I always wince when people say they like classical music, “but not the new stuff.”

Comments like that are not only shortsighted — the old stuff was, in its time, of course new and often radical — but they also don’t take into account how varied contemporary music is, and how much of it is actually quite easy to love.

Take Anders Hillborg’s second piano concerto, “The MAX Concerto,” which had its local premiere with the New York Philharmonic on Thursday. Programmed somewhat arbitrarily between works by Sibelius and Rachmaninoff, it was more entertaining than either of them, and just as well crafted.

First performed in October in San Francisco, the concerto acknowledges the lineage of its genre with playfulness and reverence, and showcases Emanuel Ax, the soloist for whom it was written, by matching and pushing his brand of modest, underrated virtuosity. Likable without being eager to please, thrilling without shameless dazzle, it is, like Ax, enjoyable simply because it’s excellent.

And, crucially, Hillborg’s concerto works regardless of how familiar a listener is with his music, or any classical music for that matter. You could be aware of the piece’s form — its nine evocatively titled sections, performed as a single, 21-minute movement — or smile at “MAX,” a contraction of “Manny Ax.” You could pick up on the opening passage’s nod to Beethoven’s “Emperor” Concerto, or a later suggestion of Bach. Or you could just sit back and sense, intuitively, the genial majesty and pleasure coursing through it all.

One of the great nice guys in music, Ax is a pianist who, over his five-decade career, seems to have made no enemies while sitting quietly, comfortably near the top of his field, whether as chamber partner to Yo-Yo Ma or as a champion of contemporary works premiering a new concerto by John Adams — “Century Rolls,” whose section “Manny’s Gym” is one of the single most beautiful movements written in our time.

Ax’s style can easily be taken for granted, and some have found in his playing a kind of boring affability, though that may be something closer to wisdom; not for nothing is he a remarkable Brahms interpreter. Hillborg, brilliantly, has composed a mirror of Ax’s pianism that resists grandiosity and theatrical gesture. While “The MAX Concerto” is difficult — the solo part uses nearly all of the keyboard and demands cool precision — it also unfurls with graceful restraint.

The strings, for instance, most often appear as glassy foundation, delicately suspended and lustrous. At times, they align with the winds to take on the full-bodied warmth of an organ, with droning tones that slowly morph into flaring, mighty radiance. The piano joins them, but later has the final word with a robust chord that requires all of Ax’s 10 fingers, yet, true to his sound, comes off with unshowy tenderness.

Pity the conductor Eun Sun Kim, who on Thursday was making her Philharmonic debut leading the Hillborg, which was written with a different conductor in mind: Esa-Pekka Salonen, the music director of the San Francisco Symphony and her across-the-street neighbor in California. (She has been at the podium of San Francisco Opera since 2021.) Awkwardly, the Philharmonic’s program note even makes a point of Salonen’s relationship with the composer, as if he were the one leading the New York premiere.

Salonen’s friendship with Hillborg, which goes back more than 40 years, paid off in the San Francisco performances: In October, the concerto had an easygoing, organic flow, but in Kim’s account on Thursday, it felt at times slack and more explicitly episodic.

She had more of an opportunity to properly introduce herself elsewhere in the program. The evening opened with Sibelius’s “Finlandia,” briskly stated with brasses that were aggressive instead of noble — the piece’s nationalism a show of force rather than a declaration of pride. More persuasive was Rachmaninoff’s Symphony No. 3, which followed the Hillborg after an intermission.

Kim’s experience in the opera house, and her background learning from opera masters like Daniel Barenboim and Kirill Petrenko, served her in lending shape to Rachmaninoff’s searching score. And she made a case for a work that is rarely heard at the Philharmonic; before this week’s performances, the symphony had appeared on just a half-dozen subscription programs since its premiere in 1936.

Throughout, Kim maintained a lush dreaminess, made even dreamier as she freely interpreted every deviation from the tempo — every ritardando, rubato and rallentando — written into the score. And, with winking clarity but resisting overstatement, she teased out the music’s quickly passing references to, for example, the “Dies Irae” chant and jazzy idioms.

A late work, in style and in Rachmaninoff’s life, the Third Symphony has never been one of his most famous pieces, and often falls between the cracks of what came before (“Rhapsody on a Theme of Paganini”) and after (“Symphonic Dances”). When the Philadelphia Orchestra brought the symphony to New York a few days after its premiere, the critic Olin Downes wrote that it said nothing new and left the impression “of a certain diffuseness.”

Nearly a century later, we know that the Third Symphony did have something new to say, even if it reveals itself more slowly, and more subtly, than some of Rachmaninoff’s warhorses. True to itself and hardly obvious — similar to Ax’s pianism — it encourages us, like the best of music, to just keep listening.

New York Philharmonic

This program repeats through Saturday at David Geffen Hall, Manhattan; nyphil.org.