Many people are too small to teach, but no one is too big," says Gregor Piatigorsky, who is a case in point.

Ever since he became first cellist of Moscow's Imperial Theater at the age of 15, fellow musicians have come to him for instruction. Now, at 73, long established as one of the world's great cellists, Piatigorsky is in his 14th year of teaching master classes at the University of Southern California to rave reviews from his students.

The role of teaching virtuoso is not without its problems. Piatigorsky recalls one especially talented student who seemed to play worse the harder the maestro tried to demonstrate proper technique. Then it occurred to Piatigorsky that he was intimidating the student, and he purposely began to make mistakes in his demonstrations. The student improved markedly and, after performing with brilliance at his graduation, he said to another student, "Mr. Piatigorsky is certainly a fine teacher—but what a lousy cellist."

Hardly. On his first American tour in 1929 his performance with the New York Philharmonic received exceptional notices. Though he was principally a soloist in his career, he achieved perhaps his greatest fame as a member of chamber music's all-star team, the "Million-Dollar Trio" of Piatigorsky, pianist Arthur Rubinstein and violinist Jascha Heifetz.

He has played with every major American orchestra and, while he has outlived many of his closest friends—composers Igor Stravinsky, Sergei Rachmaninoff and Paul Hindemith and author Aldous Huxley—Piatigorsky has no plans to retire. He sees his teaching as mutually beneficial: "I gain talented young students; they gain an old friend they can trust."

He is besieged by musicians wishing to enroll in his classes. Piatigorsky asked one prospective student, a young woman who "played exquisitely," what her dream was. She replied: "I want to be the greatest woman cellist who ever lived." He turned her down, explaining later: "She would never realize her dreams, and I would participate in something hopeless."

Then a young man, "who looked and played like a truck driver," auditioned. His dream? "My uncle plays bass in the Oklahoma Symphony," he said. "Do you think I could ever play there?" Piatigorsky told him, "We're in business!"