Born in Far Rockaway, New York, he showed musical talent, 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 as this school offered courses suited to his musical talents, but he left to study on his own as the school did not offer similar courses in mathematics.

He attended several colleges, studying mathematics and music.

While a Ph.D. student, Smullyan published a paper in the 1957

*Journal of Symbolic Logic* showing that Gödelian incompleteness held for formal systems considerably more elementary than that of Gödel's 1931 landmark paper. The contemporary understanding of Gödel's theorem dates from this paper. Smullyan later made a compelling case that much of the fascination with Gödel's theorem should be directed at Tarski's theorem, which is much easier to prove and equally disturbing philosophically. The culmination of Smullyan's lifelong reflection on the classic limitative theorems of mathematical logic is his quite readable:

- Smullyan, R M (2001) "Gödel's Incompleteness Theorems" in Goble, Lou, ed.,
*The Blackwell Guide to Philosophical Logic*. Blackwell (ISBN 0-631-20693-0).

Smullyan is the author of many books on recreational mathematics, recreational logic, etc. Most notably, one is titled

*What Is the Name of This Book?*.

He was a professor of philosophy at City College in New York.

He also is an amateur astronomer, using a six inch reflecting telescope which he ground the mirror for.