TO PUT Dave Brubeck in a box was an unwise thing to do. He'd just jump right out again, big, broad and strong, with those horn-rimmed glasses and that crazy, slightly cross-eyed smile. Call him cool, and he'd tell you that many of his jazz arrangements were so hot, they sizzled. Lump him with players of white west-coast jazz, and he'd object that he felt more black than white. Suggest he was influenced by the pelting, intellectual strain of bebop that took over jazz in the 1940s, and he would say nope, he didn't listen to it; he only ever wanted to do his own thing. Call him the usher of a new jazz age, put him on the cover of Time magazine, where he landed in 1954, and he was crestfallen. Duke Ellington deserved all that, he said, but not him. His contrarian ways went further. Give him a few bars of Beethoven, and he'd weave a jazz riff through it; but put him in the middle of a jazz set, and he would come up with classic counterpoint as strict as the "Goldberg Variations." Sing him a tune in C, and his left hand would play it in E flat; give him a jazz line in standard 4/4 time and he would play 5/4, 7/4, even 13/4 against it, relentlessly underpinning the adventure with big fat blocks of chords. He was a jazzman who struggled to read notation and who graduated on a wing and an ear from his college music school; and he was also, in later years, a composer of cantatas and oratorios who was proud to have written a Credo for Mozart's unfinished "Mass in C minor." The musicians he picked for his quartet, which dominated the popular jazz scene from 1951 to 1967, were chosen because they could break out of the box like him: Paul Desmond on feather-light, floating alto sax, Joe Morello razor-sharp and witty on drums, Eugene Wright rock-solid on bass. Their greatest success, an album called "Time Out" (1959) that sold more than 1m copies, was a collection of breezily poly tonal pieces in wild time signatures, centring on a Desmond piece called "Take Five" written in teasing 5/4, and "Blue Rondo à la Turk," devised by Mr Brubeck after hearing street musicians playing in 9/8 in Istanbul. These two pieces alone consolidated the quartet's fame on campuses and in clubs all over America; but Columbia Records refused to release the album for a year, just baffled, said Mr Brubeck impatiently, by the fact that it broke so many rules. It did, but hey, it sounded good. Whenever he sat down at the piano - an instrument as satisfying, to him, as a whole orchestra - his aim was to get somewhere he had never got before. It didn't matter how tired he was, how beat-up he felt. He wanted to be so inspired in his explorations that he would get beyond himself. He liked to quote Louis Armstrong, who once told a woman who asked what he thought about as he played: "Lady, if I told you, your mind would explode." In his own words, he played dangerously, prepared to make any number of mistakes in order to create something he had never created before. Horsebeat and heartbeat Several people had set him on this path. His mother had first taught him piano when he preferred to be a rodeo-roper; her rippling playing of Chopin round the house he remembered in a piece called "Thank You." His platoon commander in 1944, having heard him doodling on a piano, kept him away from the front line. And Darius Milhaud, his teacher after the war, taught him to see jazz as the natural idiom of America and the music of free men. Mr Brubeck believed seriously in jazz as a force for democracy: in post-Nazi Germany, in the Soviet Union, in the fragile post-war world (where he toured on behalf of the State Department) and in America's South, where he insisted on performing with his black bassist and, when he could, pushed him to the front of the stage. Yet his mission was never to make jazz freer or more popular; it was to make music, pure and simple, any way he could. He sang his first polyrhythms against the steady trot of his horse as he rode round the 45,000 acres near Concord, California, where his father managed cattle. In high school, playing at rough miners" dances in the foothills of the Sierras, he would riskily "screw up the shuffle" by adding triplets to it. He wrote on the road, dreaming up "Unsquare Dance" (in 7/4) while driving to New York, and composing "The Duke," his tribute to Ellington, against the beating windscreen wipers of his car. All this, with his use of folk songs and hymns and blues and birdcalls, his little snatches of homage to George Gershwin or Aaron Copland, and the freight-train urging of his playing, gave his jazz a flavour less of smoky dives than of open skies and plains. Critics attacked him for getting rich from it. He said he had never wanted more than the union scale. They said he was too "European," too college-focused, that his music couldn't be danced to and hadn't got swing; he pointed out the happy feet tapping at his concerts, and the number of records he sold. Above all they found it hard to believe that the most successful jazz in America was being played by a family man, a laid-back Californian, modest, gentle and open, who would happily have been a rancher all his days - except that he couldn't live without performing, because the rhythm of jazz, under all his extrapolation and exploration, was, he had discovered, the rhythm of his heart.