Laurent Schwartz
Encyclopedia
Laurent-Moïse Schwartz (5 March 1915 in Paris
– 4 July 2002 in Paris
) was a French
mathematician
. He pioneered the theory
of distributions
, which gives a well-defined meaning to objects such as the Dirac delta function
. He was awarded the Fields medal
in 1950 for his work. For a long time he taught at the École polytechnique
.
Apart from his scientific work, he was a well-known outspoken intellectual
, leaning towards socialism
.
origin, with a strong scientific background: his father is a well-known surgeon
, his uncle Robert Debré
(who contributed to the creation of UNICEF) is a famous pediatrician
, and his great-uncle-in-law, Jacques Hadamard
, is a famous mathematician.
During his training at Lycée Louis-le-Grand
to enter the École normale supérieure
, he fell in love with Marie-Hélène Lévy, daughter of the probabilist Paul Lévy
who was then teaching at the École polytechnique
. Later they would have two children, Marc-André and Claudine. Marie-Hélène was gifted in mathematics as well, as she contributed to the geometry of singular analytic spaces and taught at the University of Lille
.
Laurent's mother transmitted her interest in natural sciences, especially entomology
. Laurent collected more than 20,000 Lepidoptera
(now housed in the Muséum national d'histoire naturelle
and other museums). He even discovered several new species, now named after him.
Schwartz is a distant relative of oncologist Laurent Henri Schwartz
.
In 1934, he was admitted at the École normale supérieure, and in 1937 he obtained the agrégation
(with rank 2).
affinities and Jewish descent, life was difficult for Schwartz during World War II
. He had to hide and change his identity to avoid being deported
after Nazi Germany overran France. He worked for the University of Strasbourg
(which had been relocated in Clermont-Ferrand
because of the war) under the name of Laurent-Marie Sélimartin, while Marie-Hélène used the name Lengé instead of Lévy. Contrary to other mathematicians at Clermont-Ferrand such as Feldbau, the couple managed to escape the Nazis.
, from 1958 to 1980. At the end of the war, he spent one year in Grenoble
(1944), then in 1945 joined the University of Nancy on the advice of Jean Delsarte
and Jean Dieudonné
, where he spent seven years. He was both an influential researcher and teacher, with students such as Bernard Malgrange
, Jacques-Louis Lions
, François Bruhat
and Alexander Grothendieck
. He joined the science faculty of the University of Paris
in 1952. In 1958 he became a teacher at the École polytechnique
after having at first rejected this position. However, from 1961 to 1963 the École polytechnique refused him the right to teach, because of his having signed the Manifesto of the 121
about the Algerian war, a gesture not appreciated by Polytechnique's military administration. However, Schwartz had a lasting influence on mathematics at the École polytechnique, having reorganized both teaching and research there.
In 1973 he was elected corresponding member of the French Academy of Sciences
, and was promoted to full membership in 1975.
for his work on distributions
. He was the first French mathematician to receive the Fields medal. Schwartz encountered serious problems trying to enter the United States
to receive his medal, because of his sympathy for Trotskyism
but was ultimately successful.
The theory of distributions clarifies the (then) mysteries of the Dirac Delta function
and Heaviside step function
. It helps to extend the theory of Fourier transform
and is now of capital importance to the theory of partial differential equation
s.
. As a young socialist
influenced by Leon Trotsky
, Schwartz opposed the totalitarianism
of the Soviet Union
, particularly under Joseph Stalin
. Schwartz ultimately rejected Trotskyism
for democratic socialism
.
Schwartz campaigned against the Algerian War.
In danger of being classified as a Jew under the Nazi racial laws, he had to spend parts of World War II
in hiding under aliases
, predominantly "Laurent Sélimartin". He was related to the Debré family
.
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
– 4 July 2002 in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
) was a French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
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....
. He pioneered the theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
of distributions
Distribution (mathematics)
In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
, which gives a well-defined meaning to objects such as the Dirac delta function
Dirac delta function
The Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...
. He was awarded the Fields medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1950 for his work. For a long time he taught at the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
.
Apart from his scientific work, he was a well-known outspoken intellectual
Intellectual
An intellectual is a person who uses intelligence and critical or analytical reasoning in either a professional or a personal capacity.- Terminology and endeavours :"Intellectual" can denote four types of persons:...
, leaning towards socialism
Socialism
Socialism is an economic system characterized by social ownership of the means of production and cooperative management of the economy; or a political philosophy advocating such a system. "Social ownership" may refer to any one of, or a combination of, the following: cooperative enterprises,...
.
Family
Laurent Schwartz comes from a Jewish family of AlsatianAlsatian
Alsatian may refer to:* Alsatian, a person from the Alsace region of France or a speaker of the Alsatian language* Alsatian language, the language or dialect of the Alsace region of northeast France...
origin, with a strong scientific background: his father is a well-known surgeon
Surgeon
In medicine, a surgeon is a specialist in surgery. Surgery is a broad category of invasive medical treatment that involves the cutting of a body, whether human or animal, for a specific reason such as the removal of diseased tissue or to repair a tear or breakage...
