Martin Löb
Encyclopedia
Martin Hugo Löb was a German
mathematician
. He settled in the United Kingdom
after the Second World War and specialised in mathematical logic
. He moved to the Netherlands in the 1970s, where he remained in retirement. He is perhaps best known for having formulated Löb's theorem
in 1955.
, but escaped from the Nazis, arriving in the UK just before the outbreak of the Second World War. As an enemy alien
, he was deported to an internment camp at Hay
in Australia
in 1940, where the 19-year-old Löb was taught mathematics by other internees. His teacher, Felix Behrend, was later a professor at Melbourne University.
Löb was allowed to return to the UK in 1943, and he studied at the University of London
after the War. After graduating, he became a research student with Reuben Goodstein
at Leicester
. He completed his PhD
, and became an assistant lecturer at the University of Leeds
in 1951, where he was to remain for 20 years, becoming a reader
and then a professor
. He developed the mathematical logic
group at Leeds, making it one of the leading centres in the UK. Löb did research on proof theory
, modal logic
and computability theory
. He formulated Löb's theorem
in 1955, as a formal version of Löb's paradox, that statements that assert their own provability must be true (similar to Gödel's incompleteness theorem).
Löb's wife, Caroline, was Dutch. They had two daughters together. Löb moved to become a professor at the University of Amsterdam in the early 1970s. He remained at the University of Amsterdam until he retired. He then moved to the north of Holland, where he later died.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He settled in the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
after the Second World War and specialised in mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
. He moved to the Netherlands in the 1970s, where he remained in retirement. He is perhaps best known for having formulated Löb's theorem
Löb's theorem
In mathematical logic, Löb's theorem states that in a theory with Peano arithmetic, for any formula P, if it is provable that "if P is provable then P", then P is provable...
in 1955.
Early life and education
Löb grew up in BerlinBerlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
, but escaped from the Nazis, arriving in the UK just before the outbreak of the Second World War. As an enemy alien
Enemy alien
In law, an enemy alien is a citizen of a country which is in a state of conflict with the land in which he or she is located. Usually, but not always, the countries are in a state of declared war.-United Kingdom:...
, he was deported to an internment camp at Hay
Hay, New South Wales
Hay is a town in the western Riverina region of south western New South Wales , Australia. It is the administrative centre of Hay Shire Local Government Area and the centre of a prosperous and productive agricultural district on the wide Hay Plains....
in Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
in 1940, where the 19-year-old Löb was taught mathematics by other internees. His teacher, Felix Behrend, was later a professor at Melbourne University.
Löb was allowed to return to the UK in 1943, and he studied at the University of London
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
after the War. After graduating, he became a research student with Reuben Goodstein
Reuben Goodstein
Reuben Louis Goodstein was an English mathematician with a strong interest in the philosophy and teaching of mathematics....
at Leicester
University of Leicester
The University of Leicester is a research-led university based in Leicester, England. The main campus is a mile south of the city centre, adjacent to Victoria Park and Wyggeston and Queen Elizabeth I College....
. He completed his PhD
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
, and became an assistant lecturer at the University of Leeds
University of Leeds
The University of Leeds is a British Redbrick university located in the city of Leeds, West Yorkshire, England...
in 1951, where he was to remain for 20 years, becoming a reader
Reader (academic rank)
The title of Reader in the United Kingdom and some universities in the Commonwealth nations like Australia and New Zealand denotes an appointment for a senior academic with a distinguished international reputation in research or scholarship...
and then a professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
. He developed the mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
group at Leeds, making it one of the leading centres in the UK. Löb did research on proof theory
Proof theory
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
, modal logic
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
and computability theory
Computability theory
Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
. He formulated Löb's theorem
Löb's theorem
In mathematical logic, Löb's theorem states that in a theory with Peano arithmetic, for any formula P, if it is provable that "if P is provable then P", then P is provable...
in 1955, as a formal version of Löb's paradox, that statements that assert their own provability must be true (similar to Gödel's incompleteness theorem).
Löb's wife, Caroline, was Dutch. They had two daughters together. Löb moved to become a professor at the University of Amsterdam in the early 1970s. He remained at the University of Amsterdam until he retired. He then moved to the north of Holland, where he later died.