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Laurent Schwartz: The Vicissitudes of an Internationalist

The four lives of Laurent Schwartz

Sunday 16 October 2022, by siawi3


Laurent Schwartz: The Vicissitudes of an Internationalist

Monday 22 August 2022,

by Dan LA BOTZ

Photo: Laurent SCHWARTZ

The first of an occasional series of articles on the lives of figures of the French left.

For more than a decade, from 1936 to 1947, Laurent Schwartz (1915-2002), the famous mathematician, was a Trotskyist in France, though that was only one short period in a long life dedicated to mathematics, butterflies, and politics. In his Trotskyist period he served in the French military during the phony war, lived under the Nazi occupation as a Jew, and participated in the Resistance. Later in his life, he was active in the French anti-colonialist movements, opposing the French government and military while supporting both the Algerian and Vietnamese movements.

Schwartz always credited the Trotskyist movement with having given him his fundamental political education and above all with having made him an internationalist. Yet, even while he was a member of the Trotskyist organizations—and for several of those years Trotsky himself was alive and leading them—Schwarz often differed with the group’s strategies, its organizational approach, and its political style and sometimes declined to carry out its policies. Still even when he was a dissenter, he continued to put his life at risk for the Trotskyist party to which he belonged that was engaged in the fight against Nazism. I believe we have a lot to learn from both his appreciation of the Trotskyism and from his criticisms of the Trotskyists which are similar to some of those made by others coming out of the Trotskyist movement at that time such as Boris Souvarine and Victor Serge.

Becoming a Mathematician, A Naturalist, and a Trotskyist

Photo: Schwartz at his family’s country house in Autouillet, France. Family Archives

Photo: Laurent and his wife Marie-Hélène.

Schwartz grew up in a bourgeois family of Alsatian Jewish origin; his father was a surgeon. The young Laurent attended the highly competitive Lycée Louis-le-Grand. While at the lycée he met and fell in love with Marie-Hélène Lévy, the daughter of the famous mathematician Paul Pierre Lévy who was herself also a mathematician. Both he and his wife went on to study at the École Normale Supérieure but she contracted tuberculosis and had to drop out, though even while convalescing she also continued working on mathematics.

During the Nazi occupation, Laurent and Marie-Hélène had a child, complicating both their clandestine wartime existence, their study of mathematics, and political work. Then too there was his avid interest in studying and breeding butterflies that filled their houses with caterpillars and cocoons.

How did Laurent become a Trotskyist? The events of 1934, both the right-wing riots of February 6, 1934—interpreted by the left as a fascist attempt at a coup de état—and the attempted Nazi coup in Austria of July1934, turned Schwarz toward politics and toward the left. Apparently he heard someone—one of many at the time—say that it was a crisis of capitalism and the liberal state. Wanting to understand capitalism, he read Karl Marx and Rosa Luxemburg and then undertook a study of the French economy. When the Popular Front arose in 1935, “I willingly let myself be carried away by the broad movement,” he wrote.[1] In May 1936, Schwarz voted for the Socialist Party and was thrilled with the victory of the Popular Front, but soon became disillusioned. When in July 1936, General Francisco Franc rebelled against the Spanish Republican government, leading to the Spanish Civil War, the Popular Front government for which Schwartz had voted adopted a policy of non-intervention, refusing to support the Spanish Republic. “Non-intervention profoundly disappointed me, and constituted in my view a major political mistake.”[2] While depressed by the developments in Spain, Schwartz spirits were lifted by the French general strike of 1936.

Photo: Bourbaki gathering at Dieulefit in 1938. From left, Simone Weil,[a] Charles Pisot, André Weil, Jean Dieudonné (sitting), Claude Chabauty, Charles Ehresmann, and Jean Delsarte.

