## Laurent Schwartz

### Mathematician who put the quantum physicists straight, but could not quite manage the same trick with politicians

Laurent Schwartz, mathematician, was born on March 5, 1915. He died on July 4, 2002, aged 87.
"To discover something in mathematics is to overcome an inhibition and a tradition. You cannot move forward if you are not subversive." Both the public life and the research of the French mathematician Laurent Schwartz eloquently bear out these much-quoted words from his 1997 book of memoirs, *Un mathematicien aux prises avec le siecle*. The first French winner of the Fields Medal, his discipline's equivalent of a Nobel Prize, he also made numerous interventions in his country's civic and political life, never fearing to upset the powers that-be in his responses to France's war in Algeria or in his views on education.

Schwartz was one of the 20th century's greatest exponents of mathematical analysis, the part of pure mathematics dealing with limiting operations such as the calculus and its ramifications. His most important contribution was his theory of "distributions" or "generalised functions" (as they are often called in English), the story of which is a classic case of the interplay between applications and theory, and between physics and mathematics.

In his classic book *The Principles of Quantum Mechanics* (1930), the great British physicist Paul Dirac (1902-84), one of the founding fathers of quantum mechanics, used his formalism of so-called "delta functions". As Dirac himself knew, in mathematical terms these made no sense at all - but they worked. The challenge of creating a mathematical theory that would tame Dirac's delta functions by bringing them within the scope of rigorous mathematics tantalised both mathematicians and physicists until it was resolved by Schwartz in a series of papers beginning in 1945.

Schwartz's two-volume *Theory of Distributions* (published in French in 1950-51) was a landmark. Since then, his ideas have been widely used and greatly developed, and form part of the standard equipment of a modern mathematician or scientist.

Born during the First World War, Laurent Schwartz was the son of a surgeon. His great-uncle was a mathematician and his uncle, Professor Robert Debre, was the founder of Unicef. Not surprisingly, given this intellectual environment, he was himself a brilliant student, as gifted in Latin as he was with equations, and was admitted to the Ecole Normale Superieure in the mid-1930s.

He joined the "Bourbakists", a group dedicated to modernising French mathematics by taking on board the progress made in Germany in the 1920s and ambitiously seeking to re-establish their discipline on a new foundation. One of Schwartz's companions in this group was another mathematical prodigy and Fields Medal winner, Jean-Pierre Serre.

The intellectual ferment of these years was paralleled by political engagement. Though from a traditionally right-wing background, he was a strong supporter of Leon Blum's Popular Front Government until he became disillusioned by its failure to support the Spanish Republicans. Similarly, his sympathies for communism were soon dampened by Stalin's show trials, though he then spent ten years as a Trotskyite, up to 1947. He claimed never to regret this, even though it almost prevented him travelling to America to receive the Fields Medal.

During the war his political activities and Jewish background put him in all manner of delicate situations. Nevertheless, he managed to find a teaching position in Clermont-Ferrand in 1942 before returning to Paris in 1944. It was there, one night, that he made his mathematical breakthrough.

After the war his research and teaching at the universities of Grenoble and Nancy, and at the elite Ecole Polytechnique in Paris, were accompanied by civic activism. With Sartre, Vercors and Vailland, he protested against the Soviet invasion of Hungary in 1956.

The following year came the "Audin Affair" in Algeria. Audin, a mathematician and communist based in Algiers, was writing his thesis under Schwartz's supervision. But in June 1957 the 25-year-old father of three and opponent of French rule in Algeria was abducted by paratroopers, tortured and killed. Schwartz was tireless in his calls for justice, and organised a presentation of the young man's thesis in his absence.

Vocal in his opposition to the French campaign, he signed the famous "Declaration des 121" in favour of military insubordination. The riposte of Pierre Messmer, the Minister for the French Army (and, by the same token, of the Ecole), was to strip him of his position at the Polytechnique, for reasons of "common sense and honour". To which Schwartz replied that since the Army commanded by Messmer had sanctioned torture and promoted torturers, such remarks were absurd.

After a brief exile in New York, he regained his post two years later, to make a major contribution to the school's prestigious mathematics laboratory. Writing of this period in his memoirs, Schwartz stated his conviction that "by virtue of my persistent and energetic activity" he had been a factor in the achievement of peace in Algeria: "No more than a factor, but more than a drop in the ocean."

Other struggles followed. Schwartz campaigned against the American intervention in Vietnam and the Soviet invasion of Afghanistan and Chechnya. As a member of the Committee of Mathematicians he worked to support embattled fellow intellectuals in the Soviet Union, Morocco and Uruguay. As he said: "I have always thought that morality in politics was something essential, just like feelings and affinities."

Schwartz never offered blind allegiance to Left or Right. Above all he was, in his own words, a man who hated to see systems not working properly. In 1981 he was asked by Francois Mitterrand's new Socialist Government to help to prepare a report on the teaching of science. Two years later, he signed the "Appel des 55", opposing the education reforms proposed by Alain Savary. But a few years later, after French students had taken to the streets to defeat attempts at introducing selection into the university system, he came out in favour of precisely that.

As well as the Fields Medal, Schwartz received three prizes from the Paris Academy of Sciences, of which he was a member, and many honorary doctorates. A man with a mischievous sense of detachment, he advised non-mathematician readers of his biography to "skip" the pages devoted to his discipline (a mere 15 per cent). He was also a great collector of butterflies, with over 20,000 specimens.

© The Times, 2002