Wilhelm Ackermann

Wilhelm Ackermann
Wilhelm Ackermann inc. 1935
Born	(1896-03-29)29 March 1896 Herscheid,German Empire
Died	24 December 1962(1962-12-24)(aged 66) Lüdenscheid,West Germany
Nationality	German
Alma mater	University of Göttingen
Known for	Ackermann coding Ackermann function Ackermann set theory
Scientific career
Fields	Mathematics
Doctoral advisor	David Hilbert

Wilhelm Friedrich Ackermann(/ˈækərmən/;German:[ˈakɐˌman];29 March 1896 – 24 December 1962) was a Germanmathematicianandlogicianbest known for his work inmathematical logicand theAckermann function,an important example in thetheory of computation.

Biography

Ackermann was born inHerscheid,Germany,and was awarded a Ph.D. by theUniversity of Göttingenin 1925 for his thesisBegründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit,which was a consistency proof of arithmetic apparently withoutPeano induction(although it did use e.g. induction over the length of proofs). This was one of two major works inproof theoryin the 1920s and the only one followingHilbert'sschool of thought.From 1929 until 1948, he taught at the Arnoldinum Gymnasium inBurgsteinfurt,and then atLüdenscheiduntil 1961. He was also a corresponding member of the Akademie der Wissenschaften (Academy of Sciences) in Göttingen, and was an honorary professor at theUniversity of Münster.

In 1928, Ackermann helpedDavid Hilbertturn his 1917 – 22 lectures on introductorymathematical logicinto a text,Principles of Mathematical Logic.This text contained the first exposition ever offirst-order logic,and posed the problem of itscompletenessanddecidability(Entscheidungsproblem). Ackermann went on to constructconsistency proofsforset theory(1937),full arithmetic(1940),type-free logic(1952), and a newaxiomatizationofset 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 inLüdenscheid,West Germanyin December 1962.

See also

• Ackermann's bijection
• Ackermann coding
• Ackermann function
• Ackermann ordinal
• Ackermann set theory
• Hilbert–Ackermann system
• Entscheidungsproblem
• Ordinal notation
• Inverse Ackermann function

Bibliography

• 1928. "On Hilbert's construction of thereal numbers"inJean 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). (withDavid Hilbert)Principles of Mathematical Logic.Chelsea. Translation of 1938 German edition.
• 1954.Solvable cases of thedecision problem.North Holland.

External links

• O'Connor, John J.;Robertson, Edmund F.,"Wilhelm Ackermann",MacTutor History of Mathematics Archive,University of St Andrews
• Wilhelm Ackermannat theMathematics Genealogy Project
• Erich Friedman's page on AckermannatStetson University
• Hermes,In memoriam WILHELM ACKERMANN 1896-1962(PDF, 945 KB)
• Author profilein the databasezbMATH