At age 14, began playing the violin professionally in New York City. Under the stage name Hal Hope, he led nightclub and society bands. By 1936, he had taken up the theremin and begun featuring it in publicity for his engagements.
In 1941, Hoffman moved to Los Angeles, where he established a medical practice and had little time for musical activity. But as the only theremin player in Local 47 of the Musicians Union, he got the call in 1945 when composer Miklos Rozsa decided he wanted to use a theremin in the score to Spellbound. Hoffman began performing under his real name; he was customarily referred to as "Doctor" because he was also a podiatrist. In the wake of the film's success, he was asked to play on many more soundtracks; for instance, The Day the Earth Stood Still (1951). He was in demand for horror movie and sci fi soundtracks through the end of the 1950s.
In the late 1940s, he recorded three studio albums with bandleader Les Baxter. These were forerunners to exotica; they also influenced Sun Ra, who recorded a composition from Perfume Set to Music on his first LP, Jazz by Sun Ra. One of Hoffman's last recordings, made in 1967, was Safe as Milk by Captain Beefheart and his Magic Band, where he appeared on two tracks.
Hoffman died of a heart attack on December 6, 1967.
These albums are compiled and remastered in Waves in the Ether: The Magical World of the Theremin (2004).