Øystein Ore
Encyclopedia
Øystein Ore was a Norwegian
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...

 mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

.

Life

Ore was graduated from the University of Oslo
University of Oslo
The University of Oslo , formerly The Royal Frederick University , is the oldest and largest university in Norway, situated in the Norwegian capital of Oslo. The university was founded in 1811 and was modelled after the recently established University of Berlin...

 in 1922, with a Cand.Scient. degree in mathematics. In 1924, the University of Oslo awarded him the Ph.D. for a thesis titled Zur Theorie der algebraischen Körper, supervised by Thoralf Skolem
Thoralf Skolem
Thoralf Albert Skolem was a Norwegian mathematician known mainly for his work on mathematical logic and set theory.-Life:...

. Ore also studied at Göttingen University, where he learned Emmy Noether
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...

's new approach to abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

. He was also a fellow at the Mittag-Leffler Institute in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

, and spent some time at the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...

. In 1925, he was appointed research assistant at the University of Oslo.

Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...

’s James Pierpont
James Pierpont (mathematician)
James P. Pierpont was a Connecticut-born American mathematician. His father Cornelius Pierpont was a wealthy New Haven businessman. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in...

 went to Europe in 1926 seeking to recruit European research mathematicians. In 1927 Ore was appointed Assistant Professor of Mathematics at Yale, becoming Associate Professor in 1928, and full Professor in 1929. In 1931 he became Sterling Professor
Sterling Professor
A Sterling Professorship is the highest academic rank at Yale University, awarded to a tenured faculty member considered one of the best in his or her field...

 at Yale, a position he held until his retirement in 1968.

Ore was an AMS Colloquium Lecturer in 1941 and plenary speaker at the International Congress in 1936 in Oslo. He was also elected to the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...

 and the Oslo Academy of Science. He was also among the founders of the Econometric Society
Econometric Society
The Econometric Society is an international society for the advancement of economic theory in its relation with statistics and mathematics. It was founded on December 29, 1930 at the Stalton Hotel in Cleveland, Ohio....

.

Ore visited Norway nearly every summer. During World War II, he was active in the movements "American Relief for Norway" and "Free Norway". In gratitude for the services rendered to his native country during the War, he was decorated in 1947 with the Knight Order of St. Olav
The Royal Norwegian Order of St. Olav
The Royal Norwegian Order of St. Olav is a Norwegian order of chivalry that was instituted by King Oscar I of Norway and Sweden on August 21, 1847, as a distinctly Norwegian order. It is named after King Olav II, known for posterity as St. Olav. Nobility was abolished in Norway in 1821...

.

In 1930, Ore married Gudrun Lundevall; they had two children. He had a passion for painting and sculpture, collected ancient maps, and spoke several languages.

Work

Ore is known for his work in ring theory
Ring theory
In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...

, Galois connections, and most of all, graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

. His early work was on algebraic number field
Algebraic number field
In mathematics, an algebraic number field F is a finite field extension of the field of rational numbers Q...

s, how to decompose the ideal
Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like "even number" or "multiple of 3"....

 generated by a prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

 into prime ideal
Prime ideal
In algebra , a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers...

s. He then worked on noncommutative ring
Noncommutative ring
In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, if R is a noncommutative ring, there exists a and b in R with a·b ≠ b·a, and conversely.Noncommutative rings are ubiquitous in mathematics, and occur...

s, proving his celebrated theorem on embedding a domain
Domain (ring theory)
In mathematics, especially in the area of abstract algebra known as ring theory, a domain is a ring such that ab = 0 implies that either a = 0 or b = 0. That is, it is a ring which has no left or right zero divisors. Some authors require the ring to be nontrivial...

 into a division ring
Division ring
In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a non-trivial ring in which every non-zero element a has a multiplicative inverse, i.e., an element x with...

. He then examined polynomial ring
Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the Hilbert basis theorem, to the construction of...

s over skew fields, and attempted to extend his work on factorisation to non-commutative rings.

In 1930 the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...

. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff
Garrett Birkhoff
Garrett Birkhoff was an American mathematician. He is best known for his work in lattice theory.The mathematician George Birkhoff was his father....

, 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
Equivalence relation
In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell...

 and closure relation
Closure operator
In mathematics, a closure operator on a set S is a function cl: P → P from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S....

s, Galois connection
Galois connection
In mathematics, especially in order theory, a Galois connection is a particular correspondence between two partially ordered sets . The same notion can also be defined on preordered sets or classes; this article presents the common case of posets. Galois connections generalize the correspondence...

s, and finally to graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, which occupied him to the end of his life.

Ore had a lively interest in the history of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....

, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel
Niels Henrik Abel
Niels Henrik Abel was a Norwegian mathematician who proved the impossibility of solving the quintic equation in radicals.-Early life:...

.

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)

External links

. The source for much of this entry.
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