, his uncle Robert Debré
Robert Debré
Robert Debré was a French physician at Necker-Enfants Malades Hospital in Paris.He gave his name to the most important ....
(who contributed to the creation of UNICEF) is a famous pediatrician
Pediatrics
Pediatrics or paediatrics is the branch of medicine that deals with the medical care of infants, children, and adolescents. A medical practitioner who specializes in this area is known as a pediatrician or paediatrician...
, and his great-uncle-in-law, Jacques Hadamard
Jacques Hadamard
Jacques Salomon Hadamard FRS was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.-Biography:...
, is a famous mathematician.
During his training at Lycée Louis-le-Grand
Lycée Louis-le-Grand
The Lycée Louis-le-Grand is a public secondary school located in Paris, widely regarded as one of the most rigorous in France. Formerly known as the Collège de Clermont, it was named in king Louis XIV of France's honor after he visited the school and offered his patronage.It offers both a...
to enter the École normale supérieure
École normale supérieure
An école normale supérieure or ENS is a type of publicly funded higher education in France. A portion of the student body who are French civil servants are called Normaliens....
, he fell in love with Marie-Hélène Lévy, daughter of the probabilist Paul Lévy
Paul Pierre Lévy
Paul Pierre Lévy was a Jewish French mathematician who was active especially in probability theory, introducing martingales and Lévy flights...
who was then teaching at the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
. Later they would have two children, Marc-André and Claudine. Marie-Hélène was gifted in mathematics as well, as she contributed to the geometry of singular analytic spaces and taught at the University of Lille
Université Lille Nord de France
The University of Lille -Nord de France , located in Lille, France, is a center for higher education, academic research and doctoral studies located over multiple campuses in the Academie de Lille....
.
Laurent's mother transmitted her interest in natural sciences, especially entomology
Entomology
Entomology is the scientific study of insects, a branch of arthropodology...
. Laurent collected more than 20,000 Lepidoptera
Lepidoptera
Lepidoptera is a large order of insects that includes moths and butterflies . It is one of the most widespread and widely recognizable insect orders in the world, encompassing moths and the three superfamilies of butterflies, skipper butterflies, and moth-butterflies...
(now housed in the Muséum national d'histoire naturelle
Muséum national d'histoire naturelle
The Muséum national d'Histoire naturelle is the National Museum of Natural History in Paris, France.- History :The museum was formally founded on 10 June 1793, during the French Revolution...
and other museums). He even discovered several new species, now named after him.
Schwartz is a distant relative of oncologist Laurent Henri Schwartz
Laurent Henri Schwartz
Laurent Schwartz is a French oncologist and scientist....
.
Education
According to his teachers, Schwartz was an exceptional student. He was particularly gifted in Latin, Greek and mathematics. One of his teachers told his parents: "Beware, some will say your son has a gift for languages, but he is only interested in the scientific and mathematical aspect of languages: he should become a mathematician."In 1934, he was admitted at the École normale supérieure, and in 1937 he obtained the agrégation
Agrégation
In France, the agrégation is a civil service competitive examination for some positions in the public education system. The laureates are known as agrégés...
(with rank 2).
World War II
As a man of TrotskyistTrotskyism
Trotskyism is the theory of Marxism as advocated by Leon Trotsky. Trotsky considered himself an orthodox Marxist and Bolshevik-Leninist, arguing for the establishment of a vanguard party of the working-class...
affinities and Jewish descent, life was difficult for Schwartz during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. He had to hide and change his identity to avoid being deported
Deportation
Deportation means the expulsion of a person or group of people from a place or country. Today it often refers to the expulsion of foreign nationals whereas the expulsion of nationals is called banishment, exile, or penal transportation...
after Nazi Germany overran France. He worked for the University of Strasbourg
University of Strasbourg
The University of Strasbourg in Strasbourg, Alsace, France, is the largest university in France, with about 43,000 students and over 4,000 researchers....
(which had been relocated in Clermont-Ferrand
Clermont-Ferrand
Clermont-Ferrand is a city and commune of France, in the Auvergne region, with a population of 140,700 . Its metropolitan area had 409,558 inhabitants at the 1999 census. It is the prefecture of the Puy-de-Dôme department...
because of the war) under the name of Laurent-Marie Sélimartin, while Marie-Hélène used the name Lengé instead of Lévy. Contrary to other mathematicians at Clermont-Ferrand such as Feldbau, the couple managed to escape the Nazis.
Later career
Schwartz taught mainly at École PolytechniqueÉcole Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
, from 1958 to 1980. At the end of the war, he spent one year in Grenoble
Grenoble
Grenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Rhône-Alpes region, Grenoble is the capital of the department of Isère...
(1944), then in 1945 joined the University of Nancy on the advice of Jean Delsarte
Jean Delsarte
Jean Frédéric Auguste Delsarte was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalised shift operators. He was one of the founders of the Bourbaki group.-External links:...
and Jean Dieudonné
Jean Dieudonné
Jean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of...
