Friedrich Wilhelm Daniel Levi (February 6, 1888 – January 1, 1966) 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 ...

known for his work in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

, especially

torsion-free abelian group In mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative and the identity element is the only elem ...

s. He also worked in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), 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 mathema ...

, and

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

Early life and education

Levi was born to Georg Levi and Emma Blum in

Mulhouse Mulhouse (; ; Alsatian language, Alsatian: ''Mìlhüsa'' ; , meaning "Mill (grinding), mill house") is a France, French city of the European Collectivity of Alsace (Haut-Rhin department, in the Grand Est region of France). It is near the Fran ...

in Alsace-Lorraine, then part of the

German Empire The German Empire (),; ; World Book, Inc. ''The World Book dictionary, Volume 1''. World Book, Inc., 2003. p. 572. States that Deutsches Reich translates as "German Realm" and was a former official name of Germany. also referred to as Imperia ...

. He received his Ph.D. in 1911 under

Heinrich Martin Weber Heinrich Martin Weber (5 March 1842, Heidelberg, German Confederation, Germany – 17 May 1913, Straßburg, Alsace-Lorraine, German Empire, now Strasbourg, France) was a German mathematician. Weber's main work was in algebra, number theory, ...

at the

University of Strasbourg The University of Strasbourg (, Unistra) is a public research university located in Strasbourg, France, with over 52,000 students and 3,300 researchers. Founded in the 16th century by Johannes Sturm, it was a center of intellectual life during ...

Career

Levi served his mandatory military service in the German Army in 1906–1907, and was called up again serving in the artillery during

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

, 1914–18. Awarded the

Iron Cross The Iron Cross (, , abbreviated EK) was a military decoration in the Kingdom of Prussia, the German Empire (1871–1918), and Nazi Germany (1933–1945). The design, a black cross pattée with a white or silver outline, was derived from the in ...

, he was discharged as a lieutenant. In 1917, he married Barbara Fitting, with whom he eventually had three children (

Paul Levi Paul Levi (; 11 March 1883 – 9 February 1930) was a German communist and social democratic political leader. He was the head of the Communist Party of Germany following the assassination of Rosa Luxemburg and Karl Liebknecht in 1919. After bein ...

, Charlotte, and Suzanne). He taught at the

University of Leipzig Leipzig University (), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December 1409 by Frederick I, Electo ...

from 1920 to 1935, when 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 ...

government dismissed him because of his Jewish ancestry. Friedrich and Barbara moved to

Calcutta Kolkata, also known as Calcutta (List of renamed places in India#West Bengal, its official name until 2001), is the capital and largest city of the Indian States and union territories of India, state of West Bengal. It lies on the eastern ba ...

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

. In 1935 he accepted an offer as head of the Mathematics Department at the

University of Calcutta The University of Calcutta, informally known as Calcutta University (), is a Public university, public State university (India), state university located in Kolkata, Calcutta (Kolkata), West Bengal, India. It has 151 affiliated undergraduate c ...

. He introduced the

Levi graph In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure.. See in particulap. 181 From a collection of points and lines in an incidence geometry or a projective configuration, we ...

in 1940 at a series of lectures on

finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...

. He contributed to the understanding of

combinatorics on words Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words ...

when he articulated the Levi lemma in an article for the Calcutta Mathematical Society. In 1948, Levi became professor of mathematics at

Tata Institute of Fundamental Research Tata Institute of Fundamental Research (TIFR) is a leading research Institute under the Department of Atomic Energy of the Government of India. It is a public deemed university located at Navy Nagar, Colaba in Mumbai. It also has a centres in ...

Mumbai Mumbai ( ; ), also known as Bombay ( ; its official name until 1995), is the capital city of the Indian state of Maharashtra. Mumbai is the financial capital and the most populous city proper of India with an estimated population of 12 ...

. According to

Raghavan Narasimhan Raghavan Narasimhan (August 31, 1937 – October 3, 2015) was an Indian mathematician at the University of Chicago who worked on real and complex manifolds and who solved the Levi problem for complex manifolds. Early life and education He ...

, Levi had an important influence on the development of 20th century mathematics in India, especially by introducing modern algebra at the University of Calcutta. In 1952, he returned to Germany and was a professor at the

Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public university, public research university in Berlin, Germany. It was founded in West Berlin in 1948 with American support during the early Cold War period a ...

and later

University of Freiburg The University of Freiburg (colloquially ), officially the Albert Ludwig University of Freiburg (), is a public university, public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany. The university was founded in 1 ...

. He died in

Freiburg Freiburg im Breisgau or simply Freiburg is the List of cities in Baden-Württemberg by population, fourth-largest city of the German state of Baden-Württemberg after Stuttgart, Mannheim and Karlsruhe. Its built-up area has a population of abou ...

on the first day of 1966. A bibliography of 70 works in mathematics by Levi is included in the 1991 tribute by

László Fuchs László Fuchs (born June 24, 1924) is a Hungary, Hungarian-born American mathematician, the Evelyn and John G. Phillips Distinguished Professor Emeritus in Mathematics at Tulane University.

and Rüdiger Göbel.

Selected publications

* ''Abelsche Gruppen mit abzählbaren Elementen''. B. G. Teubner, Leipzig 919 (Habilitationsschrift, Universität Leipzig) * ''Geometrische Konfigurationen''. Hirzel, Leipzig 1929. *

Reinhold Baer Reinhold Baer (22 July 1902 – 22 October 1979) was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings, Baer groups, and Baer subplanes. Biography Baer studied mecha ...

and Friedrich Levi: ''Ränder topologischer Räume''. Hirzel, Leipzig 1930. * ''On the fundamentals of analysis. Six lectures delivered in February 1938 at the University of Calcutta''. University of Calcutta, Calcutta 1939. * F. W. Levi and R. N. Sen: ''Plane geometry''. Calcutta 1939. * ''Finite geometrical systems. Six public lectures delivered in February 1940 at the University of Calcutta''. University of Calcutta, Calcutta 1942. * ''Algebra''. University of Calcutta, Calcutta 1942.

References

External links

* {{DEFAULTSORT:Levi, Friedrich Wilhelm 20th-century German mathematicians German Army personnel of World War I Group theorists University of Strasbourg alumni Academic staff of the University of Calcutta Academic staff of Leipzig University Academic staff of the Free University of Berlin Academic staff of the University of Freiburg People from Alsace-Lorraine Scientists from Mulhouse Alsatian Jews Levites 1888 births 1966 deaths Presidents of the Indian Mathematical Society German expatriates in India People dismissed from faculty positions by Nazi Germany University of Calcutta alumni