Maggie Smith’s two Oscar wins show her towering talent — beyond Harry Potter or Downton Abbey

Headlines about the death of Maggie Smith on Friday at age 89 have zeroed in on the more recent fame she enjoyed in the United States, as the acid-tongued dowager countess in “Downton Abbey” or Professor Minerva McGonagal in the “Harry Potter” franchise.

But Smith was one of the finest British stage and screen actors of her generation, receiving nominations or trophies for her performances in theater and in movies, going back to the 1960s. Like every British thespian, she did her share of Shakespeare...