It sounds like the setup for a bad joke: What did the Wall Street type say to the college president on the golf course? Well, we don't know exactly—but it has launched a saga with weighty implications for American intellectual and civic life.

Here's what we do know: One day in the summer of 2010, Barry Mills, the president of Bowdoin College, a respected liberal-arts school in Brunswick, Maine, met investor and philanthropist Thomas Klingenstein for a round of golf about an hour north of campus. College presidents spend many...