Leopold Löwenheim �le:o:pɔl̩d ˈlø:vɛnhaɪm(26 June 1878 in

Krefeld Krefeld ( , ; ), also spelled Crefeld until 1925 (though the spelling was still being used in British papers throughout the Second World War), is a city in North Rhine-Westphalia, in western Germany. It is located northwest of Düsseldorf, its c ...

– 5 May 1957 in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

) 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, mathematical structure, structure, space, Mathematica ...

doing work in

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

. The

Nazi Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...

regime forced him to retire because under the

Nuremberg Laws The Nuremberg Laws (, ) were antisemitic and racist laws that were enacted in Nazi Germany on 15 September 1935, at a special meeting of the Reichstag convened during the annual Nuremberg Rally of the Nazi Party. The two laws were the Law ...

he was considered only three quarters

Aryan ''Aryan'' (), or ''Arya'' (borrowed from Sanskrit ''ārya''), Oxford English Dictionary Online 2024, s.v. ''Aryan'' (adj. & n.); ''Arya'' (n.)''.'' is a term originating from the ethno-cultural self-designation of the Indo-Iranians. It stood ...

. In 1943 much of his work was destroyed during a

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raid on Berlin. Nevertheless, he survived the

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, after which he resumed teaching

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. Löwenheim (1915) gave the first proof of what is now known as the

Löwenheim–Skolem theorem In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation is given below. It implies that if a countable first-order ...

, often considered the starting point for

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

. Leopold was the son of Ludwig Löwenheim, a mathematics teacher at the

polytechnic A polytechnic is an educational institution that primarily focuses on vocational education, applied sciences, and career pathways. They are sometimes referred to as ''institutes of technology'', ''vocational institutes'', or ''universities of app ...

and Elizabeth Röhn, a writer. In 1881 the three of them left Krefeld first for

Naples Naples ( ; ; ) is the Regions of Italy, regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 908,082 within the city's administrative limits as of 2025, while its Metropolitan City of N ...

and then

where Ludwig was a private scholar working on a comprehensive account of the influence of

Democritus Democritus (, ; , ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greece, Ancient Greek Pre-Socratic philosophy, pre-Socratic philosopher from Abdera, Thrace, Abdera, primarily remembered today for his formulation of an ...

on modern science. Although he hoped this would gain him a teaching job at

Humboldt University The Humboldt University of Berlin (, abbreviated HU Berlin) is a public university, public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III of Prussia, Frederick W ...

Ludwig died in 1894.

Publications

* * * * Translated as "On possibilities in the calculus of relatives" in Jean van Heijenoort, 1967. ''A Source Book in Mathematical Logic, 1879–1931''. Harvard Univ. Press: 228–251. * * *

References

External links

Löwenheim, Leopold
at encyclopedia.com * 1878 births 1957 deaths 20th-century German mathematicians German logicians People from Krefeld 19th-century German philosophers 20th-century German philosophers German male writers {{Germany-mathematician-stub

Publications

References

Further reading

External links