But he's not the "grand old man" nearing retirement taking a retrospective look back at a parade of his students through a Vaseline-coated lens of memories.
"Well, there is a little bit of that," Bresnick says, leaning back in the booth in a midtown diner where he has been sampling the apple pie. "But I don't think of myself in that role. For most of my teaching career I haven't been that much older than my students. It's only recently that students stopped calling me Martin. I'm not an authority figure, and our work revolves around a sense of communal discovery."
Bresnick likes to cite a famous Zen koan about teaching: "When the student is ready, the teacher appears."
But he is also highly attuned to the teacher-student interplay. He cites as an example his own studies with the great composer Gyorgy Ligeti (coincidentally, also a Jew).
"He was one of the greatest composers of our era," Bresnick says. "You learn from what he said about things, but also from what he did. I had that as an example. It's a way of saying, 'I am a real composer and people who study with me know that.'"
And it is as a composer that Bresnick wants to be known. He doesn't downplay the importance of teaching. On the contrary, it is an integral part of the ethos in which he was raised by his Yiddishist, socialist family.
"Teaching for me has always had a strong social component," he says. "It's part of giving back. I came out of a working-class family in the Bronx and was given a tremendous opportunity by others. I had it ingrained in me that you serve and have to share."
That's a lesson he was taught growing up in the Amalgamated Co-ops.
"I had a very devoted secular Jewish upbringing," Bresnick says. "My family were dedicated Yiddishists, I was sent to the Arbeiter Ring [Workmen's Circle] elementary school. My family ran the gamut politically from anarchist to liberal Democrats. I can still read Yiddish, and my aunt, Phylis Berk, is a well-known Yiddish singer. My mother, at 85, is still a professional storyteller who travels around the country talking about life in the shtetl."
It was a wonderful milieu in which to grow up, but not so hot for learning classical music, he admits.
"When I was little, my parents had very few classical records," Bresnick recalls. "I could memorize very quickly. Somewhere out there is a disk with me singing snippets of 'Barber of Seville' and 'The Nutcracker,' which were the two classical records they had at first. But they recognized that I had a talent, and they got me a couple of records when they could. The first time I ever heard a woodwind quintet was when I saw one live at the age of 9 on a school trip. I was completely dumbfounded by the bouquet of timbres."
It was the beginning of a career and a calling.
"I would listen to a Beethoven symphony when I was 7 and feel that I understood what was intended," he says. "I had some comprehension of the point of [writing] a symphony. And I felt, 'I can do it too.' I think I understood that it had something to do with what it means to be a human being.
"Music for many people at that age is a wonderful refuge. It offers them an ordered world. As a composer, you are making a world."
On the other hand, Bresnick was also participating in the world around him. As a teenager, he played rock guitar, graduated from the High School of Music and Art at 16 "as the youngest beatnik ever," he adds with a laugh, and was in grad school on the West Coast by 20. He saw Jimi Hendrix live, still admires Cream as "a great chamber-music group" and gigged as a working musician.
Even today, Bresnick "listens to everything," and his own compositions have a uniquely American eclecticism.
"It's Ivesian," he says, citing the great American maverick, Charles Ives, "It's totally democratic; everybody's got a right to belly up to the table and contribute."
Bresnick is a composer who can juxtapose the repetitive structures of minimalism with Stravinskian harmonies, who can use a Willie Dixon blues riff as the jumping-off point for a Brahmsian chamber piece, who can write movingly for marimba and orchestra.
If you ask him if there is any musical style that he would reject out of hand, he smiles and says, "I'm ready to accept almost any influence into my domain. My 'border guards' may ask them to show their passport first, though."
He admits to excluding only one major late-20th-century movement.
"I'm not that interested in conceptual art," he says. "Most of it has revealed itself to be poorer conceptually than any physically based art. I believe in the line from William Carlos Williams, 'No ideas but in things.' I like the pleasures of the physical world, and if I can embody something in the world of music, that's good enough."
Above all, he wants to be known as a composer first and foremost.
"No question about it," he says emphatically. "I've never thought of myself any other way. I love teaching and I'm glad to be well-regarded as a teacher, but I have no doubt of my own self-identity."
Anyone who hears Bresnick's music, live or on disk, will agree.
"The Essential Martin Bresnick" featuring the Bang on a Can All-Stars, is available on the Cantaloupe Records label.