Craig first studied civil engineering at Lafayette College in Pennsylvania, where a teacher William J. Bruce was a mentor to him.
He became an instructor at Johns Hopkins that year, but also took up work at the United States Coast and Geodetic Survey.
After 1881 Craig was totally committed to Johns Hopkins, particularly anticipating Arthur Cayley's lectures on theta functions when he came over for the Spring semester of 1882.
Besides the calculus courses, Craig taught differential equations, elliptic functions, elasticity, partial differential equations, calculus of variations, definite integrals, mechanics, dynamics, hydrodynamics, sound, spherical harmonics, and Bessel functions.
[2] When the American Journal of Mathematics was launched in 1877 Craig was tasked with recording expenses, as these were underwritten by Johns Hopkins University.