Zermelo, Ernst Friedrich Ferdinand (1871–1953)

German mathematician who made important contributions to the development of set theory, particularly in developing the axiomatic set theory that now bears his name.

Zermelo was born in Berlin and studied at Halle and Freiburg. In 1905 he became professor at Göttingen, eventually moving to Freiburg, where he resigned his post in 1935 in protest at the Nazi regime, but was reinstated in 1946.

In 1900 Zermelo provided an ingenious proof to the well-ordering theorem, which states that every set can be well ordered (that is, can be arranged in a series in which each subclass – not being null – has a first term). He said that a relation a < b (a comes before b) can be introduced such that for any two statements a and b, either a = b, or a < b or b < a. If there are three elements a, b, and c, then if a <b and b < c, then a < c. This gave rise to the Zermelo axiom that every class can be well ordered.

In 1904 Zermelo defined the axiom of choice, the use of which had previously been unrecognized in mathematical reasoning. The first formulations of axioms for set theory – an axiom system for German mathematician Georg Cantor's theory of sets – were made by Zermelo in 1908.