Editing Wilhelm Ackermann (section)

==Biography==
Ackermann was born in [[Herscheid]], [[German Empire|Germany]], and was awarded a Ph.D. by the [[University of Göttingen]] in 1925 for his thesis ''Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit'', which was a consistency proof of arithmetic apparently without [[Peano axioms|Peano induction]] (although it did use e.g. induction over the length of proofs). This was one of two major works in [[proof theory]] in the 1920s and the only one following [[David Hilbert|Hilbert's]] school of thought.<ref name="MTbiography" /> From 1929 until 1948, he taught at the Arnoldinum Gymnasium in [[Steinfurt|Burgsteinfurt]], and then at [[Lüdenscheid]] until 1961. He was also a corresponding member of the Akademie der Wissenschaften (''Academy of Sciences'') in Göttingen, and was an honorary professor at the [[University of Münster]].

In 1928, Ackermann helped [[David Hilbert]] turn his 1917 &ndash; 22 lectures on introductory [[mathematical logic]] into a text, ''[[Principles of Mathematical Logic]]''. This text contained the first exposition ever of [[first-order logic]], and posed the problem of its [[Gödel's completeness theorem|completeness]] and [[Decidability (logic)|decidability]]  ([[Entscheidungsproblem]]). Ackermann went on to construct [[consistency proof]]s for [[set theory]] (1937), [[Peano arithmetic|full arithmetic]] (1940), [[Logic|type-free logic]] (1952), and a new [[axiomatic set theory|axiomatization]] of [[set theory]] (1956).

Later in life, Ackermann continued working as a high school teacher. He kept engaged in the field of research and published many contributions to the foundations of mathematics until the end of his life.  He died in [[Lüdenscheid]], [[West Germany]] in December 1962.