Wilhelm Ackermann

Wilhelm Friedrich Ackermann ( born March 29, 1896 in Beautiful Becke ( Hershey ), † December 24, 1962 in Lüdenscheid ) was a German mathematician.


Ackermann studied 1914-1924 with interruptions caused by participation in the First World War, mathematics, physics and philosophy at the University of Göttingen. He was a student of David Hilbert in Göttingen and was made famous by the eponymous Ackermann function, an example of a recursive function that is not primitive recursive.

In 1924 he received his doctorate in Hilbert with the work " justification of, tertium non datur 'by means of Hilbert 's theory of consistency ." He then received a fellowship that allowed him to stay in Cambridge for three years.

In Göttingen he joined in 1928 the preparatory service for teachers in secondary schools from. He then worked for a year at the former Konrad Schlaun - secondary school in Münster active. From 1929 to 1948 he taught at the high school Arnoldinum in Burg Steinfurt, 1935, he was promoted to the teacher. In 1948, he returned to his hometown Lüdenscheid, where he taught until 1961 at the Scholl -Gymnasium. In 1957 he was promoted to technical secondary school teacher of mathematics.

He was a corresponding member of the Academy of Sciences in Göttingen and honorary professor at the Westfälische Wilhelms-Universität Münster. Ackermann 1962 was one of the seven founding members of the German Association for Mathematical Logic and Foundations of Exact Sciences ( DVMLG ).

Together with David Hilbert in 1928 he wrote the book outlines the theoretical logic. Given the time already advanced age of Hilbert, he was the principal author. He was also known for work on the decision problem of predicate logic, the consistency of elementary number theory and set theory. In particular, in 1955 he created the Ackermann set theory.

He died unexpectedly at the age of 66 years on 24 December 1962. Three days earlier, he stopped at the Westfälische Wilhelms -Universität Münster a lecture on mathematical research. In Münster, he stopped the run by Hans Hermes Institute regularly lectures on mathematical logic and foundations of mathematics.

An answer to the question why Ackermann has not embarked on an academic career, gives Constance Reid: " Hilbert was very Opposed to marriage for young scientists anyway. [ ... ] Later, When Wilhelm Ackermann, with splat he had worked and Collaborated on a book, married, Hilbert was very angry. He refused to do anything more zu weiterer Ackermann 's career. "

Spoken survives to do so by Hilbert 's statement: " Oh, that's wonderful. This is good news for me. Because if this man is so crazy that he married and even has a child, I am freed from any obligation to do something for him. "

The fact that Ackermann had, despite his considerable teaching found time for mathematical work, is impressive. For example, he taught in the summer half of the year 1929 26 weeks Arnoldinum hours and was there at times even the only mathematics teacher. In the obituary of Arnoldinums says, " but senior teacher Dr. Ackermann was not only a well- respected and popular teacher, but also a world -renowned scientist ."

During his studies in Göttingen he met Fritz Latvians Meyer (1891-1953) know that intermittently for four semesters in Göttingen operation 1920-1922 further studies. The passionate alpinist boots Meyer made together with the Ackermann Gratüberschreitung Huder bench top -Kaiser head - high luck with overnight stay at the Lamsenjochhütte.


  • The consistency of the axiom of choice, in 1924, news of the Society of Sciences in Göttingen, Volume 1924, pp. 246-250
  • Justification of the " tertium non datur " means the Hilbert 's theory of consistency, 1925, Mathematische Annalen, Volume 93, pp. 1-36
  • To Hilbert's construction of the real numbers, 1928, Mathematische Annalen, Volume 99, pp. 118-133
  • About the satisfiability of certain Zählausdrücke, 1928, Mathematische Annalen, Vol 100, pp. 638-649
  • Studies on the elimination problem of mathematical logic, 1935, Mathematische Annalen, Volume 110, pp. 390-413
  • For elimination problem of mathematical logic, 1935, Mathematische Annalen, Volume 111, pp. 61-63
  • Contributions to the decision problem of mathematical logic, 1936, Mathematische Annalen, Volume 112, pp. 419-432
  • The consistency of the general set theory, 1936, Mathematische Annalen, Volume 114 (1937 ), pp. 305-315
  • Amount Theoretical justification of logic, 1938, Mathematische Annalen, Volume 115, pp. 1-22
  • For consistency of number theory, 1940/1941, Mathematische Annalen, Volume 117, pp. 162-194
  • A system of the type- free logic. Volume I, Leipzig, 1941.
  • Mechanical construction of a portion of Cantor's second number class, 1951, Mathematical Journal, Volume 53, Issue 5, pp. 403-413
  • For axioms of set theory, 1955, Mathematische Annalen, Volume 131 (1956 ), pp. 336-345
  • Contradiction -free construction of a type- free logic., 1951/52, Mathematical Journal, Volume 55, pp. 364-384
  • Contradiction -free construction of a type- free logic. II, 1953, Mathematical Journal, Volume 57, pp. 155-166
  • Philosophical remarks on the mathematical logic and the mathematical basis for research. In: " Ratio, Volume 1, 1957.
  • A type- free system of logic with sufficient mathematical application capability I., 1958, Archive for mathematical logic and basic research, Volume 4, pp. 3-26
  • A type- free system of logic with sufficient mathematical application ability II, 1960/61, Archive for mathematical logic and basic research, Volume 5, pp. 96-111