There may be no more diverse, unpredictable jazz piano player, song to song, than Jean-Michel Pilc. Go hear him at Smalls or the Kitano in New York, or put on any of his nearly 20 records, and you might encounter a violent, thundering assault on “So What,” followed by a wistful, crystalline fragmentation of “Scarborough Fair” and then a thorny, hardhearted “Tenderly.”

He is self-taught but erudite, with an extensive knowledge of the Western classical tradition and jazz piano history. He can erect towering two-handed Baroque architecture, or knock you down with rhythmic force, or break your heart with harmony like Bill Evans, sometimes within the same piece. He has the chops to execute his wildest impulses.

Pilc was born in Paris 54 years ago. His formal education was scientific and technical. He graduated from École Polytechnique, the French equivalent of M.I.T., and worked as an engineer for three years on a television satellite project in Toulouse. In 1988 he quit his day job and devoted himself to his passion, the piano.

Autodidacts often develop unusual styles. (Think Vijay Iyer.) But Pilc disputes any cause-and-effect relationship. “Players of my generation and before are mostly self-taught,” he says. “Jazz schools are not that old. I had piano lessons, but only until I was 10. My real lessons were recordings. I would put on a record by Earl Hines or Bud Powell, then go to the piano and try to imitate what I heard. That’s how I learned this music. It’s a language. A language is something you learn by yourself.”

In 1995 he moved to New York. “In France, I realized that the big festivals, the big venues, the front pages, were for American musicians,” he says. “Jazz is American like wine is French.” He is now a U.S. citizen. Over 20 years, recognition of his unique creativity has come in the form of grants (including a Guggenheim), documentary films (Jean-Michel Pilc: A Portrait by John McCormick), academic appointments (he teaches at NYU and the New School) and consistent strong reviews in the major outlets of the jazz press. But even in a career marked by extreme independence, Pilc has never done anything as unprecedented as his new album, What Is This Thing Called?, on Sunnyside.

He provides the backstory: “I asked my friend [pianist] Dan Tepfer to record it for me, because I loved the sound of his Bach album [Goldberg Variations/Variations, also on Sunnyside], which he engineered himself at Yamaha Artist Services [in New York]. Dan set up the equipment in the studio, then left. So I was alone with the piano for three nights. I just had to press a button and play. That’s a dream situation. You can’t believe what a difference it makes. For three days I played whatever came to me.”

But Pilc acknowledges that he had a concept for the project: “I had an idea for variations because I did them a lot in concerts. There is a reason why Bach and Mozart did theme-and-variations. It is so inspiring. You have this central element that you can twist and turn and expand. You make constant discoveries.” The theme Pilc chose was Cole Porter’s “What Is This Thing Called Love?” He plays it once, for 80 seconds, freely. Then he offers 29 variations, in durations from 30 seconds to seven minutes.

In a 68-minute album, he does not wear out the tune. He pursues it into multitudinous tempos and keys and crevices. The album feels like a single, spontaneous, richly varied imaginative arc. Some pieces, like “Giant,” improbably overlay Coltrane’s “Giant Steps” upon Porter’s song. “Cole” and “Dawn” are extended, alluring, relatively explicit interpretations. On “Look” and “Run,” the thematic connection is elusive. “Chimes” and “Dance” are gone in a flash, momentary Porter manifestations from Pilc’s subconscious. “The tune was always somewhere in my mind, like a moon triggering the tides,” he says. He points out that the format of theme-and-variations, so important in Western classical music, is uncommon in jazz. “Jazz players tend to do one variation. But I always encourage my students to keep going. I tell them, ‘You’re going to find stuff you didn’t know you could do. You’re going to learn surprising things about the song and about yourself.'”

What is important about Pilc’s project is not its cleverness but its outcome in so much memorable music. The album ends with its longest track, a moving summation and resolution called “Now You Know What Love Is.” Porter’s song is present from the start as a timorous question, but this time Pilc offers answers, in deep reflections and loose lyric unfoldings and firm chords, all suggesting that love is surrender. “It was the last piece I recorded on a Saturday night, very late,” says Pilc.

“I knew it was the end. I could not play anything more.”