In 1924, the University of Oslo awarded him the Ph.D. for a thesis titled Zur Theorie der algebraischen Körper, supervised by Thoralf Skolem.

Ore gave an American Mathematical Society Colloquium lecture in 1941 and was a plenary speaker at the International Congress of Mathematicians in 1936 in Oslo.

As a teacher, Ore is notable for supervising two doctoral students who would make contributions to science and mathematics: Grace Hopper, who eventually became a United States rear admiral and computer scientist and who was a pioneer in developing the first computers, and Marshall Hall, Jr., an American mathematician who did important research in group theory and combinatorics.

In 1930, the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether.

He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject.

Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel.