this work. In more elementary number theory, Ore's harmonic numbers are the numbers whose divisors have an integer harmonic mean. As a teacher, Ore is notable for teaching mathematics to two doctoral students who would make contributions to science and mathematics: Grace Hopper, who would eventually become a United States rear admiral and computer scientist, who was a pioneer in the development of 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's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life. He wrote two books on the subject, one on the theory of graphs and another on their applications. Within graph theory, Ore's theorem is one of several results proving that sufficiently dense graphs contain Hamiltonian cycles. 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. Books by Ore Les Corps Algébriques et la Théorie des Idéaux (1934) L'Algèbre Abstraite (1936) Number Theory and its History (1948) Cardano, the Gambling Scholar (Princeton University Press, 1953) Niels Henrik Abel, Mathematician Extraordinary (U. of Minnesota Press, 1957) Theory of Graphs (1962) Graphs and Their Uses (1963) The Four-Color Problem (1967) Invitation to Number Theory (1969) See also Deficiency (graph theory) Geodetic graph Magma (algebra) Ore algebra Ore condition Ore's conjecture Ore extension Ore number Ore's theorem Schwartz–Zippel lemma Universal algebra References External links . The source for much of this entry. 20th-century Norwegian mathematicians Combinatorialists Lattice theorists Yale University faculty Historians of mathematics 1899 births 1968 deaths Yale Sterling Professors