[1] He worked as a cryptanalyst and Japanese translator for the Office of the Chief of Naval Operations during World War II.

During 1949–1951 he held an appointment at the Institute for Advanced Study during which he proved Moise's theorem that every 3-manifold can be triangulated in an essentially unique way.

[5] Moise joined the School Mathematics Study Group when it started in 1958, as a member of the geometry writing team.

[1][5] Moise retired from Queens College in 1987 and started a second career studying 19th century English poetry.

[3] In the middle and late 1960s, Moise was among the few members of the senior faculty at Harvard University who strongly and publicly opposed the Vietnam War.