Sixty-five years ago, historian John William Ward had the insight that for better or worse, Andrew Jackson’s victory over the British at New Orleans on January 8, 1815, made him the “Symbol for an Age.” There are those who would argue that the battle also made him president fourteen years later; but Jackson’s rise was more complicated—and far more calculated—than these narratives suggest.

New Orleans was the culmination of Jackson’s already impressive military career, and it established the man in …