, where he spent seven years. He was both an influential researcher and teacher, with students such as Bernard Malgrange
Bernard Malgrange
Bernard Malgrange is a French mathematician who works on differential equations and singularity theory.He proved the Ehrenpreis–Malgrange theorem and the Malgrange preparation theorem....
, Jacques-Louis Lions
Jacques-Louis Lions
Jacques-Louis Lions ForMemRS was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John Von Neumann prize in 1986. Lions is listed as an ISI highly cited researcher.-Biography:After...
, François Bruhat
François Bruhat
François Georges René Bruhat was a French mathematician who worked on algebraic groups. The Bruhat order of a Weyl group, the Bruhat decomposition, and the Schwartz–Bruhat functions are named after him....
and Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
. He joined the science faculty of the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
in 1952. In 1958 he became a teacher at the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
after having at first rejected this position. However, from 1961 to 1963 the École polytechnique refused him the right to teach, because of his having signed the Manifesto of the 121
Manifesto of the 121
The Manifesto of the 121 was an open letter signed by 121 intellectuals and published on 6 September 1960 in the magazine Vérité-Liberté. It called on the French government, then headed by the Gaullist Michel Debré, and public opinion to recognise the Algerian War as a legitimate struggle for...
about the Algerian war, a gesture not appreciated by Polytechnique's military administration. However, Schwartz had a lasting influence on mathematics at the École polytechnique, having reorganized both teaching and research there.
In 1973 he was elected corresponding member of the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
, and was promoted to full membership in 1975.
Mathematical legacy
In 1950, Schwartz was awarded the Fields medalFields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
for his work on distributions
Distribution (mathematics)
In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
. He was the first French mathematician to receive the Fields medal. Schwartz encountered serious problems trying to enter the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
to receive his medal, because of his sympathy for Trotskyism
Trotskyism
Trotskyism is the theory of Marxism as advocated by Leon Trotsky. Trotsky considered himself an orthodox Marxist and Bolshevik-Leninist, arguing for the establishment of a vanguard party of the working-class...
but was ultimately successful.
The theory of distributions clarifies the (then) mysteries of the Dirac Delta function
Dirac delta function
The Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...
and Heaviside step function
Heaviside step function
The Heaviside step function, or the unit step function, usually denoted by H , is a discontinuous function whose value is zero for negative argument and one for positive argument....
. It helps to extend the theory of Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
and is now of capital importance to the theory of partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s.
Personal opinions
Apart from his scientific work, Schwartz was a well-known outspoken intellectualIntellectual
An intellectual is a person who uses intelligence and critical or analytical reasoning in either a professional or a personal capacity.- Terminology and endeavours :"Intellectual" can denote four types of persons:...
. As a young socialist
Trotskyism
Trotskyism is the theory of Marxism as advocated by Leon Trotsky. Trotsky considered himself an orthodox Marxist and Bolshevik-Leninist, arguing for the establishment of a vanguard party of the working-class...
influenced by Leon Trotsky
Leon Trotsky
Leon Trotsky , born Lev Davidovich Bronshtein, was a Russian Marxist revolutionary and theorist, Soviet politician, and the founder and first leader of the Red Army....
, Schwartz opposed the totalitarianism
Totalitarianism
Totalitarianism is a political system where the state recognizes no limits to its authority and strives to regulate every aspect of public and private life wherever feasible...
of the Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
, particularly under Joseph Stalin
Joseph Stalin
Joseph Vissarionovich Stalin was the Premier of the Soviet Union from 6 May 1941 to 5 March 1953. He was among the Bolshevik revolutionaries who brought about the October Revolution and had held the position of first General Secretary of the Communist Party of the Soviet Union's Central Committee...
. Schwartz ultimately rejected Trotskyism
Trotskyism
Trotskyism is the theory of Marxism as advocated by Leon Trotsky. Trotsky considered himself an orthodox Marxist and Bolshevik-Leninist, arguing for the establishment of a vanguard party of the working-class...
for democratic socialism
Democratic socialism
Democratic socialism is a description used by various socialist movements and organizations to emphasize the democratic character of their political orientation...
.
Schwartz campaigned against the Algerian War.
In danger of being classified as a Jew under the Nazi racial laws, he had to spend parts of World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
in hiding under aliases
Pseudonym
A pseudonym is a name that a person assumes for a particular purpose and that differs from his or her original orthonym...
, predominantly "Laurent Sélimartin". He was related to the Debré family
Debré family
The Debré family is a French family including several prominent politicians and physicians. The family's ancestor, rabbi Simon Debré, was born in Westhoffen, Alsace....
.
See also
- Schwartz distribution
- Schwartz kernel theoremSchwartz kernel theoremIn mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz himself have a two-variable theory that includes all reasonable...
- Schwartz space
- Schwartz–Bruhat function
External links
- Biography of Laurent Schwartz from the American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
- Review of Schwartz's autobiography, same source