After graduation he worked as a tutor and was an assistant teacher in Elizabethtown before studying for the ministry and obtaining a license to preach from the Presbytery of New Brunswick.

[1] In "The Numbers of Carlton", a set of 22 essays written in 1827-1828, Caldwell presented mathematical analyses to show that a building a central railroad for North Carolina would have economic and accessibility advantages over a system of canals.

[4] These essays, distributed as pamphlets and compiled in book form (in 1828) were influential in winning public support for the railroad.

[7] When the university declined his request to fund an astronomy program, he purchased telescopes from France with his own money in 1824.

[8] When he constructed the university's astronomical observatory in 1830 in his backyard, it was the first one built solely for educational purposes in the United States.