We should mention that during the years 1934-35 while becoming a serious leftist, Schwartz also joined with a group of a dozen mathematicians to carry out a fundamental revision of the foundations of mathematical pedagogy. The collective called itself Nikolas Bourbaki, a fictious mathematician, and published Éléments de mathématique (Elements of Mathematics) which dealt with topics such as set theory, abstract algebra, topology, and other matters. Under Bourbaki’s name, they eventually published some 19 books and many articles.[3]

In October 1936, after talking it over with his wife Marie-Hélène, Schwartz joined the Communist Party, despite what he saw as its sectarianism and its cant and jargon (langue de bois). He writes in his memoir that he was motivated to join by the fact that he felt at the time that what was needed was a large and powerful working-class party. But about the time that he joined, in August of 1936, Stalin’s trials of the Bolshevik leaders Grigory Zinoviev and Lev Kamenev began, with the absent Leon Trotsky depicted as the central organizer of an anti-Soviet conspiracy. As it happens, shortly before the trials a family friend had given Marie-Hélène a copy of Trotsky’s My Life, which Schwartz had also read, and consequently he found it incredible that Trotsky should have turned into a counter-revolutionary. At that time, Schwartz had never heard of either a French Trotskyist party, but an avid reader of all the newspapers and magazines, in Le Petit Parisien, he came across an interview with the Trotskyist Fred Zeller that included the address of the offices of his party. So, a day or two later, Schwartz went to the Trotskyist party offices where he met several of Trotskyist leaders and activists, and was impressed with their “political intelligence.”[4]

Later in that same month of October 1936 that he had become a Communist, Schwartz became a Trotskyist. There were in fact two Trotskyist organizations in France, the Parti ouvrier internationaliste (POI or Internationalist Workers Party), which he had joined, and the rival Parti communiste internationaliste (PCI and the Internationalist Communist Party). About that same time, Schwartz read and reread Trotsky’s The Revolution Betrayed, with its analysis of the Soviet Union, but Schwartz rejected what he saw as Trotsky’s pessimistic view that given the circumstance the degeneration of the Soviet Union was inevitable. Schwartz recalls in his memoir that he believed that had Trotsky taken power he might have steered the Soviet Union in a different direction. Schwartz read too and was greatly impressed by Trotsky’s History of the Russian Revolution, and at that time he also read and found useful Victor Serge’s From Lenin to Stalin (1937) and valued Boris Souvarine’s Stalin (1935), though it was condemned by the Trotskyists.

His Differences with Trotsky

Trotsky also wrote brilliantly on the situation in Germany, calling for a “united front”[5] between the Communist and Socialist parties in order to block and to defeat Adolf Hitler and his Nazis. But writes Schwartz, “It is remarkable that Trotsky was so clear about the necessity of a united front within Germany before Hitler came to power, and that the Trotskyists of the entire world have been always been so tragically unable to form a united front with anyone.”[6] Schwartz understands that in France in the 1930s or during the war, with the Trotskyists slandered and vilified as agents of Hitler, that it was impossible to form a united front with the Communist or Socialist parties, but he was also critical of the Trotskyists for their inability in that period to form alliances with groups such as Marceau Pivert’s Gauche révolucionnaire (Revolutionary Left) in France and with the Partido Obrero Unificado Marxista (POUM – Workers Party of Marxist Unification) in Spain. Moreover, he criticized Trotsky’s formula of “marching separately and striking together” combined with full “freedom of criticism” of other parties in the united front. That, said Schwartz, completely undermined any united front from the beginning. “One must establish a mutual dialogue, but the Trotskyist party thought it could polemicize in the time of a united Front, just as if it didn’t exist.”[7]

Schwarz also though that the Trotskyist approach to Spain was “tainted with mistakes.” Schwarz writes that, “The POUM was a revolutionary Marxist and non-Stalinist party, very close to the Trotskyists.” But, “Instead of supporting this strong party, the Fourth International supported the ‘Spanish Trotskyist party,’ a phantom that no one has ever found to have more than two members, Munis and Carlini, rather pale figures compared to the leaders of the POUM. (Calini claimed that the Trotskyists had twelve members in Spain.) This is one of the least glorious moments of Trotskyist sectarianism.”[8]

Schwarz writes, and the reader can clearly see from his remarks cited above, “While I adopted Trotskyism, I continued to think independently, though my differences with Trotsky’s party were not few.” Schwartz’s mentions that he shared many of Victor Serge’s criticisms. Looking back at Trotsky in the 1920s, Schwartz recalls that he was shocked when he read Trotsky’s pamphlet In Defense of Terrorism, which defended the Bolshevik terror during the Russian Revolution, and felt similarly about Their Morals and Ours, seeing in it the “germs of tyranny.”[9] Schwarz writes that, “The politics of the Trotskyist party in France also provoked doubts.” At the time of the French general strike of June 1936, Trotsky wrote, “The socialist revolution in France has begun.” Yet, says Schwarz, the Trotskyists refused to join the Popular Front because of the participation of the petty-bourgeois Radical Party. Instead, Schwartz observes, they entered the Socialist Party, from which they were soon excluded.

