The book is a children's biography of Nathaniel Bowditch, a sailor and mathematician who published the mammoth and comprehensive reference work for seamen: The American Practical Navigator.

In Revolutionary War–era Salem, Massachusetts, a young Nat Bowditch, the smallest member of a sea-faring family, astounds his schoolteacher with his talent for mathematics.

He dreams of someday attending Harvard University but is forced by his family's financial hardships to quit school and work in his father's cooperage.

Upon the fulfillment of his servitude, he takes a job as a surveyor, which quickly evolves into a career as an officer and supercargo on various merchant ships.

[1] In a retrospective essay about the Newbery Medal-winning books from 1956 to 1965, librarian Carolyn Horovitz wrote of Carry On, Mr. Bowditch, Rifles for Watie, The Witch of Blackbird Pond and The Bronze Bow: "All have value, all are told skilfully.