John Luther Adams has never been inside the main auditorium of Carnegie Hall. It’s not a fact that distinguishes him greatly in his hometown, Fairbanks, Alaska, where he has lived for four decades. There Mr. Adams, now 61, was first known as an environmental activist who helped secure passage of the Alaska Lands Act in 1980, before dedicating himself full time to music and building a small but fervent following as a composer of hypnotically immersive musical landscapes. But when Mr. Adams attends his first concert in Carnegie Hall’s Stern Auditorium on Tuesday, he will be in the unusual position of doing so as a newly minted Pulitzer Prize laureate hearing his winning work, “Become Ocean,” played there for the first time.

“It’s certainly nothing I ever aspired to,” Mr. Adams said of the Pulitzer for music in an interview at a coffee shop in Manhattan Valley. (He and his wife, Cynthia, recently bought an apartment nearby that they refer to as their “urban cabin.”) “But there’s no question of it in any way changing what I do. The artist Richard Serra says there’s a point at which you’re working from within the art itself because all your influences have been assimilated and you’re just following the work wherever it leads you. I have a very strong sense of that adventure and of my obligation to the work.”

Adventure and obligation combine in remarkable ways in Mr. Adams’s music. His studies at CalArts in the 1970s left him with a zest for experimentation, particularly with structure, resulting in interlocking patterns and conflicting tempos in much of his music. His performance instructions sometimes turn the concert hall inside out and upend the traditional orchestral setup.

The sense of obligation arises from Mr. Adams’s commitment to the environment. Abandoning his political work to focus on composition required a leap of faith, he said. “Implicit in that leap was the faith that in its own way music can matter every bit as much as politics, and perhaps more,” he explained. “I’ve been trying to make good on that leap ever since, and if anything, that faith has deepened. I believe now that art is more essential to solving the problems facing the human animal than politics.”