Wilhelm Ackermann

Who was Wilhelm Ackermann?

Wilhelm Friedrich Ackermann was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

Ackermann was born in Herscheid municipality, 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 full Peano induction. 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 in Göttingen, and was an honorary professor at the University of Münster.

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. Ackermann went on to construct consistency proofs for set theory, full arithmetic, type-free logic, and a new axiomatization of set theory.