MacTutor
The subversive approach to maths and politics
Laurent Schwartz, who has died aged 87, was the ideal of the French intellectual. The undisputed master of his subject, everywhere respected as a very great mathematician, he had been a student at the Ecole Normale Supérieure and became a professor at the Ecole Polytechnique.
A renowned teacher, he was always active in defending and improving education in France. But he was also a political activist who fought endlessly, not for any political party, but against injustice. Finally, he was well known as a collector of butterflies (he was said to possess some 20,000).
He was born during the first world war, the son of a wealthy and distinguished family: his father was a surgeon. After the Lycée Janson-de-Sailly in Paris, he gained admission to the Ecole Normale Supérieure, where he discovered both mathematics and politics. A group of students were analysing the work of German mathematicians. This was the time of the Popular Front of 1936, and Schwartz was attracted to the Communist party, but shocked at learning of Stalin's trials in the Soviet Union, he turned instead to the Trotskyists, who were denouncing the Soviet state as "degenerate".
With the armistice of 1940, Schwartz found himself writing his mathematics thesis in Clermont-Ferrand, where the Germans regarded the university as their particular enemy (it had taken refuge there when Strasbourg was annexed to Germany). It is remarkable that this thesis on real and imaginary exponentials was written in these conditions, which were even worse for someone who was Jewish. But the thesis was finished and accepted in 1943 and Schwartz was given his first university post at Nancy.
There, he became one of the 20th century's greatest exponents of mathematical analysis by evolving his theory of "distributions" -- or "generalised functions" as they are called in English -- that won him, just before his 35th birthday, the American Fields Medal, his discipline's equivalent of the Nobel Prize. He was the first Frenchman to win this award. His two-volume Theory of Distributions, published in French in 1950-51, became a landmark.
But his political activities caused him trouble. Although he had left the Trotskyist organisation in 1947, he was refused admission to the United States when he wanted to collect the Fields Medal, and it was some time before he was allowed in. He justified the twin activities of mathematics and politics by saying that in mathematics you could not achieve anything unless you were subversive, questioning what had gone before, and in world affairs there occurred events that you could not accept.
Appointed to Paris as professor of mathematical analysis, he continued his research and teaching while joining such figures as Bertrand Russell to protest against war crimes, and against the Soviet invasion of Hungary in 1956. He never forgot, and often referred to, the example of Emile Duclaux, director of the Institut Pasteur, who had been one of the most resolute defenders of Dreyfus.
In 1957, Schwartz became involved in the affaire Audin, the case of the 25-year-old communist and teacher of mathematics in Algiers, who disappeared after being arrested by French paratroopers. Schwartz, then teaching at the Polytechnique, organised a meeting at the Sorbonne, presenting Audin's mathematical work, and launching a Committee-Maurice-Audin, which had the support of many university teachers and people such as François Mauriac and Jean-Paul Sartre.
In 1960, Schwartz was one of those who signed the Manifeste des 121, encouraging young men to refuse to serve in the French army at war in Algeria. As a result, he was suspended from his post at the Polytechnique for two years.
In 1964, he was awarded the Grand Prix of the Académie des Sciences for his work on mathematics (he was elected to the Académie in 1975). In 1966, at the Polytechnique, he founded the Centre de Mathématique, which combined teaching and research, and he carried out his own work on distribution theory there. He directed this centre for 17 years.
During the 1980s, having been appointed president of the national committee for the evaluation of universities, he produced a number of reports for the government. He insisted on the need for a more rigorous selection in the admission of students and on the need for university teachers to undertake research in their subjects. These demands did not make him a popular figure.
In 1997, he published his autobiography, Un mathématicien aux prises avec le siècle (A mathematician grappling with the century). On the first page, he assured readers that they could skip the passages devoted to mathematics, which formed only 15% of the book, although he also wrote that "mathematics have filled my life". Algeria was not forgotten. In October 2000, he publicly demanded that the French republic should recognise that it was guilty of having used torture in the Algerian war.
He married Marie-Hélène Lévy in 1938. They had a son who died aged 28, and a daughter.
[Laurent Schwartz, mathematician, born March 5 1915; died July 4 2002]
Douglas Johnson, Wednesday August 7, 2002 © Guardian Newspapers Limited