He grew up with his parents, maternal grandmother and his brother in a racially mixed neighborhood; in 1900, in his block, there were three Black and five white families.

Cox was offered a scholarship to study violin at the Prague Conservatory of Music, but chose to pursue his interest in mathematics instead.

Besides mathematics, Cox also took courses in German, English, Latin, history, hygiene, chemistry, education, philosophy and physics.

Cox returned to pursue a career in teaching, as an instructor of mathematics at a high school in Henderson, Kentucky.

In the autumn of 1919, he was appointed as a professor in physics, chemistry and biology at Shaw University in Raleigh, North Carolina where he also became chairman of the Department of Natural Sciences.

Cox received the Erastus Brooks fellowship in Mathematics ($400 per year) in autumn 1924 and followed Williams to McGill University in Montreal.

[citation needed] He moved back to Cornell in the spring semester of 1925, and finished his dissertation, The polynomial solutions of the difference equation af(x+1) + bf(x) = φ(x), in the summer of the same year.

[1] On 16 September 1925, Cox began teaching mathematics and physics at the then all-black, poorly funded West Virginia State College.

Among his students was his son Elbert Lucien Cox, and William Schieffelin Claytor, the third African-American to get a Ph.D. in mathematics.

He gave the department a great deal of credibility; primarily because of this personal prestige as a mathematician, as being the first black to receive a Ph.D. in mathematics, because of the nature and kinds of appointments to the faculty that were made while he chaired the Department, and because of the kinds of students that he attracted to Howard to study mathematics at both the undergraduate and master's levels.

The Elbert F. Cox Scholarship Fund, which is used to help black students pursue studies, is also named after him.

Mathematician Talitha Washington championed Cox leading to the November 2006 unveiling of a plaque in Evansville[5] commemorating his pioneering achievement.