Many theater artists have their opening night rituals, but it was Hal Prince’s approach to the day after that has long been the stuff of legend.

The morning after an opening, Mr. Prince, the inventive Broadway giant who died this week at the age of 91, would always schedule a meeting for his next show. Regardless of how the night went, there he was, bright and early the next morning, back at work. On to the next show. Always the next show.

It is difficult to overstate just how outsized an influence Mr. Prince has had on the trajectory of musical theater, an art form that has been regularly pronounced frivolous, irrelevant and obsolete, only to reinvent itself time and again. Many of the key moments of renewal and revolution in the past 65 years of musical theater were thanks to Mr. Prince himself.

Mr. Prince co-produced his first musical when he was 26. A charming comedy about a labor strike at a pajama factory, “The Pajama Game” did not exactly promise to be a commercial juggernaut. The production was in such dire financial straits that on opening night, Mr. Prince worked in the wings as an assistant stage manager to save a few dollars. “The Pajama Game,” of course, went on to become a smash success, launching Mr. Prince’s career — as well as that of a young choreographer named Bob Fosse — and earning Mr. Prince his first of 21 Tony Awards.