Leopold Löwenheim was a German

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....

, known for his work 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...

. The Nazi

Nazism

Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...

 regime forced him to retire because under the Nuremberg Laws

Nuremberg Laws

The Nuremberg Laws of 1935 were antisemitic laws in Nazi Germany introduced at the annual Nuremberg Rally of the Nazi Party. After the takeover of power in 1933 by Hitler, Nazism became an official ideology incorporating scientific racism and antisemitism...

 he was considered only three quarters Aryan

Aryan

Aryan is an English language loanword derived from Sanskrit ārya and denoting variously*In scholarly usage:**Indo-Iranian languages *in dated usage:**the Indo-European languages more generally and their speakers...

. In 1943 much of his work was destroyed during a bombing raid on Berlin. Nevertheless, he survived the Second World War, after which he resumed teaching mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

.

Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem

Löwenheim–Skolem theorem

In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ...

, often considered the starting point for model theory

Model theory

In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....

.

Important publications

Primary:

• 1915, "Über Möglichkeiten im Relativkalkül," Mathematische Annalen
  Mathematische Annalen
  Mathematische Annalen is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann...
  
  76: 447–470. Translated as "On possibilities in the calculus of relatives" in Jean van Heijenoort
  Jean Van Heijenoort
  Jean Louis Maxime van Heijenoort was a pioneer historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and from then until 1947, an American Trotskyist activist.-Life:Van Heijenoort was born in Creil, France...
  
  , 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 228–251.

Secondary:

• Brady, Geraldine, 2000. From Peirce to Skolem. North Holland. Contains a detailed exegesis of the proof in Löwenheim (1915), and discusses how Thoralf Skolem
  Thoralf Skolem
  Thoralf Albert Skolem was a Norwegian mathematician known mainly for his work on mathematical logic and set theory.-Life:...
  
  simplified that proof and extended the scope and generality of the theorem.

External links