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, structure, space, models, and change. History On ...

known for his work in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...

, 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 e ...

s. He also worked in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

set theory Set theory is the branch of mathematical logic that studies 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 mathematics, is mostly conce ...

, 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 (3 ...

Early life and education

Levi was born to Georg Levi and Emma Blum in

Mulhouse Mulhouse (; Alsatian: or , ; ; meaning '' mill house'') is a city of the Haut-Rhin department, in the Grand Est region, eastern France, close to the Swiss and German borders. It is the largest city in Haut-Rhin and second largest in Alsace a ...

in Alsace-Lorraine, then part of the German Empire. He received his Ph.D. in 1911 under

Heinrich Martin Weber Heinrich Martin Weber (5 March 1842, Heidelberg, 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, and analysis. He is ...

at the

University of Strasbourg The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers. The French university traces its history to the ea ...

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 (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...

, 1914–18. Awarded the

Iron Cross The Iron Cross (german: link=no, Eisernes Kreuz, , abbreviated EK) was a military decoration in the Kingdom of Prussia, and later in the German Empire (1871–1918) and Nazi Germany (1933–1945). King Frederick William III of Prussia es ...

, 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 being ...

, Charlotte, and Suzanne). He taught at the

University of Leipzig Leipzig University (german: Universität Leipzig), 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 Decemb ...

from 1920 to 1935, when 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 ...

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

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

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

. 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; CU) is a public collegiate state university in India, located in Kolkata, West Bengal, India. Considered one of best state research university all over India every year, ...

. 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 fo ...

in 1940 at a series of lectures on

finite geometry Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...

. 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 af ...

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 public deemed research university located in Mumbai, India that is dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the ...

Mumbai Mumbai (, ; also known as Bombay — List of renamed Indian cities and states#Maharashtra, the official name until 1995) is the capital city of the Indian States and union territories of India, state of Maharashtra and the ''de facto'' fin ...

. 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 In mathematics, in the theory of several complex variabl ...

, 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 research university in Berlin, Germany. It is consistently ranked among Germany's best universities, with particular strengths in political science and t ...

and later

University of Freiburg The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public research university located in Freiburg im Breisgau, Baden-Württemb ...

. He died in

Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...

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 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 __NOTOC__ Year 919 ( CMXIX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. Events By Place Byzantine Empire * March 25 – Romanos Lekapenos, admiral (''droungarios'') of the ...

(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 and Baer groups. Biography Baer studied mechanical engineering f ...

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 University of Calcutta faculty Leipzig University faculty Free University of Berlin faculty University of Freiburg faculty 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