He subsequently studied mathematics at Yale University, where he was a member of Skull and Bones[1]: 47–8  and obtained a BA in 1883 and the PhD in 1885 with a thesis supervised by Hubert Anson Newton, on some work of William Kingdon Clifford and Arthur Cayley.

Newton encouraged Moore to study in Germany, and thus he spent an academic year at the University of Berlin, attending lectures by Leopold Kronecker and Karl Weierstrass.

When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1932.

His work on axiom systems is considered one of the starting points for metamathematics and model theory.

In 2002, the American Mathematical Society established the E. H. Moore Research Article Prize in his honor.