Szirmai was a graduate of the Budapest Academy of Music, studying piano and composition (with Hans Koessler).

Szirmai received a doctorate in music from the University of Budapest,[1] and was devoted to creating works for the stage.

He was music editor for such Broadway luminaries as Jerome Kern, Cole Porter, Richard Rodgers and George Gershwin, and for a collection of the British duo Gilbert and Sullivan.

"I would call the material a rich musical heritage," Szirmai told The New York Times.

"[3] Though he lived in America for most of his later years and was a good friend of Gershwin, Szirmai eschewed the jazz styles popular at the time; in addition to the folk music of his native Hungary, his music shows the influence of German Romanticism, particularly Felix Mendelssohn and Robert Schumann, whom he most admired.