Schwarz not only differed with Trotsky and some of his own comrades on theoretical and strategic questions, but sometimes on tactics as well. Schwarz recounts how after the Popular Front’s victory, the Communists organized a workers’ demonstration against the Socialist Party, and that the head of his Trotskyist cell told its members to go there, if possible, with a pistol. Schwarz writes, “I disapproved of such an absurd suggestion and didn’t go.”[10] Yet, despite all of his differences, Schwartz stuck with the Trotskyist group that had provided him his political education and had instilled in him a deep commitment to internationalism.

From Military Service to Nazi Occupation

When he graduated from the École Normale in July 1937, Schwarz decided to do his obligatory two years of military service immediately and was assigned to an anti-aircraft defense post at a base near Metz, near the German border, and a year later to a base at Laon, also in northern France. He disliked the uncultured lieutenants and preferred the non-commissioned officers who knew more about the weapons. Mostly, having no one to talk to about science or politics, he was bored. “Bored, bored, bored.”[11] Luckily there was a local public library in Laon where he checked out books on physics, chemistry, biology, natural science, geography, economic geography, economic history, and some literature, “to fill up the lacunas” in his education.

When the Munich agreement was signed on September 30, 1938, Schwarz writes, “I understood immediately what Munich represented and I violently rejected the capitulation.” The Popular Front had collapsed, Franco was on the path to victory in Spain, Munich had given Hitler the Sudetenland, and Schwarz found the French military to be disorganized and unprepared. The situation was extremely discouraging. Shortly before the French declaration of war against Germany in 1939, he was transferred to a garrison near Paris where he was able to reestablish contact both with his family and his Trotskyist comrades. The announcement of the Hitler-Stalin non-aggression pact, he notes “didn’t surprise us. We knew Stalinism.”[12] With the defeat of the Spanish Republic by Franco, Schwarz writes, “I felt like a tiny feather on the immense checkerboard of the world, a drop of water in the middle of an ocean of events completely beyond my influence. My two years of military service [which ended in September 1939] seemed to me to be a complete waste.”[13]

Still his wife was getting better. While convalescing from tuberculosis, Marie Hélène, studying with Laurent, earned her certificate in rational mechanics (the mathematical study of motions generated from specific forces, as opposed to statics), secured her professional license, and finally felt well enough to return more seriously to the study of mathematics and began to publish articles. Laurent, now a lieutenant, taught the art of firing anti-aircraft guns to reserve officers at a military base at Biscarrosse-Bourg in southwestern France.

On September 3, 1939, following the German invasion of Poland, France declared war on Germany, but during what is called the drôle du guerre (the phony war) there was little fighting between the declaration and April 1940 when the Battle for France began until May 10 until June 25, 1940 when the French surrendered. As Schwartz observes, the French bourgeoisie and government seemed to have little stomach for fighting the Nazis who had so quickly defeated France and entered Paris. Marshal Phillippe Pétain became the head of state, met with Hitler and shook his hand, and that began the country’s wartime collaboration with Nazi Germany. The armistice signed by Pétain’s Vichy government, at first divided France into a German occupied zone in the north and along the west coast and a Vichy ruled “Free Zone” in the southeast.

The persecution of Jews began in September 1940 with new laws excluded that excluded Jews from certain occupations and business, followed in August 1941 by a ban on Jews using radios or telephone, and shortly thereafter with the banning of all Jews from public places and the bombing of synagogues. In November of 1942, the German Army occupied the Free Zone, carrying their anti-Semitic policies with them. There were some 340,000 Jews living in France, about half of them immigrants from other European countries. The Vichy government collaborated with the Nazis in rounding up and deporting 75,000 to death camps, where about 72,500 were killed.

Throughout the period from 1940 to 1945, like many Jews in France, Laurent and Marie Hélène relocated to the Free Zone and then moved from one small rural town to another attempting to hide themselves and their new born child. Eventually they went to the small portion of France occupied by the Italian fascists. Laurent worked at various teaching jobs as they struggled to keep food on the table, while they continued to study mathematics, and he as always to raise butterflies. They secured false papers, and led a clandestine life while at the same time Laurent remained active in Trotskyist groups and in the underground resistance.

