Wilhelm Ackermann

Wilhelm Friedrich Ackermann (/ˈækərmən/; German: [ˈakɐˌman]; 29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

Wilhelm Ackermann
Wilhelm Ackermann in c. 1935
Born	29 March 1896 Herscheid, German Empire
Died	24 December 1962 (aged 66) Lüdenscheid, West Germany
Nationality	German
Alma mater	University of Göttingen
Known for	Ackermann function, Ackermann coding, Ackermann set theory
Scientific career
Fields	Mathematics
Doctoral advisor	David Hilbert

Biography

Ackermann was born in Herscheid, 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 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 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 (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).

In turn, Hilbert's support vanished when Ackermann got married:

Oh, das ist wunderbar. Das sind gute Neuigkeiten für mich. Denn wenn dieser Mann so verrückt ist, daß er heiratet und sogar ein Kind hat, bin ich von jeder Verpflichtung befreit, etwas für ihn tun zu müssen.

Oh, that is wonderful. Those are good news for me. Because if this man is so crazy to marry and even have a child, then I am no longer responsible to do anything for him.

— Anita Ehlers. Liebes Hertz! Physiker und Mathematiker in Anekdoten. Basel: Birkhäuser Verlag, 1994, p. 161. See also Constance Reid Hilbert.

Later in life, Ackerman continued working as a high school teacher. Still, he kept continually 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, Germany in December 1962.

See also

• Ackermann coding
• Ackermann ordinal
• Ackermann set theory
• Ackermann function
• Inverse Ackermann function

Bibliography

• 1928. "On Hilbert's construction of the real numbers" in Jean van Heijenoort, ed., 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 493–507.
• 1940. Zur Widerspruchsfreiheit der Zahlentheorie, Mathematische Annalen, vol. 117, pp 162–194.
• 1950 (1928). (with David Hilbert) Principles of Mathematical Logic. Chelsea. Translation of 1938 German edition.
• 1954. Solvable cases of the decision problem. North Holland.

External links

• O'Connor, John J.; Robertson, Edmund F., "Wilhelm Ackermann", MacTutor History of Mathematics archive, University of St Andrews.
• Wilhelm Ackermann at the Mathematics Genealogy Project
• Erich Friedman's page on Ackermann at Stetson University
• Hermes, In memoriam WILHELM ACKERMANN 1896-1962 (PDF, 945 KB)
• Author profile in the database zbMATH