Mr. Riggio, a self-made entrepreneur from Bensonhurst who opened his first bookstore in 1965 at age 24, described the “transformational” experience of walking into Dia in Chelsea in 1997 and discovering Serra’s three monumental “Torqued Ellipses.” “I saw infinite possibilities,” Mr. Riggio said, explaining the visceral connection he felt to the imposing steel sculptures. He purchased them on the spot as a gift to Dia and later served as its board chairman, contributing more than $30 million to the building of Dia:Beacon, which opened in 2005. “I began this journey with Dia, and then, all of the sudden, we’re fascinated by Minimalism and into Judd, [Dan] Flavin, [Fred] Sandback and on and on.”

The couple’s focus has expanded to embrace the Italian Arte Povera movement that was contemporaneous with Minimalism in the 1960s and ’70s. Dominating the walls of the Riggios’ expansive Bridgehampton home are vibrant tapestries by Alighiero Boetti, distressed canvases by Alberto Burri, numbers from the Fibonacci sequence in blue neon by Mario Merz and reliefs in salt and Elmer’s glue on lead by Pier Paolo Calzolari, including one etched with Italian words meaning “When the dreamer dies, what happens to the dream?”

“For me, it becomes fun to try to grasp these riddles and complex issues the artists were looking to solve,” said Mr. Riggio, who is retiring soon. (Barnes & Noble was sold last month.) The Riggios are being honored on July 13 at the Parrish Art Museum in nearby Water Mill for their longtime support of that institution.

Following are edited excerpts from the conversation.