Composer Marvin Hamlisch, who died Monday at the age of 68, was — to borrow a phrase from one of his biggest hits — one singular sensation.

It’s not just that he was an EGOT (one of a handful of individuals who has won all four major showbiz awards, the Emmy, Grammy, Oscar and Tony), as well as a Pulitzer Prize winner, a combination matched only by Richard Rodgers, another great songwriter from an earlier age.

Nor is it the fact that he is the only composer in the history of the Academy Awards to win all three music categories on the same night: best song and best score for “The Way We Were,” best adaptation score for his use of Scott Joplin rags in “The Sting.” (Bounding onto the stage to collect his third Oscar on April 2, 1974, he told the audience, “I think we can talk as friends.”)

Or even his stunning workload, having just finished a new musical (“The Nutty Professor,” which opened July 31 in Nashville); started work on the score for Steven Soderbergh’s HBO film on Liberace, “Behind the Candelabra”; and serving as principal pops conductor in six American cities, dashing from gig to gig playing his own music and that of everyone else from Gershwin to Cole Porter.

It was that he did so much, so well, and remained so cheerful about his place in American music despite the fact that his biggest hits were behind him and his favorite venue — the American theater — kept rejecting his more recent efforts (“Smile,” “Sweet Smell of Success,” “Imaginary Friends”).

Hamlisch just kept going, always excited about whatever new project he had. Visiting L.A. in 2009 and talking to Variety during the awards-season campaign for Soderbergh’s “The Informant!” (a delightful score that wasn’t nominated but should have been), the composer was as energized as he was back in the 1970s.

That energy translated easily to his concert appearances. Hamlisch was a born performer. One of his favorite parlor tricks was sitting down at the piano, encouraging the audience to shout out potential song titles and creating a song on the spot. It was always clever and often funny.

But he was also a serious musician. While most of his 30-plus feature film scores were comedies (and his Latin American-revolution music for Woody Allen’s “Bananas” still slays), he was equally talented at dramatic music. Everyone remembers his nostalgic theme for “The Way We Were,” but he also wrote a powerful score for Alan J. Pakula’s “Sophie’s Choice” that may qualify as his finest work in film.

And he remains the only composer in the 50-year history of the James Bond franchise to be Oscar-nominated not only for a song (“Nobody Does It Better,” a 1977 hit for Carly Simon) but for his score for the film (“The Spy Who Loved Me”) as well.

His use of turn-of-the-century Scott Joplin rags in “The Sting” helped launch a resurgence of interest in the African-American composer. Hamlisch’s rendition of Joplin’s “The Entertainer” reached No. 3 on the Billboard pop charts in early 1974 and won a Grammy for pop instrumental performance.

Among his theater work, it’s hard to overstate the impact of “A Chorus Line” on Broadway in 1975. This backstage look at Broadway dancers, conceived and directed by Michael Bennett with score by Hamlisch and lyricist Ed Kleban, was a phenomenon at the time and became one of the longest-running shows in Great White Way history. Hamlisch’s show-stopping anthem “One” is its best known, but the score just brims with great numbers (“At the Ballet,” “Dance: Ten, Looks: Three,” “What I Did for Love”).

As Hamlisch’s fellow Oscar winners for “The Way We Were,” lyricists Alan and Marilyn Bergman, put it earlier this week: “The world will miss his music, his humor, his genius.” But the world will remember what he did for love, and it won’t just be the way we were.