“An exhibit isn’t like reading a book; it has to be fun and create emotions,” he said. “Naturally, if along with the emotions we are able to transmit a concept or two, the game becomes more interesting.”

The director of the Uffizi, Eike Schmidt, described Mr. Galluzzi as the world’s most eminent scholar of Leonardo’s scientific writings, though Mr. Galluzzi admits his expertise does not extend to Leonardo’s artistic accomplishments. Authenticating paintings is “not my vocation,” he said. But he has collaborated with investigators trying to unmask the makers of fake copies of Sidereus Nuncius, Galileo’s observations on the cosmos.

For a man who preaches the digital gospel, he still pens his scholarly writings by hand, he said, a self-described “hyper-corrective” with an old-school approach to writing. Typing got in the way of reflection and meditation, he said. “One of my privileges is that I have secretaries who type up my handwritten notes,” he said, smiling.

After 36 years at the helm of the museum, Mr. Galluzzi is thinking about retirement. “I want to leave when I am still of sound mind and body,” to pursue independent research and study, he joked.

His dance card is certainly booked. He serves on many committees, advisory boards and scientific commissions, and a year ago he was named president of the national committee marking the 500th anniversary of Leonardo’s death, which falls in 2019.

But his true legacy is that of Leonardo and Galileo. “We are meteors that leave no trace,” he said, adding after a beat. “Unless you become Leonardo or Galileo.”