How do you solve a problem like John Zorn?

The man is uncategorisable, unpindownable, and – because he almost never gives interviews – unaskable. Composer, impresario, producer, saxophonist, general mover-and-shaker of things musically radical, he's all over the place, constantly reinventing himself, constantly trying out something new.

Start with the bare bones. Zorn was born in 1953 to an artsy Jewish family in Queen's, New York. As a teenager he played bass in a surf band and taught himself the rudiments of harmony and orchestration. He picked up the saxophone at college in Missouri and became increasingly seduced into free jazz and performance art. Back in New York in the mid-1970s he set to organising gigs in lofts and makeshift spaces around Manhattan and founded a performance art collective called Theatre of Musical Optics that held two fingers aloft to any notion of genre or boundary.

From then on Zorn would play, write, write about, record and curate all manner of music. Hardcore punk, metal, cartoon, contemporary classical, klezmer – you name it, Zorn has probably tried it. He names Lee Konitz among his all-time heroes and made his breakthrough recording with a disc of Enio Morricone covers. As a producer he founded The Stone, an avant-garde jazz venue in Alphabet Village, and, later, the experimental record label Tzadik. As a composer he devised a series of groundbreaking game pieces involving strict rules, role playing and flashcard instructions. As a performer his regular outlets included the klezmer quartet Masada (with Joey Baron, Dave Douglas and Greg Cohen) and the outlandish punk band Naked City (with Baron, Bill Frisell, Fred Frith and Wayne Horowitz). He also had a knack of drawing together musicians of any breed and eking out the common ground. "People are so obsessed with the surface they can't see the connections," he once said. "But they are there."

This Saturday, to celebrate his 60th birthday, the BBC Scottish Symphony Orchestra and their principal guest conductor Ilan Volkov devote an entire evening to the comparatively classical side of Zorn. Though he began composing in the 1970s, the programme focuses on music from the last couple of decades: there are two pieces from 1996 – Kol Nidre and Orchestra Variations; there's a song for soprano and orchestra, La machine et de l'être, written in 2000; there's the sprawling Aporias (1994), originally a 40-minute studio album for piano, children's choir (here voices from St Mary's Cathedral, Edinburgh) and orchestra; and there's a new piece, suppôts et suppliciations, which has been specially commissioned by the BBC and receives its world premiere on Saturday.

Is there any way to explain what the evening might sound like? "When it comes to summing up a trademark Zorn style, I'm at a loss," says Volkov. "There are too many disparate styles to pin him down. Zorn describes himself as an 'additive' composer – he said 'the entire storehouse of my knowledge informs everything I do'. So there are elements of homage in his work, but they're not glaring like in Berio's Sinfonia. What we'll mostly hear in this portrait concert is Zorn's orchestral voice. With the exception of Kol Nidre, which emerged from the Masada project, the pieces are in a modernist vein."

Despite his melting pot approach, and his alter ego as a fearless improviser, Zorn doesn't incorporate improvisation into his orchestral music: every note is written out in the parts. "He's devoted to the idea of a big community of players, crossing the boundaries of classical and electronic and jazz and rock and roots," says Volkov. "But there are some techniques he isn't interested in mixing up. It's difficult for orchestral musicians to improvise in a large group. For Zorn, if he's got the chance to work with an orchestra, he wants to get the best he can out of them."

In many ways that phrase sums up Zorn's approach to working with all musicians. "Part of the strength of how he works is that he goes off in all directions," Volkov says. "And he gathers the best musicians around him. That's a special quality. He's an ambitious person. He's able to look at a group of players and to see how to tap into their particular talents. That's why he's so good at collaborations."

Volkov describes Zorn's classical output as "seriously influential. Look at the Game Pieces he wrote in the 1970s – these are still really relevant. A lot of people are trying this kind of structured improvisation now, but they all need to take into account what Zorn did with these pieces back then. He's been writing classical music for more than 40 years, but it's only recently his classical music has started getting programmed. And there's never been a concert entirely dedicated to his music – until now."

Why the delay? Volkov shrugs. "Maybe it's because he's so multifaceted he falls between the cracks. He's not published by a conventional publisher like Faber or Universal or Schott, so he gets overlooked by conventional orchestras."

It's not for a lack of engagement on Zorn's part. Volkov says when they first began discussing the portrait concert and considered a programme that would set Zorn's work in a broader context, he asked Zorn what kind of music he'd like to be programmed alongside. "He answered: Carter, Ives, Boulez. He really knows his stuff. He knows the classics of modern repertoire, but is totally on top of the rarities too. And look at the classical music he's been releasing on his Tzadik label – people like Frank Denyer and Jerry Hunt. Their music is important but obscure."

Incidentally, The Herald did test the waters for an interview with Zorn, but was given the expected response: he does not speak to the press. "He's hands-on with everything in his life," says Volkov. "He's a workaholic, someone who can't delegate very well. And he doesn't like other people writing about what he does. He likes to keep it mysterious. Even when I've contacted him about this programme he's kept his discussion very vague. It's not that he doesn't believe in writing about music; he has published several books of collected writing about music. But when it comes to his own music, he just likes to keep it vague."

Ilan Volkov and the BBC Scottish Symphony Orchestra play the music of John Zorn at City Halls, Glasgow, on Saturday.