Simon, at seventy-four, is in the midst of a late-career renaissance. On his new album, he sings, “I’m never gonna stop.” Illustration by Stanley Chow

“Paul Simon tries really hard with the word ‘motherfucker.’ But he has trouble with it.” This was the verdict of the critic Rob Sheffield, writing in the Village Voice in 1997. It was a tricky time for anyone who loved Paul Simon, and surely not an easy time for Simon himself. He had just released an album of songs from “The Capeman,” his ill-fated Broadway musical, which had become about as notorious as the teen-age killer who inspired it. The album wasn’t a cast recording, because Simon did almost all of the singing, delivering even the saltiest exchanges with a delicate precision that some found unduly quaint. It had been more than a decade since “Graceland,” and more than three decades since “The Sound of Silence,” and it seemed possible that Simon, one of the most accomplished overthinkers in the history of popular music, had at last grown tired of being himself. A man who once famously—if softly—proclaimed himself a rock and an island was now proclaiming himself a Puerto Rican hoodlum named Salvador Agron. “The Capeman” closed after only sixty-eight performances, and many Simon fans probably didn’t even bother to check to see if there were any sparkling little melodies tucked away on the accompanying album. (There were.)

Simon responded to the disappointment by staging one of rock music’s greatest late-career comebacks. Starting in 2000, with “You’re the One,” Simon has turned out a series of clever, quietly audacious albums, containing some songs that are as good as any he has made. He has earned plenty of gravitas over the years, but he seems too restless to spend it, embarking instead on a series of experiments in rhythm and texture, and honing in his lyrics a shrugging acceptance of an imperfect world. Where some of his contemporaries were effortlessly cool, Simon always seemed like a rock star who “tries really hard,” as Sheffield put it. But now, more than half a century into Simon’s career, it is much easier to see his determination to try hard as an asset, a weapon against complacency and cheap sentiment. The title track to “You’re the One” began with a lover’s prayer. “May twelve angels guard you while you sleep,” he sang, and he let the lyric reverberate for a moment before delivering the punch line: “Maybe that’s a waste of angels, I dunno.”

In Simon’s lyrics, the decisions are invariably mixed: he once told the music journalist Paul Zollo, “I try to get all the opposites into the same song, if I can.” The longer he sings, the less he knows for sure. For “Surprise,” from 2006, he recruited Brian Eno to compose a “sonic landscape” that uplifted a rather sombre set of songs, although he appended a new fan favorite: “Father and Daughter,” from the soundtrack to “The Wild Thornberrys Movie,” an animated feature. “So Beautiful or So What,” from 2011, was a career highlight, a reflection on love and God that seemed partly addressed to his wife, the singer and songwriter Edie Brickell, whom he married in 1992. At one point, Simon, uncharacteristically overcome, bumped up against the limits of his chosen form, singing, “I loved her the first time I saw her—I know that’s an old songwriting cliché.”

And now the “motherfucker” is back. In June, Simon will release his thirteenth solo album, “Stranger to Stranger,” which is friskier and funnier than its recent predecessors—his most danceable music in decades. He meets his old nemesis near the end, in a song called “Cool Papa Bell,” named for the great Negro League center fielder. “Motherfucker,” Simon mutters, as the warm feelings of the chorus dissipate. “Ugly word.” For a moment, he doesn’t seem to be singing at all. But then he continues, adding melody and alighting upon a rhyme that encourages us to hear the music in what came before:

Ubiquitous and often heard

As a substitute for someone’s Christian name

And I think yeah the word is ugly—all the same

Ugly got a case to make

His brief on behalf of ugliness is belied, naturally, by music that fails to be ugly in the least. (Nothing that he sings can break the spell cast by Vincent Nguini, a guitarist from Cameroon whose buoyant lines have enlivened his music ever since “The Rhythm of the Saints,” in 1990.) Simon doesn’t apologize for his conviction that music should be easy on the ears. He has shown little interest in the grit and grunge that often signal rock-and-roll authenticity, and even now, at seventy-four, he sings in a voice that is boyish and clear. More than any other musician of his age and stature—more than Bob Dylan or Aretha Franklin or Mick Jagger, more than Paul McCartney or Joni Mitchell—he seems unburdened by the years, and by his own reputation. He has managed to become neither a wizened oracle nor an oldies act, and his best songs convey the appealing sensation of listening to a guy who is still trying to figure out what he’s doing. “I’m never gonna stop,” he sings, at the end of “Cool Papa Bell”—only, and inevitably, to reverse himself a few minutes later, on the album’s finale, “Insomniac’s Lullaby.” It ends with a promise, and a benediction: “We’ll eventually all fall asleep.” Knowing Simon, it won’t be soon, or for long.

In 1972, when Simon was still best known as one half of Simon & Garfunkel, he gave an interview to Rolling Stone in which he considered his place in the musical pantheon. “I never compare myself with the Rolling Stones,” he said. “I always was well aware of the fact that S. & G. was a much bigger phenomenon in general, to the general public, than the Rolling Stones.” The intervening decades have largely reversed this perception. The Rolling Stones endure—in memory and, to a lesser extent, onstage—as the paradigmatic rock-and-roll band. Meanwhile, Simon & Garfunkel have been eclipsed by their own beloved songs: the duo itself is less iconic than “The Sound of Silence” or “Mrs. Robinson” or “Bridge Over Troubled Water.” Later in the interview, Simon expressed a cautious but prophetic hope that his late production would outpace those early hits. “Maybe I’m not gonna do my thing until I’m fifty,” he said. “People will say then, ‘Funny thing was, in his youth he sang with a group.’ ” As it happened, Simon was forty-four when “Graceland” appeared, and for many listeners it served as an introduction to a singer and songwriter whose past they knew only vaguely, if at all.

Not long after Simon’s fiftieth birthday, on an episode of MTV’s “Beavis and Butt-head,” Beavis referred to him as “that dude from Africa that used to be in the Beatles.” In fact, Simon was born in Newark and grew up in Queens, and he was a songwriter and a perfectionist by the time he was a teen-ager. He formed a fruitful but complicated partnership with Art Garfunkel, a neighborhood friend who had both a limpid tenor voice and mixed feelings about being perceived merely as a lovely singer. Simon & Garfunkel weren’t quite the Beatles, but their five albums are stocked with more left turns and experiments than you might remember. “Bookends,” from 1968, includes the wistful hit “America,” which was recently revived in an advertisement for another spry seventy-four-year-old from New York: Bernie Sanders. But it also contains “Save the Life of My Child,” a surreal excursion that starts with a squelch of Moog synthesizer and includes a ghostly, disconcerting snippet—we would now call it a sample—of Simon & Garfunkel singing “The Sound of Silence.”