Skolem, Albert Thoralf
SKOLEM, ALBERT THORALF
(b. Sandsvaer, Norway, 23 May 1887: d. Oslo, Norway, 23 March 1963)
Skolem was the son of Even Skolem, a teacher, and Helene Olette Vaal. He took his examen artium in Oslo in 1905 and then studied mathematics (his preferred subject), physics, chemistry, zoology, and botany. In 1913 he passed the state examination with distinction.
In 1909 Skolem became an assistant to Olaf Birkeland and in 1913–1914 traveled with him in the Sudan to observe the zodiacal light. Then, in 1915–1916, he studied in Göttingen. In the latter year he returned to Oslo, where he was made Dozent in 1918. He received his doctorate in 1926.
Skolem conducted independent research at the Christian Michelsens Institute in Bergen from 1930 to 1938, when he returned as full professor to the University of Oslo. He retired in 1950. On several occasions after 1938 he was a visiting professor in America. Skolem served as editor of various mathematical periodicals and was a member of several learned societies. In 1962 he received the Gunnerus Medal in Trondheim.
Skolem published more than 175 works. His main field of research was the foundations of mathematics: but he also worked on algebra, number theory, set theory, algebraic topology, group theory, lattice theory, and Dirichlet series. Half of his works are concerned with Diophantine equations, and in this connection he developed a p-adic method. In 1920 he stated the Skolem-Löwenheim theorem: If a finite or denumerably infinite sentential set is formulable in the ordinary predicate calculus, then it is satisfiable in a denumerable field of individuals.
Skolem freed set theory from Cantor’s definitions. In 1923 he presented the Skolem-Noether theorem on the characterization of the automorphism of simple algebras. According to this theorem, it is impossible to establish within a predicate calculus a categorical axiom system for the natural numbers by means of a finite or denumerably infinite set of propositions (1929).
Most of Skolem’s works appeared in Norway, although his monograph Diophantische Gleichungen(1938) was published in Berlin. With Viggo Brun, he brought out a new edition (1927) of Netto’s textbook on combinatorial analysis, for which he wrote all the notes and an important addendum.
Skolem also investigated the formal feasibility of various theories and concerned himself with the discovery of simpler, more constructive demonstrations of known theorems. He was especially influenced by the mathematicians Sylow and Thue.
For a bibliography of Skolem, see T. Nagell. “Thoralf Skolem in Memoriam,” in Acta mathematica110 (1963), which lists 171 titles. On his life, see also Erik Fenstadt. “Thoralf Albert Skolem in Memoriam,” in Nordisk Mathematisk Tidsskrift, 45 (1963), 145–153, with portrait; and Ingebrigt Johansson. “Minnetale over Professor Thoralf Skolem,” in Norske Videnskåps-Akademi i Oslo Arbok 1964 (1964), 37–41.
"Skolem, Albert Thoralf." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (October 19, 2018). http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/skolem-albert-thoralf
"Skolem, Albert Thoralf." Complete Dictionary of Scientific Biography. . Retrieved October 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/skolem-albert-thoralf
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.