Rethinking Revolutionary Theory

As Schwarz writes, revolutionary theory of the First World War period had been built on the notion of “revolutionary defeatism,” that is calling in the case of war for the defeat of one’s own government. It was that conception that tended to dominate the thinking of the small Trotskyist parties in France that were initially opposed to any support for the Allies—Great Britain and France—and called instead turning the war into a revolution. But Marcel Hic, a young and influential Trotskyist leader argued that occupied France had become an oppressed nation and had to fight together with the Allies for France’s right to self-determination. The problem was, “…how to fight against the Nazis and not submit to the orders of our capitalist adversaries.”[14] Many of the Trotskyists—a majority of the POI agreed—though that position was ultimately defeated in 1942. Schwarz writes,

I was fundamentally in agreement with the content of [Hic’s position]…but I didn’t dare to say what I really thought, because I would be contradicting myself. I suffered from a kind of schizophrenia, in a certain weak sense of the word. On the one hand, the ten commandments of Trotskyism and of Lenin concerning the previous war clearly stipulated bringing about the defeat of owns own imperialism in a civil war. On the other hand, it was patently obvious that such a development was impossible. Fighting Nazism seemed an absolute necessity, beginning with updating our language which still dated from the last war. The result of this split inside myself was without a doubt, as it was for many Trotskyists, to render our action sterile, ineffective. [15]

Schwartz believed that Trotsky had in fact radically revised his position in 1940, claiming that Trotsky had written, “We must defend our cities, our towns, our churches, our intellectual life, workers and peasants, against Nazi barbarism.”[16] And, said Schwarz, Trotsky himself had called upon American workers to push Roosevelt to enter the war.[17] The French, he says, were, however, unaware of Trotsky’s latest positions.

Though he was a Jew, and a husband, with a wife, and a new baby, and though he had many doubts and criticism of the Trotskyists, he continued to work with his organization during the Nazi occupation, his life always in peril. He divides the POI members’ experiences in this period into three groups. One group worked on organizing fraternization with German soldiers to win them to anti-fascism and a fight against the Nazis. Some of those POI members published a newspaper called Arbeiter und Soldat (Worker and Soldier) and actually did succeed in organizing a group of 27 German soldiers, but a spy in their midst turned them. The soldiers were shot, while the Trotskyists were tortured and deported to German concentration camps. A second group worked in the unions in the factories to organize against collaborationist bosses, and a few of them became influential union leaders in the post-war period. The third group was made up of Trotskyists either completely isolated in very small groups. One of the small groups in which he was involved published pamphlets and newspapers, among them the principal Trotskyist paper La Verité (The Truth). He himself, using his various aliases, was engaged in the dangerous work of distributing the papers and brochures, and he had a few close calls, as did Marie Hélène .

“The Trotskyist resistance, despite its undeniable courage, remained pretty ineffective,” writes Schwarz. “There were less than 200 of us!” They might have joined the maquis, the French resistance, but not only were many in the group opposed politically because of the role of General Charles de Gaulle, but there was also the danger of being assassinated by the Stalinists. Summing up this period Schwartz writes, “Trotskyism had given me during my years at the Normale a remarkable political education (formation), clearly more advanced and sophisticated than that of most of the young people of my age. But the extremism and the sectarianism of its ideas, and its cant, undermined my commitment during the Occupation.”[18] At the end of the war, Schwarz was also disappointed by the Trotskyist Fourth International’s inability to discuss the holocaust. “No one mentioned the Jews.”[19] Schwartz had, in this period, become a leader of what was referred to by its opponents as the “rightwing” of the Trotskyist movement, together with Albert Demazière, Paul Parisot, and Yvan Craipeau. But by 1947 he had left the Trotskyists and later joined the Socialist Party.

It was in 1944-45, as Paris was liberated, that Schwartz made his discovery of what in mathematics are called “distributions” or sometimes “generalized functions,” his great contribution to mathematical theory. Though, when in 1950 the International Mathematical Union awarded him the Fields Medal (comparable to the Nobel Prize), the United States refused to admit him to the country for the ceremony. In any case, with the war over, he now pursued his academic career in earnest. He became a professor at Nancy University, then moved to the Sorbonne in 1952, and in 1958 he became a professor as well at the École Polytechnique (EP). He taught there until 1980.

