There was always something to talk about. The avant-garde music that verged on conceptual art but was delivered at a relaxed and buoyant foxtrot. The memorable melodies that sat atop a virtuosic harmonic conception, emphasizing unexpected dissonances. The blues that were an unchanging constant. For those who couldn’t tell he was an unusual musician simply from listening, the visuals were a helpful guide: outrageously idiosyncratic percussive piano techniques and long, spastic dances, not to mention a wardrobe of impeccable flash and taste.

At the beginning, Thelonious Monk was a shadowy figure known only to fellow-innovators. To help generate publicity, the Blue Note label dubbed him “the high priest” for his first records, as a bandleader, in the late nineteen-forties. After Monk spent a few more years in penniless obscurity, suddenly, most of New York City went to the Five Spot, where he was in residence for multiple months in 1957. From there he became a household name and one of the biggest draws on the European circuit. In 1964, he even appeared on the cover of Time magazine, and was profiled by Lewis Lapham, in the Saturday Evening Post, although most of the mainstream press during Monk’s lifetime made unhappy allusions to craziness, infantilism, and negroid primitivism. Eventually, the record companies decided that he wasn’t a religious icon (“the high priest”) but a warrior instead, and his last significant major-label release, “Underground,” depicted him on the cover with guns, grenades, and a captured Nazi.

During Monk’s ascendency, his style was so different from that of any other bebop or modern-jazz pianist. It was stubborn, incantatory, utterly African. Occasionally, when his left hand opened up and gave an accurate quotation of glorious Harlem stride, it became downright anachronistic. Some of the cognoscenti were bewildered, at least at first. Most of the skeptics ended up admiring his compositions, although certain great musicians, like Miles Davis, Lennie Tristano, and Oscar Peterson, would continue to dislike aspects of his playing. Ironically, Davis began his ascendency with a performance of Monk’s “ ’Round Midnight.” The ironies are compounded when you remember that Monk would always be irritated about how Davis used incorrect chord changes, not just on “ ’Round Midnight” but on “Well, You Needn’t,” as well.

After his death, in 1982, scholars and fans settled down and began doing the serious work of parsing the complexities and clearing away the controversies. In 1983, the boutique label Mosaic Records launched with “The Complete Blue Note Recordings of Thelonious Monk.” The quietly stunning cinéma-vérité documentary “Straight, No Chaser,” directed by Charlotte Zwerin, was released, in 1989. In 2002, “The Thelonious Monk Fake Book” collected accurate lead sheets, edited by Steve Cardenas and Don Sickler. In 2009, Robin D. G. Kelley published “Thelonious Monk: The Life and Times of an American Original,” a hefty, family-authorized, and definitive factual biography, which declared that Monk was bipolar and offered clues, if not final answers, about why Monk spent his last years withdrawn and silent.

There are sixty-odd Monk pieces still in the active repertoire, something that cannot be said of any other composer’s work. Monk has varied musical tributes from Charles Mingus (“Jump Monk”), Sonny Rollins (“Disco Monk”), Eric Dolphy (“Hat and Beard”), Andrew Hill (“Monastery”), McCoy Tyner (“The High Priest”), and hundreds of others. Many of the remaining jazz celebrities are on the board of the Thelonious Monk Institute, which, for almost three decades, has sponsored the world’s biggest jazz contest.

Monk’s perfect package of accessible surrealism has proved to be catnip to a long line of painters, critics, modern dancers, novelists, and, especially, poets. A collected set of the complete poems written about Monk would fill a small library, most on a theme similar to Abbey Lincoln’s lyric to “Blue Monk”:

Going alone

life is your own

but the cost sometimes is dear.

Being complete

knowing defeat

keeping on from year to year.

The poets are correct. Monk will always challenge conventional jazz. In “Straight, No Chaser,” Tommy Flanagan and Barry Harris offer duo performances of “Well, You Needn’t” and “Misterioso.” Flanagan and Harris are swinging, but both are far from their magical best, and the result (intentionally or unintentionally—only Zwerin knows) shows how tame and unexciting “normal” bebop piano can be when compared to Monk.

