Wilhelm Friedrich Ackermann (; ; 29 March 1896 – 24 December 1962) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

best known for his work in

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...

and the

Ackermann function In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total ...

, an important example in the

theory of computation In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how algorithmic efficiency, efficiently they can be solved or t ...

Biography

Ackermann was born in Herscheid,

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...

, and was awarded a Ph.D. by the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

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). This was one of two major works in

proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Barwise (1978) consists of four corresponding part ...

in the 1920s and the only one following Hilbert's school of thought. From 1929 until 1948, he taught at the Arnoldinum Gymnasium in

Burgsteinfurt Steinfurt (; Westphalian: ''Stemmert'') is a city in North Rhine-Westphalia, Germany. It is the capital of the district of Steinfurt. From roughly 1100-1806, it was the capital of the County of Steinfurt. Geography Steinfurt is situated north ...

, and then at

Lüdenscheid Lüdenscheid () is a city in the Märkischer Kreis district, in North Rhine-Westphalia, Germany. It is located in the Sauerland region. Geography Lüdenscheid is located on the saddle of the watershed between the Lenne and Volme rivers which ...

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 The University of Münster (german: Westfälische Wilhelms-Universität Münster, WWU) is a public research university located in the city of Münster, North Rhine-Westphalia in Germany. With more than 43,000 students and over 120 fields of stud ...

. In 1928, Ackermann helped

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...

turn his 1917 – 22 lectures on introductory

into a text, ''

Principles of Mathematical Logic ''Principles of Mathematical Logic'' is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text ''Grundzüge der theoretischen Logik'', on elementary mathematical logic. The 1928 first editi ...

''. This text contained the first exposition ever of

first-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

, and posed the problem of its completeness and decidability (

Entscheidungsproblem In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the state ...

). Ackermann went on to construct

consistency proof In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...

s for

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...

(1937), full arithmetic (1940), type-free logic (1952), and a new

axiomatization In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contai ...

(1956). In turn, Hilbert's support vanished when Ackermann got married: 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

in December 1962.

Bibliography

*1928. "On Hilbert's construction of the

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...

s" in

Jean van Heijenoort Jean Louis Maxime van Heijenoort (; July 23, 1912 – March 29, 1986) was a historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and an American Trotskyist until 1947. Life Van Heijenoort was born ...

, 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

) ''

''. Chelsea. Translation of 1938 German edition. *1954. ''Solvable cases of the

decision problem In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whe ...

''. North Holland.

References

External links

* *
Erich Friedman's page on Ackermann
at

Stetson University Stetson University is a private university with four colleges and schools located across the I–4 corridor in Central Florida with the primary undergraduate campus in DeLand. The university was founded in 1883 and was later established in 1887 ...

Hermes, ''In memoriam WILHELM ACKERMANN 1896-1962''
(PDF, 945 KB)
Author profile
in the database zbMATH {{DEFAULTSORT:Ackermann, Wilhelm 1896 births 1962 deaths Computability theorists People from Lüdenscheid People from the Province of Westphalia University of Göttingen alumni University of Münster faculty German Lutherans 20th-century German mathematicians German logicians German philosophers German male writers 20th-century Lutherans Members of the Göttingen Academy of Sciences and Humanities

Biography

See also

Bibliography

References

External links