Understated and unarrogant, Ax can be taken for granted. But he has long been, and continues to be, one of the finest American pianists.“A young pianist with the hard-to-forget name of Emanuel Ax has one thing going for him before he plays a note,” the New York Times critic Donal Henahan wrote in 1973. “But brand identification, as advertising men term it, helps in the long run only if the product delivers, and Mr. Ax’s recital at Alice Tully Hall on Monday night fortunately carried the stamp of quality.”The occasion was Ax’s New York debut, and it was the opening flourish of a banner few years. At the Marlboro Festival in Vermont that summer, Ax gave his first concert with Yo-Yo Ma, the cellist he has spent his career playing and quipping with, the friend who calls him “the big brother I never had.” Soon, there was a date on the Young Concert Artists series, a Carnegie Hall appearance, a victory in the Arthur Rubinstein International Piano Master Competition and, in February 1975, an eloquent first recording.That stamp of quality had become indelible, and it has since endured. Of course, Ax, 74, protests that the half-century career he has enjoyed following that inaugural hometown bow has been largely the product of good fortune. Never mind his Avery Fisher Prize or his 19 Grammy nominations (and eight wins), his long list of premieres or his generosity and ease as a chamber music partner to Ma and other eager collaborators. Even now, Ax will only reluctantly allow that he has much talent at all.“I just started, and I stuck to it; I liked it,” Ax said of playing the piano during a recent interview at Tanglewood, where he was joining the Boston Symphony Orchestra for a Brahms concerto as he has many, many times before. “I think the sheer enjoyment of it is a talent in itself.”From left, Leonidas Kavakos, Ax and Yo-Yo Ma, who as a trio have been working their way through arrangements of the Beethoven symphonies.Hilary ScottThat’s Manny, as everyone calls him. He has said things like this forever, sought to share the spotlight or point it wholly elsewhere. And his modesty, which he wraps in a jesting smile and a famous bonhomie, is at the heart of his pianism and personality alike.“Whatever his musical decisions are, they are never ones that would draw attention to himself,” said the conductor Esa-Pekka Salonen, who has known Ax for four decades and will premiere a piano concerto by Anders Hillborg with him and the San Francisco Symphony in October. “So in the very, very best sense of the word, he kind of eradicates himself out of the picture.”Might that mean, though, that Ax is taken for granted? After all, how many artists have performed at his level for so long? How many have treated us so reliably to such taste and good sense as he? How many have had his ability, not unlike that of his late associate Bernard Haitink, to make music sound so simply right?Ax ranks among the very finest of American pianists. Yet he would never admit it. As Ma put it, “He doesn’t go around saying, ‘And I did this.’” In fact, Ma recalled, when Ax told him that this article was happening, he said, “I don’t know why they’re doing this.”“I told him it’s because he’s old,” Ma said, bursting into laughter.Ma, left, and Ax in 1989.PhotofestMa — who, aside from the pianist Yoko Nozaki, Ax’s wife since 1974, has probably heard him play more than anyone — has a theory about why Ax is the way he is. “One thing that I can safely say, over the 50 years I’ve known him, is that he operates by a very strict code of conduct,” he said.The code, Ma went on, means that Ax never speaks ill of other pianists, and does what he can to bolster them instead. He insists on being kind, on looking at the brighter side of things. He goes to unusual lengths to build trust with fellow performers because the music, in the end, depends on it.“Somewhere along the line, he saw some things that he didn’t like, and he decided that he was not going to be that,” Ma explained. “He’s seen the consequences, and that’s why the code of conduct exists. It’s not some arbitrary thing.”AX WAS BORN in the Soviet Union in 1949, in what is now Lviv, Ukraine — though he still calls it Lwów, the Polish name it held in the interwar years. During the Holocaust, his parents, Joachim and Hellen, survived the concentration camps but lost, he said, “everybody.” They wed after the war and left for Warsaw when Ax was 7. He didn’t return to Lviv until six years ago, when he visited at the invitation of Philippe Sands, whose book “East West Street” movingly recounts the history of that contested city.Ax as a boy.Lauren Lancaster for The New York TimesAx with his parents, who left the Soviet Union and eventually settled in the United States.Lauren Lancaster for The New York TimesAx said that he only really remembered the opera house where he had first heard music, but Ma has heard him talk about a darker recollection, too: “I think he remembers a big parade in the town, and he knew the exact spot where it was. He backtracked and realized that that must have been when Stalin had died.”Warsaw led to Winnipeg, and Winnipeg to Manhattan, where the family settled into an apartment on the roof of a building across the street from Carnegie Hall. Ax was 12, and the hall, where he will play works by Beethoven and Schoenberg in April, became his playground. “I haunted the place,” he said.Great pianists crossed his path, older ones like Artur Rubinstein and younger artists such as Vladimir Ashkenazy, and he speaks of them with the excitement of a fan and the insight of a colleague. For Emil Gilels, he reserves telling enthusiasm.