Vijay Iyer’s music can be jubilant and dramatic, but Iyer is not. He tends to stand slightly farther from someone he is speaking with than people usually do. Seated, he sometimes leans back from an engagement, as if the extra room allowed him more time to reach a judgment. His gaze is examining, and he occasionally looks at people askance, which makes him appear skeptical. In conversation, he seems cautious but precise and quietly determined. He stands with his feet spread and his knees locked, like someone in the military. He has a round, handsome face and a sharp nose. His expression is not fixed, but it doesn’t vary a lot. People usually take him for an accountant, he says.

Lately, Iyer, who is forty-four and a Harvard professor, has been the most lauded piano player in jazz. Reviewing Iyer’s record “Break Stuff,” his twentieth, released last February, the critic Steve Greenlee wrote, “He may be the most celebrated musician in jazz.” Iyer appreciates the sentiment, but it makes him uncomfortable, too. “I have never thought of myself as a great pianist,” he told me. “I thought of putting myself in the service of some larger trajectory. For me, every choice is to take us closer to the next choice. I never had formal training and no one ever told me not to do anything on the piano, so I always thought of my progress as a series of accidents.” The observation that one hears often about Iyer, and that is not usually made about a musician whose career is twenty years old, is that he hasn’t yet achieved his potential. A strain of traditional authority appears to have withheld its approval, however. He considers it significant that he has never been invited to play at the Village Vanguard, for example. The history of jazz has white musicians and black musicians, but it doesn’t have brown ones, he said. Iyer is Indian-American. His surname is Raghunathan; he changed it to Iyer after college, at Yale, where he majored in mathematics and physics.

Iyer is currently the Metropolitan Museum of Art’s artist-in-residence, and in March he will perform during the course of eighteen days at the opening of the Met Breuer, the former home of the Whitney Museum. Iyer’s residency was Limor Tomer’s idea. Tomer oversees Live Arts at the Met, and she wanted to see “what a deep engagement with the Met’s galleries would look like to someone like Vijay.” For more than a year, Iyer and Tomer have been walking around the museum discussing what he might do. As one of his first events, on an evening last October, he played the pipe organ in the gallery where weapons and armor are displayed. The organ occupies a balcony at one end of the gallery. Iyer arrived a little before six. He hadn’t played a pipe organ before. Someone asked what the program would consist of, and he said, a little uncertainly, “All the hits.”

Iyer pressed several keys. “I’m an expert, because I watched the YouTube video on how to play the pipe organ,” he said. For a few minutes, he held down keys and pulled out stops and pressed a few pedals with his feet; then he stood. “It’s a little like sailing a yacht all by yourself, out there on the ocean, with all there is to take care of,” he said.

Tomer sat on a folding stool to one side of the organ, which was built by Thomas Appleton, a Boston craftsman, in 1830. “It’s the ultimate goyische instrument,” she said. “I love that he’s subverting it. It’s a reverse-colonial moment.”

Iyer was to play two programs, each twenty minutes long, and at six o’clock he placed his phone above the keyboard to keep track of the time. He played a single note, then another, then three together and held them. People began gathering on the floor among the armor and on a balcony at the far end of the gallery. The single-note figures lengthened into phrases and lines and began to swirl and spill over one another and form clusters that resolved periodically but did not come to rest. Iyer played mostly with his eyes closed, opening them only to find a stop.

He ended by holding down several keys, then he walked to the balustrade and waved. “I kept trying to play harder, as if that would make a difference,” he told me. “It’s like trying to turn on a light switch harder, but I can’t get that out of my arms.” For the second piece, he played three works of his own, which seemed more orderly. At the balustrade, he made a small bow.

Two of the first people to approach him were Andrea Morgan and Maria Castillo, whom he had gone to college with. “You looked very priestly when you bowed,” Castillo said. The three left the museum together to have a drink.

I asked if they had imagined at Yale that Iyer would become the musician that he has. “The idea of a professional jazz career then sounded fictional—even today,” Morgan said.

“It’s a bad idea,” Iyer said.

“I would never recommend it to any young person. We were very practical people.”

“A terrible idea,” Iyer said.

“You always had other stuff you were doing.” This was said in a consoling tone.

Iyer followed his sister, Pratima, to Yale—she is a scientist in Georgia who works in public health. Their parents’ marriage was arranged in India. In the mid-nineteen-sixties, Iyer’s father, Raghu, came to the University of Florida to obtain a doctorate in pharmacology. After a year, his wife, Sita, joined him. “Basically, the door was open to certain kinds of non-Western immigrants, ones with technical training—scientific, or medical,” Iyer said. “Hence all those stereotypes about Asians being doctors and engineers. They were curated by policy.”

Raghu got a job in Albany, New York, where Iyer was born, and then another, when Iyer was two, in Rochester. Iyer’s parents started him on the violin the next year. In high school, he was a member of a regional youth symphony that toured once a year. Pratima took piano lessons, and from as early as Iyer can recall he also “started banging on the piano.” As a teen-ager, he played keyboards in a band covering songs by the Police and Prince. At the end of tenth grade, he auditioned for the school’s jazz ensemble. There was already a piano player, so at first Iyer was assigned the vibraphone. The band director liked his playing but told him that he needed a deeper understanding of the music’s vocabulary. In the library, Iyer found records by Thelonious Monk, and was affected by his “staggering empathy, those pointed voids that he would finish with such a different sense of completeness.”

When Iyer began looking for colleges, he didn’t think he was fitted to attend a conservatory. “I was still figuring things out,” he told me. “I didn’t know that I would, or even could, be a musician.” He had skipped seventh grade, so he was sixteen when he arrived at Yale. He auditioned for the college symphony and didn’t get in, and he began to take the violin less seriously. There was a piano in the dining hall, and after dinner he would play it. In his second year, he was accompanied by Jeff Brock, a bass player who is now the chair of the mathematics department at Brown. “People were looking a bit askance—who are these guys playing dinner jazz?—but then we were sort of embraced,” Brock says. Iyer also began writing music, mainly in imitation of Monk and Billy Strayhorn, Ellington’s collaborator, whom he studied in a workshop taught by the musician Willie Ruff. Ruff, who had gone to Yale and was known for playing bass with Dwike Mitchell in the Mitchell-Ruff duo, remembers Iyer as “quiet and industrious.”