ANNAPOLIS, Md. — Sarah Benson last encountered college mathematics 20 years ago in an undergraduate algebra class. Her sole experience teaching math came in the second grade, when the first graders needed help with their minuses.

And yet Ms. Benson, with a Ph.D. in art history and a master’s degree in comparative literature, stood at the chalkboard drawing parallelograms, constructing angles and otherwise dismembering Euclid’s Proposition 32 the way a biology professor might treat a water frog. Her students cared little about her inexperience. As for her employers, they did not mind, either: they had asked her to teach formal geometry expressly because it was a subject about which she knew very little.

It was just another day here at St. John’s College, whose distinctiveness goes far beyond its curriculum of great works: Aeschylus and Aristotle, Bacon and Bach. As much of academia fractures into ever more specific disciplines, this tiny college still expects — in fact, requires — its professors to teach almost every subject, leveraging ignorance as much as expertise.

“There’s a little bit of impostor syndrome,” said Ms. Benson, who will teach Lavoisier’s “Elements of Chemistry” next semester. “But here, it’s O.K. that I don’t know something. I can figure it out, and my job is to help the students do the same thing. It’s very collaborative.”