“I think he’s in a way the most sane pianist,” Ax said. “It’s so direct, absolutely self-confident, unarrogant, logical, beautiful, and just done just right. You walk out and you say, ‘That’s the way it should be.’ Of course, then you hear Richter, and you say, ‘No, that’s the way it should be.’ And then you hear Horowitz.”Ax studied at Juilliard with Mieczyslaw Munz, and endured several competitions before he triumphed in the Rubinstein. Even then, his virtues were not those typical of winners. For all his “dream technique,” as a critic described it in 1975, he immediately seemed a deeper musician than most. “His interpretations are warm, solid and straightforward,” Tim Page wrote in The Times in 1985, styling him as “a deeply satisfying pianist” — traits you can hear on his recording of the Chopin “Ballades” from the same year, or his later Haydn and Brahms.Ax performing with the conductor Esa-Pekka Salonen in 2011; the two will be reunited when they premiere a new concerto with the San Francisco Symphony in October.Barbara Davidson/Los Angeles Times, via Getty ImagesIf consistency has been Ax’s hallmark, he has never been entirely reducible to type. He dabbled with period instruments for a while, joining Charles Mackerras and the Orchestra of the Age of Enlightenment to record the Chopin concertos with brilliance and verve; his dedication to new music, which has seen him premiere scores by composers including John Adams and Missy Mazzoli, has been striking for a pianist of his stature.“I don’t think he sees it as a duty,” Salonen said of Ax’s commitment to contemporary works. “I think he thinks it’s normal. He thinks this is something that musicians do.”Chamber music, though, was with Ax from the start. He studied with the legendary tutor Felix Galimir as a teenager, then went on to form, among other groups, his duo with Ma, a piano trio with Ma and Isaac Stern, a piano quartet with the addition of Jaime Laredo, and, most recently, another trio with Ma and Leonidas Kavakos, with whom he is working his way through arrangements of the Beethoven symphonies.Ax’s fundamental approach to chamber music reflects his “devotion to where he landed, and to the aspirations of the system,” Ma said, to “the idea of republicanism, that you can be not hierarchical.” Their relationship was forged on jokes told in the Juilliard cafeteria, where they met when Ma was 15 and Ax was 21, but also on an ideal of equality in shared music, Ma said; this, at a time when pianists were still billed as accompanists to stars, or spoken of in the possessive sense.And it is chamber music, or more precisely playing with friends, that keeps Ax from retiring. He thinks about it more than he used to, he said; he missed giving concerts during the pandemic, but he also felt liberated from the deep anxiety that has always come with them.Ax in 1973.Christian Steiner/YCA“I get very nervous when I play, and I really wish I could get over it,” Ax said, confiding that the feeling can be worse now than before. “It’s not even a musical worry, it’s more about getting things right, you know — wrong notes and things like that.”Ax is modest even about these strains; Ma compared the pressure that Ax has always felt to that suffered by Martha Argerich, whose stage fright and perfectionism have led her largely to abandon solo recitals. But he suspects that Ax is not there yet.“Something in me tells me that he’s not going to stop, because performing also does something for him that is a pillar in his life,” Ma said. “It’s solidifying. I wouldn’t say that it’s like he needs it, but there’s a mutuality that’s good.”Ask Ma what makes Ax special as a pianist, and he will say that it is how he gives music the sense that everything has been thought through. He will note how revealing it is that Ax so adores Brahms, whose works are all about restraint, about reaching for things that are kept out of reach. He will marvel, with more than a hint of exasperation, that Ax still practices for four hours a day, that he is still so prone to doubt; he will grant, though, that doubt serves a purpose in Ax’s life.“He experiences that — he lets himself experience that — because he doesn’t want to say, ‘I know everything,’” Ma said.But Ma will say all this only when asked to elaborate. Otherwise, when he answers the question of what defines Ax as a pianist, he responds with just one word.“Musicianship.”Ax, left, with students from Kids 4 Harmony at Tanglewood.Hilary Scott More