IN the mid-1980s, a University of Arizona surgery professor, Marlys H. Witte, proposed teaching a class entitled “Introduction to Medical and Other Ignorance.” Her idea was not well received; at one foundation, an official told her he would rather resign than support a class on ignorance.

Dr. Witte was urged to alter the name of the course, but she wouldn’t budge. Far too often, she believed, teachers fail to emphasize how much about a given topic is unknown. “Textbooks spend 8 to 10 pages on pancreatic cancer,” she said some years later, “without ever telling the student that we just don’t know very much about it.” She wanted her students to recognize the limits of knowledge and to appreciate that questions often deserve as much attention as answers. Eventually, the American Medical Association funded the class, which students would fondly remember as “Ignorance 101.”

Classes like hers remain rare, but in recent years scholars have made a convincing case that focusing on uncertainty can foster latent curiosity, while emphasizing clarity can convey a warped understanding of knowledge.

In 2006, a Columbia University neuroscientist, Stuart J. Firestein, began teaching a course on scientific ignorance after realizing, to his horror, that many of his students might have believed that we understand nearly everything about the brain. (He suspected that a 1,414-page textbook may have been culpable.)