They’re brewing up a revolution down on Lafayette Street. And even theater reactionaries seem destined to be swept up in its doubt-defying ardor.

“Hamilton,” Lin-Manuel Miranda’s independent-minded new musical for the masses at the Public Theater, shot open like a streamlined cannon ball on Tuesday night. When one of the young rebels who populate this vibrant work says, “History is happening in Manhattan,” you can only nod in happy agreement.

“Happening” qualifies as both an adjective and a verb in this instance. Adapted from Ron Chernow’s 2004 doorstop biography of Alexander Hamilton — “the 10-dollar founding father without a father,” as the show’s lyrics put it — this speeding bio-musical has become the most fashionable (and unobtainable) ticket in town.

More important, “Hamilton,” which is directed with vigor and finesse by Thomas Kail and features the multifarious Mr. Miranda in the title role, persuasively transfers a thoroughly archived past into an unconditional present tense. Written and composed by Mr. Miranda, this work may reap the pattern-bestowing benefits of two centuries of hindsight. Yet it exudes the dizzying urgency of being caught up in momentous events as they occur.