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Wilhelm Ackermann ( 1896 - 1962 )  Category ( Mathematicians ) [suggest a correction]
 

Wilhelm Friedrich Ackermann was born on 29 March 1896 in Schönebeck (Kr. Altena), Germany. He was a mathematician best known for what is known as the "Ackermann Function," an important example within the theory of computation.

Ackermann was awarded his Ph.D. by the University of Goettingen 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 full Peano induction (although it did use e.g. induction over the length of proofs). From 1929 until 1948, he taught at the Arnoldinum Gymnasium in 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 Universität Münster (Westphalia).

In 1928, Ackermann helped David Hilbert turn his 1917-22 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 completeness and decidability (Entscheidungsproblem). Ackermann went on to construct consistency proofs for set theory (1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).

Ackermann's later works consist of consistency proofs for set theory (1937), full arithmetic (1940), type free logic (1952), further there was a new axiomatization of set theory (1956), and a book Solvable cases of the decision problem (North Holland, 1954). In 1957, Ackermann published Philosophische Begründung zur mathematischen Logik und zur mathematischen Grundlagenforschung and its English translation Philosophical observations on mathematical logic and on investigations into the foundations of mathematics. This paper, written for non-experts in the subject, gives an excellent overview of how Ackermann viewed mathematical logic.

Ackermann died on Christmas Eve, 24 December 1962 in Lüdenscheid, Germany.


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