Nathaniel Bowditch loves to work with numbers. School is Nat's favorite time. Unfortunately Nat must give up his dream to go to Harvard when he must quit school to work for his father. Later, he becomes an indentured servant, working in a ship's chandlery. In spite of his situation, Nat continues his education by teaching himself. He works all day in the chandlery and in the evenings fills his notebooks with everything he wants to learn.

Nat's diligence pays off. When Nat's nine-year indenture is through, he is given the opportunity to go to sea where the things he has learned may be put to use. Sailing is dangerous, not only because of enemies on the high seas, but because - Nat discovers - many of the books and tables sailors use for navigation have errors - errors that cost lives. With the same diligence he used to teach himself, Nat begins to compile information for a new book to correct these errors and give every sailor knowledge of navigation.

Carry On, Mr. Bowditch is the biography of a man who, although unable to finish school, educated himself so thoroughly that sailors still use the book he wrote in the eighteenth century.