While no longer a Trotskyist, Laurent remained political, on the left, and an internationalist. In 1956 he joined with Bertrand Russell to protest the Soviet invasion of Hungary to crush the workers’ revolution there. In 1957, together with François Mauriac and Sartre, Schwartz helped to organize the Committee-Maurice-Audin. Schwartz protested French paratroopers’ murder of Audin, a 25-year-old communist and teacher of mathematics in Algiers. He also arranged to award Audin his advanced degree in mathematics posthumously. Perhaps most famously, in1960, Schwartz signed the Manifesto of 121, which encouraged young men to refuse to serve in the French army as long as it was at war in Algeria. That led the EP to suspend him from teaching position from 1962 to 63. His son Marc André, who was also active in that movement opposing France in Algeria, was apparently kidnapped by French right-wingers, an experience that may have led to mental illness and eventually to his suicide.[20]

Photo: Laurent Schwartz in Vietnam Family Archives

In 1960 Schwartz and other in the Socialist Party’s left wing who opposed the French war in Algeria split and then joined with other former Socialists and some ex-Communists founded the Unified Socialist Party (PSU). Schwartz stood in solidarity with Algeria’s war of independence, During the late 1960s and 1970s, Schwartz actively opposed the U.S. war in Vietnam, and in the 180s he also opposed what he called the Soviet Union’s “Vietnam war” in Afghanistan, even though he recognized a Soviet colonial government would be more progressive than the Taliban, because any imperialist war was intolerable. Throughout his life, Laurent Schwartz, though he abandoned his earlier commitment to Trotskyism for which he had repeatedly risked his life, remained a humanist, an anti-imperialist, and a socialist.

The picture that Schwartz paints of French Trotskyism in the Great Depression of the 1930s and during World War II is that of a small band of committed revolutionary socialists, divided into rival groups because of their differences on various questions, heroically resisting the Nazis but failing to have much of an impact because because of the persecution they faced from Nazis and the Communist Party, and because they could not find their place in the French resistance, in part due to their often sectarian in their strategy and tactics, Schwartz faults himself for being unable to voice his views and assert them in the Trotskyist POI, but clearly that was also a reflection of the character of the group with little toleration for differences. One has to admire Schwartz’s loyalty to the Trotskyist group and its dangerous work, as well as his perspicacity in identifying the group’s mistakes and limitations. And one has to admire too the leading role he played an important role on the left, especially in the anti-colonial movement.

Dan La Botz


[1] Laurent Schwartz, Un mathématicien aux prises avec le siècle (Paris: Éditions Odile Jacob, 1997), p. 105. All translations are mine.

[2] Schwartz, Un mathématicien, p. 108.

[3] Schwartz, Un mathématicien, pp. 158-177. See these two short video about Nikolas Bourbaki “The greatest mathematician that never lived” by Pratik Aghor at and “Bourbaki – a Tale of Mathematics, Lions and Espionage” by The Ferret at

[4] Among those he met in this period were: Paul Parisot, Albert Demazière, Marcel Beaufrère, Marcel Hic, David Rousset, Pierre Naville, Roland et Yvonne Filiatre, Yvan Craipeau, and Gérard Bloch.

[5] In the Trotskyist tradition, the term “united front” refers to an alliance between working class parties and is different than a “popular front” which is an alliance between working class parties and petty bourgeois or bourgeois parties.

[6] Schwartz, Un mathématicien, p. 122.

[7] Schwartz, Un mathématicien, p. 122.

[8] Schwartz, Un mathématicien, p. 124.

[9] Schwartz, Un mathématicien, p. 126.

[10] Schwartz, Un mathématicien, p. 133.

[11] Schwartz, Un mathématicien, p. 139.

[12] Schwartz, Un mathématicien, p. 142.

[13] Schwartz, Un mathématicien, p. 143.

[14] Schwartz, Un mathématicien, p. 181.

[15] Schwartz, Un mathématicien, pp. 130-31.

[16] I have been unable to locate this quotation from Trotsky.

[17] I am unaware of any article where Trotsky argues that position.

