas Heatherwick and his studio have produced an impressively diverse body of work, from the cauldron for the 2012 London Olympics, to the U.K. Pavilion at the 2010 World Expo in Shanghai, and a number of city-wide projects throughout London, including an update to its iconic double-decker buses. Many of their projects have been designed with an eye to delight users and challenge the norm, engaging public social interaction through unconventional typologies. The Rolling Bridge at the Grand Union Canal in London, for example, curls up into a circular sculpture rather than opening up as a drawbridge; and the circular Spun chair is as much a seat as it is a ride that leisurely allows users to rotate like a spin-top toy.

The studio's approach is driven with a curiosity, distilled down to a central query. Can you make a park out of a desert? Can a building express on the outside what goes on inside? What shape should make a monument make against the guy? Can you squeeze a chair out of a machine, the way you squeeze toothpaste out of a tube? Like riddles from the sphinx, these are among the many questions presented to viewers at Provocations: The Architecture and Design of Heatherwick Studio, on view at New York's Cooper Hewitt, Smithsonian Design Museum through Jan. 3. The show marks the third and final installation of the traveling retrospective, which began at the Nasher Sculpture Center in Dallas last fall, followed by a run at the Hammer Museum in Los Angeles. Collecting the studio's unique and imaginative design concepts to products and furniture, to temporary installations, large-scale building projects and infrastructure, it's the first major museum exhibition to present the studio's work in the U.S., where they currently have a number of projects in the works. Pier 55, a $130-million, manmade urban park on Manhattan's West Side, is slated for completion in 2018. The studio is also collaborating with Bjarke Ingles Group on the design of a new Google campus in Mountain View, California.

We spoke with Heatherwick at the Cooper Hewitt to discuss contrariness, collaboration, designing for the public sector, and the process of putting the retrospective together.

Your studio celebrated its 20th anniversary last year. How has reaching that milestone provided perspective on your practice?

For me, the studio is just beginning! It takes a while to develop a system and to be trusted to work at the scale that you aspire to. Now we have a team of 170 architects, designers, and engineers, and we’ve developed ways of working with each other within that team. We’re not experts, but we’re experts in not being experts in the way we work.

It also takes a long time to complete big architectural projects. Even though we’ve been going at it for two decades, we’ve only just finished our first buildings in the last few months. Most architects build their first projects when they’re in their fifties; I feel very lucky to still be in my forties and doing the work I’ve been doing.

What have you hoped to express with this exhibition?

The exhibition represents a collection of urges, impulses, tests, and early experiments which I hope will be the basis for the next 20 years of what we do. When we started, I had to beg architects to work for me because my work didn’t look like "normal" architecture. People have also referred to me as a sculptor, but I’ve never studied sculpture in my life. For our previous show [in 2012, at London's Victoria & Albert Museum], the curator came to our studio, which is kind of a cluttered collection of stuff, and responding to that, wanted the show to be shown just as the studio. To some extent, you could say exhibitions are a collection of junk [laughs]—actually, to me, junk is a great word! Growing up, my house was filled with junk, and junk shops were the most exciting places, because you never knew what you would find.

You don’t normally step back from your work like this, and this show has been a chance to see the funny juxtapositions of projects that have never sat alongside each other before. I’m looking forward to quietly wandering around myself a bit more. It’s similar to when we did a book—I’ve always liked books with lots of juicy things to see. Partly, that’s just me hedging my bets: If you don’t like this project, well, maybe you’ll like that one! With every project, the concern is, "What’s the appropriate thing?" The initial discussions within our design team are always about what approach to take, and what attitude to have inside you as you begin each thing. Whether it's an exhibition design or an object, there isn’t a set strategy or approach: It’s more about finding and thinking of the best solutions for the problem at hand. In this case, how do you show more than 70 projects that a curator has asked to show, and let them each come forward?

As the head of a design studio that works across a wide range of scales and mediums, what has been your approach to the exhibition format?

When I was growing up, architecture exhibitions tended to be very dry and heavy. The models didn’t have an experiential dimension—the approach was so abstract that there was a denial of the real world. But my passion is the real world: I don’t see any desire to design for any other world. It’s got so much possibility that’s unfulfilled, always, that you can see as you walk or cycle around any city. In showing these projects here at the Cooper Hewitt, the urge is to try to make and bring things alive as much as possible—to present that reality, or the potential of reality, as clear as possible, and certainly not to wallow in the abstraction of an idea.

Communication is something that you have to think about when designing buildings, to begin with: There are so many factors to take into account, and people that need to become part of it, whether that’s city planners, mayors, or building control officers. You’re not always successful, but if you can just clearly present across what you’re trying to do, there's a refreshing dimension to it that could potentially even excite people.

Many of your projects have become iconic symbols of London, and more broadly, the U.K. How do you approach such large-scale civic and public works, which involve a strong element of placemaking or cultural identity?

Quite early on, I realized I wasn't excited by private projects, or other people's personal fantasy projects, because they were already other people doing those things very well; there were plenty of amazing private residences, apartments, and extraordinary works in galleries—that was the mode that very creative work tended to fit into. It seemed the in-between bits were the rubbish bits, and those were in our streets, the infrastructure around us, and in the public buildings, hospitals, factories, and power stations. Because it's hard—very, very hard—to make public things in democracies be special. There's so much friction from so many parties, and anxieties and worries that stem from that.

There's greater potential in this realm of work, if you can manage to get through it. I thought, well, why not apply my energy and determination to an area where you don’t expect anything to be special? If you achieve any amount of specialness in that sector, it will mean something. Whereas another special thing in an art gallery is sort of expected, expectations are so phenomenally low for projects in the public realm. Often in that context, things don’t have the confidence to have their own spirit, and tend to take on a sort of generic design; it’s why we’ve devoted a lot of the studio's energy into impacting the wider public with things that have character. And that’s led by the formative experiences I’ve had of things which catch your imagination as you’re growing up as a child. In what we do, and the collaborators we work with, we try to focus on the bits that feel like they make some kind of a difference. You’ve got to believe the best in other people; that's the basis that has helped our projects to happen.

Many of your works, as you mentioned, have been described as sculptural, even biomorphic. How do you think technology, nature, and engineering will continue to come together in design?

My passion lies in ideas and team experience. In aesthetic terms, there's no natural or scientific predisposition towards things that are, say, curvaceous as my work also tends to be described. There's an interest in context—and I grew up in a context wherein every new building was extremely rectilinear, flat and formless, and detail-less. My response to a world where everything seems astonishingly two-dimensional, with an absence in form that captures light, was to make projects that felt complementary to that—to explore what form you could give. However, if everything were extremely curved or something like that, we'd probably be the first to do all the square things! We always consider: What will be seen as special or precious to the human experience? There's a space for the other, whatever that other is. We don't approach things purely from the stance of self-expression, though; rather, it's a response through analysis of problem-solving, and to us, that's one of the problems, in some contexts, that you're working with.