If jazz for you means tradition and inheritance, maybe Herbie Hancock can change your mind. At the very least, he’d like to make you think twice about what “tradition” means. The pianist and composer has never been interested in upholding any stylistic conventions — “I like to break things,” he said when we spoke last week — but he does insist on a few trusty ideals. For him, jazz will always mean cross-pollination, adventurism and faith in what’s ahead.

After double-majoring in music and engineering at Grinnell College, Mr. Hancock joined Miles Davis’s band in 1963, close on the heels of his own debut album. Immediately, his piano playing represented some big new possibilities, connecting the shaded harmonies of Romanticism and the earth tones of the blues. By decade’s end, venturing into jazz-rock fusion, Mr. Hancock had figured out how to make synths and electric keyboards sound splintered and percussive. On albums like “Head Hunters,” “Thrust” and “Mr. Hands,” he put a kick of futurism into funk. A few years later, he turned right back around, returning to an acoustic format years before jazz’s neoconservative moment dawned.

More recently, Mr. Hancock’s fusion recordings from the 1970s and ’80s have become a touchstone for younger musicians, and he has welcomed these new acolytes into his own creative process. The crossover stars Terrace Martin and Thundercat will join Mr. Hancock onstage this Thursday, when he plays the Beacon Theater in New York.

Speaking from his home in Los Angeles, Mr. Hancock reflected on five decades at the vanguard of American music, and dangled promises of a new record — the product of that intergenerational exchange — which he said could begin trickling online, track by track, in the next few weeks. This would be a welcome development from Mr. Hancock, 79, who hasn’t released an album in nearly a decade, and has not made one devoted to original music in twice as long.