[18] Schwartz, Un mathématicien, p. 186.

[19] Schwartz, Un mathématicien, p. 271.

[20] “The four lives of Laurent Schwartz,” posted in martin’s blog on Sat, 07/02/2015 – 22:54,

New Politics. August 22, 2022



The four lives of Laurent Schwartz

Posted in martin’s blog on Sat, 07/02/2015 - 22:54,

I recently came across Laurent Schwartz’s autobiography, published in French in 1997, and in English in 2001. Maybe for reasons which I’ll indicate, it has not become a well-known book; but there is much to be extracted from it.

Schwartz was a Trotskyist from when he was shocked by the Moscow Trials, in 1936, at the age of 21, until 1947; and an energetic left activist all his life, often cooperating with Trotskyists.

In 1946-7 he had become active enough to serve on the day-to-day leading committee of the small French Trotskyist movement, and to be invited to work for the movement full-time as its secretary. He quit the movement in 1947, and so, soon after, did almost all the figures of the so-called “right wing” of the French Trotskyist movement at that time, to whom he was closest - Albert Demazière, Paul Parisot, Yvan Craipeau, and others.

Schwartz broke from Trotskyism more thoroughly than Craipeau and Parisot ever did, but remained active, especially in solidarity with Algeria’s war of independence (1954-62), against the US war in Vietnam (later 1960s and early 70s), against what he calls the USSR’s “new ’Vietnam’ war” in Afghanistan (early 1980s), and in a Committee of Mathematicians which campaigned, sometimes successfully, for the freedom of mathematicians who were political detainees in countries from the USSR to Uruguay. He was also a prominent member of the PSU, a leftish split from the Socialist Party generated by opposition to the Algerian war.

His day job, all that time, was as a university professor of mathematics, and an eminent one. His most famous mathematical discovery, which in 1950 won him the Fields Medal (maths’ equivalent of the Nobel Prize), was made in 1944, while he was still a Trotskyist activist.

Schwartz’s later activism was not the usual sedate academics’ business of signing letters to the newspapers from time to time. He organised committees, spoke at meetings. His activity against France’s war in Algeria got him sacked from his university job for a year (1962-3). His son Marc-André, also active, was kidnapped by French right-wingers; though Marc-André escaped after two days, the kidnapping left him so scarred that he became mentally ill, frequently attempted suicide, and eventually succeeded.

The autobiography shows that Schwartz remained in contact with Craipeau and Parisot, and often worked with Trotskyists. But he explains his break with Trotskyism on the grounds - surely read back onto his 1947 mind with the hindsight of 1997, when, at the age of 82, he produced his autobiography - that Trotskyists fail to recognise that the working class is not and will never become educated enough to aspire to social power. “The proletariat and peasantry do not progress sufficiently in the educational system, not only because of defects in the structure of the system, but because of their own lack of ambition”. Schwartz, oddly for someone in the very hierarchical French university system, considers contemporary education too “egalitarian” and not “selective” enough.

Yet he recounts, with obvious pride, that some people still considered him a Trotskyist, and says that one friend’s political definition of him as “a former Trotskyist” is accurate. He is proud of his Trotskyist past, not ashamed of it.

Having (at the time, or in later rationalisation) made such a fundamental break with Trotskyism, he puts nothing in his autobiography about the debates in the Trotskyist movement either in his time or later. The French Trotskyist movement in 1946-7 was hot with debate. Parisot and others had, for a short while after 1948, links with Max Shachtman’s Workers Party in the USA. Craipeau remained active on the left until his death and sardonically entitled his 1999 autobiography “Memoirs of a Trotskyist Dinosaur”. He had been (in 1937) the first Trotskyist advocate of a “bureaucratic collectivist” description of Stalin’s USSR, and later wrote extensively to argue that it was state-capitalist.

Schwartz comments on none of that. But he attributes his internationalism to his Trotskyist past, and from that internationalist viewpoint gives a vivid picture of many political episodes.

The autobiography is a difficult book. Schwartz, not a modest man, describes himself as still energetic at 82 and having an exceptional memory. It must be true: he could not otherwise have led the life he led, or produced the book.

But I suspect, and am sometimes sure, that at 82 Schwartz is sometimes reading later thoughts back onto earlier events. The book reads as if dictated to an amanuensis (Isabelle Rozenbaumas, a historian who has since become a film director); scarcely copy-edited; poorly translated from French into English; and scrappily proof-read.

