Songfacts®:

• The Pirates of Penzance is a comic opera in two acts, with music by Arthur Sullivan and libretto by W. S. Gilbert. This comedic patter song from the work is perhaps the most famous song in Gilbert and Sullivan's oeuvre. It is sung by Major General Stanley at his first entrance, towards the end of Act I.
• The song lampoons the "modern" educated British Army officer of the later 19th century, a man with a well-rounded education in all subjects but the military.
  
  I'm very good at integral and differential calculus
  I know the scientific names of beings animalculous
  In short, in matters vegetable, animal, and mineral
  I am the very model of a modern Major-General
  
  Despite being very well-educated, this "modern" major-general has very little knowledge about military matters, favoring obscure facts about math and science.
• The character who sings "I Am the Very Model of a Modern Major-General" was said to be modeled on the real-life Field Marshal Garnet Joseph Wolseley, an Anglo-Irish officer in the British Army. Rather than being offended by the caricature, Wolseley would sing the song to amuse his friends.
• Because of a tide of unauthorized Gilbert & Sullivan productions in America, the British pair opened The Pirates of Penzance in New York - their only premiere outside London.