Everybody knows the song "If I Were a Rich Man" from the Broadway and Hollywood hit Fiddler on the Roof (1971). Indeed, it keeps playing in my head after watching Joseph Dorman's documentary about the Yiddish writer whose stories inspired it. But not many these days are familiar with Aleichem's own story, or his other work, or his impact on Jewish culture and literature in general. Born Solomon Rabinovich in a Ukrainian shtetl, Aleichem (1859-1916) was one of the first Jews from his community to assimilate, moving to Kiev to work the stock market under his birth name while writing stories in Yiddish drawn from his hometown under the name that became his persona. Good thing he kept his night job; he failed as an investor but went on to create a robust new literature that is also an artifact of a demolished world. Dorman's portrait is engrossing, but his Ken Burns style doesn't match his subject's vitality.