Mansfield was born in New Haven, Connecticut, son of a sea captain, Stephen Mansfield. He graduated from Yale in 1777, and taught in New Haven and Philadelphia. In 1800 he married Elizabeth Phipps, daughter of an American Naval Officer. In 1801 he had printed some scientific papers titled Essays Mathematical and Physical, which were brought to Jefferson's attention by Senator Abraham Baldwin. Jefferson appointed Mansfield captain of engineers, so he might become a professor at West Point. After moving to West Point, Mansfield was appointed Surveyor General in Summer of 1803. Jefferson was dissatisfied with the performance of Rufus Putnam, whose surveys in the Congress Lands of Ohio were poorly executed. Putnam was also a Federalist. In 1801, the position had been offered to Andrew Ellicott