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

Krefeld Krefeld ( , ; li, Krieëvel ), 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, Germany. It is located northwest of Düsseldorf, ...

– 5 May 1957 in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitu ...

) 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 ...

doing 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 ...

. The

Nazi Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in ...

regime forced him to retire because under the

Nuremberg Laws The Nuremberg Laws (german: link=no, Nürnberger Gesetze, ) 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 ...

he was considered only three quarters

Aryan Aryan or Arya (, Indo-Iranian *''arya'') is a term originally used as an ethnocultural self-designation by Indo-Iranians in ancient times, in contrast to the nearby outsiders known as 'non-Aryan' (*''an-arya''). In Ancient India, the term ...

. In 1943 much of his work was destroyed during a

bombing A bomb is an explosive weapon that uses the exothermic reaction of an explosive material to provide an extremely sudden and violent release of energy. Detonations inflict damage principally through ground- and atmosphere-transmitted mechanica ...

raid on Berlin. Nevertheless, he survived the

Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposi ...

, after which he resumed teaching

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

. 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-ord ...

, 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 (math ...

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

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

Naples Naples (; it, Napoli ; nap, Napule ), from grc, Νεάπολις, Neápolis, lit=new city. is the regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 909,048 within the city's adm ...

and then

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

Democritus Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. No ...

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

Humboldt University Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiati ...

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 German philosophers German male writers {{Germany-mathematician-stub

Publications

References

Further reading

External links