In 1835, through an unlikely turn of events, the young United States became the beneficiary of the estate of one James Smithson, a British scientist of considerable means who had never set foot on American soil. The gift of $500,000 (about $12 million today) carried the stipulation that it be used to create an institution for the “increase and diffusion of knowledge.”

How amazing—and baffling—this windfall must have seemed! The responsibility was tremendous, in terms of the amount, the perception, …