Skolem, Thoralf Albert (1887–1963)

Norwegian mathematician who did important work on Diophantine equations and who helped to provide the axiomatic foundations for set theory in logic.

Skolem was born at Sandsvaer and educated at Oslo, where he became professor in 1938. He wrote 182 scientific papers, but they remained largely unread, partly because they were written in Norwegian.

Skolem's main work was in the field of formal mathematical logic. From papers published in the 1920s emerged what is now known as the Löwenheim–Skolem theorem, one consequence of which is Skolem's paradox: if an axiomatic system (such as axiomatic set theory) is consistent (that is, satisfiable), then it must be satisfiable within a countable domain; but Georg Cantor had shown the existence of a neverending sequence of transfinite powers in mathematics (that is, uncountability). Skolem's answer was that there is no complete axiomatization of mathematics.

Before such subjects as model theory, recursive function theory, and axiomatic set theory had become separate branches of mathematics, he introduced a number of the fundamental notions that gave rise to them.