“I was always interested in ideas and innovations,” said Mr. Heatherwick, a wiry 45-year-old whose face is framed by ringlets. He was interviewed in New York for the opening of his first major American exhibition, “Provocations: The Architecture and Design of Heatherwick Studio” (through Jan. 3). It fills the third-floor gallery of the Cooper Hewitt, Smithsonian Design Museum with models and photographs of some projects that have confounded expectations.