He is a smooth object that spins out of one’s grasp, as easily as a ball bearing shaped like his middle name, Sphere. The minute you pin him down, he’s dancing in another corner. A child can march to his 4/4 time, yet so many of his internal minimal rhythms are fantastically complex Afro-Cuban derivatives, confusing to all but the initiated. He’s one of the original Afro-futurists—a noble lineage that includes Sun Ra (“Space Is the Place”) and the Art Ensemble of Chicago (“Black Music: Ancient to the Future”)—yet he also programmed campy and sentimental parlor piano songs from the days of yesteryear.

Jazz musicians began playing “standards” from the American popular songbook to generate a specific feeling, neither a blues nor a musical but some mysterious intersection of the two. After Louis Armstrong, the artist who gave the most early energetic life to this essential chiaroscuro was Billie Holiday. As a young man, Monk would lie in bed and stare at a photo of Holiday taped to his ceiling, illuminated by a single red light bulb.

In his maturity, Monk would always play a standard redone in harmonic and melodic terms just as specific as an original Monk composition. The most absurd of those standards might be “Just a Gigolo,” a song about being a male escort, which was originally written as an Austrian tango, by the Italian composer Leonello Casucci, before being popularized in America with lyrics by the Romanian-Jewish Broadway great Irving Caesar. Monk is all the way inside the tune while simultaneously impossibly distant. His reading of the original melody is relentlessly accurate, so it must be the manipulation of tone and accompaniment that produces such a complex final product.

The composer James Newton says that “Timbre is the least investigated and most misunderstood element of African music.” In “Just a Gigolo,” the sonority is as un-European as a piano can possibly be (and perhaps a good reminder that Picasso and his fellow-Cubists were deeply influenced by African art). But the rules and regulations concerning voice-leading in European music are not discarded. Indeed, Monk understands the pure harmonic potential of “Gigolo” better than Cascucci or Caesar, offering a sweet-and-sour palette that heightens the song’s solemn ambivalence. In the end, while Monk’s “Just a Gigolo” remains absurd, it can also reduce one to tears.

Video footage can help when assessing the performing arts, but not always. There is nothing more boring than decent jazz on a flawed video. However, in the case of Monk, videos are always a true bonus, especially the videos of the working quartet with Charlie Rouse, in the nineteen-sixties. Rouse is a stoic gladiator, the bands swing so hard, and Monk’s pianistic physicality and interpretive dance explode through the screen. One date in particular is glorious: in Tokyo, on May 23, 1963, a crew of smart visual and audio technicians placed one of Monk’s greatest bands, with Rouse, Butch Warren, and the incandescent Frankie Dunlop, against a simple modernist backdrop and let them blow. The version of “Just a Gigolo” from that performance is in “Straight, No Chaser,” and the rest of the songs are available on YouTube.

Although nobody was more laconic than Monk, none of the twentieth-century jazz greats were especially verbose when an outsider asked them about their music. They didn’t say much, because how could they start? Where to begin? Either you get the perfect balance of references and realities contained in that May 23, 1963, video—race, blues, swing, melody, harmony, time, fashion, clave, avant, folklore, academy, mystic, complex, simple—or you don’t. If you do get it, then, as Monk himself said, “Always know.” In case “Always know” isn’t clear, there’s another line of Monk’s that was copied down by his student Steve Lacy: “You’ve got to dig it to dig, you dig?”

The dozens of cryptic Monk aphorisms are key. Here’s one that isn’t yet in print. My friend Dean Estes hung out with him in Minneapolis in the sixties, and Monk spent the week saying, “White is right. Two is one.” Years later, Dean realized that Monk was talking about the civil-rights images dominating the television news. Two isn’t one, so white wasn’t right.

His wife, Nellie, called him Melodious Thunk. Happy hundredth birthday, Thelonious Monk.