Dave Brubeck is 91 today, which if you buy into the theory that jazz made its recorded debut in 1917, when the Original Dixieland Jazz Band cut “Livery Stable Blues”, means he’s pretty much as old as recorded jazz itself.

For listeners coming to jazz via classical music, Brubeck remains the obvious point of entry. Albums like Brandenburg Gate Revisited and Bernstein Plays Brubeck Plays Bernstein, the Brubeck Quartet’s 1960 collaboration with Leonard Bernstein and the New York Philharmonic, have clear points of connection back to the European mother music. In their formal construction, Brubeck classics like ‘Blue Rondo à la Turk’, ‘The Duke’ and ‘Three Get To Ready’ riff as fulsomely off Brubeck’s compositional studies with Darius Milhaud as anything explicitly to do with jazz tradition. And yet here’s the big Brubeck mystery. This prodigiously popular musician, whose hit record ‘Take Five’ migrated from geeky experiment to jazz anthem, who celebrated his 80th and 85th birthdays on stage at the Barbican with the London Symphony Orchestra – how come his music can speak to an audience with little interest in jazz, while also spurring on culturally marginalised Black jazz musicians like Anthony Braxton, Andrew Hill and Cecil Taylor early on in their careers?

This question gets to the core of why Brubeck, for this writer, remains such a vital presence. Brubeck is a problem. Solutions in jazz, and music generally, are fair enough but too often lean on reflex impulses – technique as a directory of pre-learnt finger manoeuvres that guarantee you safe passage between two points in time. In Brubeck’s playing, though, standard solutions rarely apply because he’s not interested in putting together music as it already exists/once existed.

If the harmonic basis of your music is founded on Bach and the blues; if you play left hand patterns rooted in Jelly Roll Morton and Fats Waller while your right hand arpeggiations flow out of Chopin and Rachmaninov; if you’re a composer who fixes forms at the same time as being a sonic explorer who lets dense chromatic harmony spill over into clusters that have no function other than as sound, these different strains are never likely to coexist smoothly and seamlessly. You’ve unlocked a Pandora’s keyboard of cultural tensions and Brubeck is man enough to admit that, on one level, his music is stylistically inconsistent. A clean-cut, unified, categorisable, explainable ‘musical product’? No it’s not – but that’s precisely what is so inspiring about it.

The misnomer that Brubeck is a ‘classically taught’ pianist is at the root of many misunderstandings. There was a classically taught pianist Brubeck, but it wasn’t Dave. It was his mother Bessie who travelled to London in 1926 to study with Dame Myra Hess and Tobias Matthay. Any West Coast American in the mid-1920s travelling to London for piano lessons with Hess and Matthay showed matchless devotion to the cause, and later Brubeck’s mother would take lessons with Henry Cowell. But Dave resisted his mother’s attempt to teach him classical piano. He realised he had an innate ability to copy by ear his mother’s playing, and that of her other students, and fuse that with the jazz he was hearing on the radio. He was already making music ‘composed’ of other music through trial-and-error improvisation.

When Brubeck uttered his famous statement that he’s essentially ‘a composer who plays piano’ it was turned against him as an admission of technical inadequacy. But Brubeck was touching on deep truths about the relationship between jazz composers and their instruments. In classical performance the division of labour between composer and performer has historically been set in stone; it’s up to the composer to do the conceptualising on paper, and the performer’s role is to reproduce the resulting notes within clear boundaries known as ‘interpretation’.

As Brubeck performs his classic piece ‘The Duke’, such is its integrity as a through-conceived composition that he often chooses to play it ‘straight’, without improvisation. The bass part passes through all 12 key centres, and the piece is carefully balanced between its opening theme and an answering section, with über-sophisticated, meticulously worked out, inner harmonic movement. There’s nothing much improvisation could bring to it. Orchestrating ‘The Duke’ for an ensemble of classical musicians would be wholly feasible, and a transcribed version would remain a fulfilling musical experience.

But Brubeck’s ‘Blues for Newport’ isn’t so much an autonomous composition, more an invitation for improvisation. Brubeck’s theme consists of a melodic blueprint that only properly flowers as a performance gathers steam. If transcribed for classical players, it’s likely the result would be inconsequential. The musicians would grind to a tongue-tied halt after the 12 bar theme, lacking the cultural tools to generate the performance onwards through improvisation.

And when Brubeck improvises on ‘Blues for Newport’, juxtaposing radically different types of material, and making conscious decisions about where to put key dramatic moments, it’s enough to pose the question, which is more composed – the composition or the improvisation?

Cecil Taylor chose to sit behind Brubeck in New York jazz clubs during the mid-1950s to figure out his left hand patterns, and Anthony Braxton still cites Brubeck as a model for the musician he always aspired to be, because Brubeck tackles these awkward composition/improvisation questions head on. ‘Blue Rondo à la Turk’ is essentially a collage of a formalist composition in rondo form – famously toying with shifting groupings of 9/8 – interlocked with blues choruses left open for improvisation. The composed material and the improvisation comment on each other; Brubeck the jazzman and Brubeck the composer existing on stage together.

When I hear Brubeck’s cluster-packed solo on ‘Pick Up Sticks’ from his hit record Time Out, or remember Brubeck concerts I’ve attended where harmonic frameworks hang in the air as general points-of-reference rather than being explicitly stated (check out ‘Truth’ from Brubeck’s 1973 album We’re All Together For The First Time or ‘I Got Rhythm’ from 40th Anniversary Tour Of The UK to hear what I mean) part of me wonders how Brubeck manages to be popular while sounding like that. Then I remember his classical background.

It’s his composer’s sensibility that allows it to work. Brubeck concerts are exhilarating because neither the audience, nor Brubeck himself, knows where his imaginative experiments will lead him. ‘Take Five’ might be neoclassically elegant, or roar towards stride piano, or scatter time like a Sun Ra collective improvisation. A seemingly innocuous standard like ‘You Go To My Head’ or ‘These Foolish Things’ will almost certainly have its inner harmonies re-built; I’ve even got an ‘unofficial’ Brubeck ‘Foolish Things’ that without warning jumps into double time boogie-woogie, before settling back into a languid ballad tempo. Why? Simply because Brubeck’s composer’s brain thought of it and then his improviser’s fingers made it work.

The composer side of Brubeck gives his improvisations a particular sense of direction and structure. Key centres are juxtaposed, re-jigged and forced to coexist. Harmonic patterns develop into climax sections with obvious traces of Chopin, Liszt and Brahms. Romantic gestures bump into rude stride piano; like Stravinsky, when filtered through Brubeck’s brain, this material comes out the other side branded with a new identity. Strange happenings, adventurous stylistic connections. Brubeck has demolished the usual boundaries people use to orientate themselves around music. He’s a fantastic problem to have.