Thoralf Albert Skolem.

Thoralf Albert Skolem (pronounced "SKOHlum") was born on May 23, 1887, in Sandsvaer, Norway. He was the son of Even Skolem and Helene Vaal. His father was an elementary school teacher, but most of the family were farmers. Skolem passed the concluding examinations of the Norwegian Gymnasium in 1905 and immediately went to the University of Oslo to study mathematics and science. He was graduated with the highest distinction in 1913 after completing a dissertation on the algebra of logic. By this time, he had already spent four years as an assistant to physicist Olaf Kristian Bernhard Birkeland, with whom he published his first scientific papers. Skolem spent another two years as Birkeland's assistant before going abroad to Göttingen, Germany, in 1915 to study for a year. From 1916 to 1918, he was a research fellow at the University of Oslo, and then he was appointed to a newly created position as assistant professor. Mathematical logic was in a state of chaos at the beginning of the twentieth century. Although the main concepts were already introduced and some interesting results were found, not enough was known to indicate which concepts were fundamental. Mathematics was thought of as an axiomatic system in which certain self-evident statements were taken as axioms and results were deduced by using logic. It was hoped that all the true mathematical statements could be derived by manipulating symbols according to explicit rules, but no one had the slightest clue how to prove that this was actually so. In his early works, Skolem was one of the first to indicate that it may not be possible to derive all the true mathematical statements. He published an important paper in 1920; from it emerged what is now known as the Löwenheim-Skolem theorem. Skolem proved that if a countable set of sentences is satisfiable, then it is satisfiable within a countable domain. INSET: Thoralf Albert Skolem.