SOUTH BEND, Ind. — This city, according to Americans with only a vague notion of it, is a down-home, run-down, industrial, beautiful, Catholic kind of place. It is progressive and conservative, country and urban, dangerous and quaint. A college town, really, but with high poverty. And corn.

South Bend has proved oddly illegible to the rest of the country, ever since its (now-former) mayor, Pete Buttigieg, attracted national attention with his campaign for president. What you make of him may depend on what you make of the place that is at the foreground of his entire biography in government. But is that place a prosperous university town? A struggling post-industrial city? A community that has combated blight like Detroit, or that more closely resembles Ann Arbor?

Many voters, Mr. Buttigieg said, have indeed been confused.

“They often assume because of the link to Notre Dame,” he said, “that this is a tidy, white, wealthy, homogeneous college town.”