A Mathematician Grappling with His Century

"Many people nowadays seem to consider scientists, mathematicians and others, like people uninterested in moral questions, locked away in their ivory towers and indifferent to the outside world," writes Laurent Schwartz, winner of the Fields Medal in 1950, in his autobiography A Mathematician Grappling with His Century.

What Schwartz grappled with was the social and political issues that wracked France, Europe and the world in the mid-20th century. Chapter titles of this remarkable story include Trotskyist, The War against the Jews, Algerian Involvement, For an Independent Viet Nam, The Distant War in Afghanistan.

The reader will find few theorems in this book. Except for a brief discussion on Schwartz's most important mathematical contribution, the concept of distributions, which generalized the notion of function and allowed for a considerable broadening of calculus, most of the math in this book is written from a historical perspective and largely accessible to non-mathematical readers. As Schwartz writes, mathematics "concerns only about 15% of the volume."

What concerns the rest is Schwartz's great passion besides mathematics: his devotion to the struggle for oppressed people and for human rights.

As a young student Schwartz was admitted to the École Normale Superieure (ENS) in 1934, France's then main research academy. In fact, he just squeaked by with one of the lowest admission test scores! But he was quickly swept up in the exceptional intellectual level of the ENS. His teachers were Choquet, Frechet, Borel, Julia, Cartan, Lebesgue, Hadamard, a who's who of modern mathematics. As he writes, "The life of the ENS was a marvel for a young person of my temperament. In one blow, the field of mathematics became infinitely wide."

But on top of his love of mathematics, profound world events were making themselves felt in every corner of French life, especially at the university. The mid-1930s were the years of the French Popular Front with its slogan of "bread, peace, and freedom". His years at the ENS saw the evolution of a relatively privileged young boy from a politically conservative background into a militant left-winger. Schwartz devoured the works of Lenin and Trotsky, the leaders of the Russian Revolution. He was particularly won over by Rosa Luxemburg's The Accumulation of Capital, which "used mathematical formulas to prove that capitalism could not survive without colonialism." He describes his metamorphis as "spectacular."

The book journeys through his years in the military following the collapse of the Popular Front government, his escape from Paris after the victory of the pro-Nazi Vichy regime, and his attempts to teach and do research while waging a political struggle during World War II. Schwartz found his way to Clermont-Ferrand, where many French mathematicians had relocated. Life as a Jewish man, and Trotskyist sympathizer, led to several harrowing near misses with the police, and daily life included the search for enough food. Eventually, Schwartz and his wife, Marie-Helène, assumed false identities. In fact, the invention of distributions occurred while Schwartz was still using the name Selemartin.

"I have been involved in many activities besides mathematics, sometimes to such a point that my research suffered," explains Schwartz. On top of his political activities, "I have had another great passion, almost as intense as that for mathematics: . . . entomology, and particularly butterfly collection." This love absorbed Schwartz as a young child and never left him. In the middle of a chapter on "The war against the Jews," we are presented with an "entomological interlude," a fascination for a family of Attacidae or Saturniidae moths. Among other things, World War II forced Schwartz to temporarily abandon his butterfly collecting. His political affiliations caused visa problems that made visits to the United States difficult, and as a result Schwartz made many more trips to Third World countries. Remarkable excursions into the forests of Brazil, India, and Mexico led to the revitalization of his collection passion. Today he has one of the largest collections in Europe, approximately 19,000 butterflies collected over a 44-year period.

Also described in great detail is his association with the famous Bourbaki group of mostly French mathematicians who had such a deep impact on 20th century mathematics. There is much anecdotal material on Bourbaki and Schwartz's relations with its most prominent members: Cartan, Weil, Borel, Lang, Serre, and Dieudonné.

After the war, Schwartz began to distance himself politically from the Trotksyist movement. But he never diminished his commitment to human rights. Schwartz states that he dedicated the rest of his life to promoting justice, organizing support for national liberation movements, and analyzing the "appropriate" response to the burning social questions of the day. He was a leader in the "Action committee of intellectuals against the war in North Africa" and a prominent figure in support of Algerian resistance to French colonialism. He was active in support of Vietnamese independence and a leader in the anti-war movement. He spoke out against the Soviet invasion of Afghanistan.

The book concludes with his work with the Committee of Mathematicians, formed in 1974 to demand the release of mathematicians and other scientists around the world imprisoned for their alleged anti-government activities or views. Schwartz summarizes that the work of the Committee served two important functions: securing the release of the imprisoned, and showing the rest of the world that mathematicians can be absorbed by issues beyond their research.

The chapters of Laurent Schwartz's autobiography are organized to separate the significant periods of his life. Each one is filled with rich descriptions of events and the "players." His development as a mathematician and active member of the international mathematical community was a fascinating journey, aptly conveyed with a writing style that really gives the reader the feel of a fellow traveler.

As Schwartz writes, "I am deeply non-violent. I hate violence. But the world which I discovered during my years at the ENS was filled with terrible violence: capitalist exploitation, colonialism, fascism, Stalinism... Revolution was then in the air of the time, inevitable and certain... I devoted a large part of my life to politics. But still, of course, mathematics remained by primordial interest. I always wanted to 'change the world,' to change life."

Note: Laurent Schwartz died on July 4, 2002, after this review was completed.

Bob Dobrow (bdobrow@mathcs.carleton.edu) is Assistant Professor of Mathematics at Carleton College in Northfield, Minnesota. His research interests are in probability and he maintains The Probability Web at http://www.mathcs.carleton.edu/probweb/probweb.html. He plays cello and helps homeschool his three sons. Having spent most of his years in Boston and New York City, he now lives in a lovely town whose motto is "Cows, Colleges, and Contentment."