Born in Far Rockaway, New York to Eastern European Jewish parents (originally spelling their name as Schmulian), Smullyan showed musical talent from a young age, winning a gold medal in a piano competition when he was aged 12. The following year, his family moved to Manhattan and he attended Theodore Roosevelt High School in The Bronx, which offered classes suited to his musical talents. He left to study on his own, as the school did not offer similar courses in mathematics. He studied mathematics and music at several colleges (including Pacific University and Reed College) before receiving an undergraduate degree from the University of Chicago in 1955 and a Ph.D. in mathematics from Princeton University in 1959. He completed his doctoral dissertation, titled "Theory of formal systems", under the supervision of Alonzo Church.