Laurent Schwartz

Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. Alumnus of the École normale supérieure, he was awarded the Fields medal in 1950 for his works on the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. 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.

Biography

Family

Laurent Schwartz comes from a Jewish family of Alsatian 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 École polytechnique. Later they would have two children, Marc André and Claudine. Marie-Hélène was gifted for 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.

Education

According to his teachers, Laurent 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 (with rank 2).

World War II

As a man of Trotskyist affinities and Jewish descent, life was difficult for Laurent Schwartz during World War II. He had to hide and change his identity to avoid being deported. 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.

Later career

Laurent Schwartz taught mainly at École Polytechnique, 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.

Mathematical legacy

In 1950, Laurent Schwartz was awarded the Fields medal for his work on distributions. He was the first French mathematician to receive the Fields medal. Schwartz encountered serious problems to enter the United States to receive his medal, because of his sympathy for Trotskyism.

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 equations.

Personal opinions

Apart from his scientific work, Laurent Schwartz was a well-known outspoken intellectual. As a young socialist influenced by Leon Trotsky, Schwartz opposed the totalitarianism of the Soviet Union, particularly under 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 WWII in hiding under aliases, predominantly "Laurent Sélimartin". He was related to the Debré family.