Schwartz was part of the Bourbaki group of French mathematicians. He argues that the Bourbaki project would have been impossible except that André Weil, one of its founders, had gone to Germany to study with Emmy Noether and others in the 1920s, when most French mathematicians were trying, for chauvinist reasons, to ban Germans from international mathematical conferences.

Even he had done nothing in politics and had not made his great mathematical discovery in 1944, Schwartz’s role in Bourbaki would be a remarkable life’s work. The group produced 19 books, over many years, as a systematic rewriting of large areas of mathematics in the way that Noether and her colleagues had rewritten algebra.

It was an extraordinary procedure, maybe the only example in history of important books being produced in a more-or-less planned way by a committee. Each area of mathematics was successively named as the subject for a book. (There were many arguments about the order).

One member of the group would then write a “zero-th” draft of a book. The draft would be “completely demolished” in the group’s stormy, rowdy monthly meetings. The main organiser of the group once it got going, Jean Dieudonné, whom Schwartz describes as doing mathematics full-tilt 18 hours a day, every day, would threaten to walk out, or actually walk out, at almost every meeting.

Then another member would write another draft. Then another, another... until “around the seventh or eighth version”, the group finally conceded that a draft was ready to publish under the authorship of the fictitious “Nicolas Bourbaki”. The result was not a textbook, nor a report of research - members of the group wrote their own textbooks, and research reports, separately - but an attempted model of how the particular area of mathematics could be systematised and generalised.

The project never achieved its stated goal. Pure mathematics was expanding much faster than the group’s attempts to systematise it, and the group never tried to integrate applied mathematics. But Schwartz is surely right to say that Bourbaki changed the whole style of mathematics.

The book includes large chunks of mathematics, recounted as to another mathematician specialising in Schwartz’s chosen areas, with few explanatory concessions even to professional mathematicians specialising in other areas. Schwartz had a fourth life as an ardent butterfly collector, and there is a lot in the book about butterflies.

He recounts that in the 1920s French mathematicians refused, for chauvinist reasons, to pay attention to German mathematics (which then led the world), and even sought to ban German mathematicians from international conferences.

Schwartz met the other Bourbaki mathematicians during World War 2, which, as a Jew and a Trotskyist in France, he survived only through luck. He moved to the Vichy area, and then to the small Italian-occupied part of France, living in small hamlets, maintaining multiple identities, sometimes meeting people who (he later discovered) really knew he was Jewish but chose to protect him, but often finding French people who hated Jews and the English much more than they disliked the Nazis.

At one point he survived a round-up at a railway station - in which, as was routine, the Gestapo ordered all men to undress and took for deportation all who were circumcised - only because he noticed the officers gathering and slipped out early enough.

His post-Trotskyist political activity reads as that of a “Third-Worldist”, but his attitudes are not like that at all.

He criticises, for example, the fringes of the Vietnam movement in Europe and the USA who went for terrorist activity as the most militant form of solidarity: “a dangerous insanity which recalls the insanity of today’s fundamentalist Islam... a generally more or less concealed anti-semitism, called ’anti-Zionism’.”

He describes himself “breaking with” Noam Chomsky, because Chomsky “continued to support Pol Pot for too long”. Schwartz became a member of a committee to expose Pol Pot’s atrocities in Cambodia.

On Afghanistan he comments: “One might claim that we shouldn’t have expended so much energy on the expulsion of the Soviets... their social program was so much better than the Taliban’s. But... the Red Army was a foreign conquering army, bringing bombings, massacres, torture and mass executions. The Afghans unanimously revolt against it... it was impossible not to support them.”The final result is execrable...But it was the... Soviet repression which gave rise to civil war and the Taliban“. Similarly, Schwartz does not regret opposing the Shah of Iran even though”the regime of the Ayatollahs is obscurantist and uses torture even more". Schwartz depicts himself as clearly aware that FLN rule in Algeria, or Stalinist rule in Vietnam, would be horrible, even while he was active in solidarity with their struggles against imperialism.

It is not because he looks to an independent working-class “Third Camp”. He sees a moral obligation to stand against repression, and sees no reason why that stand should require illusions about the victims of repression.

There are worse compasses in politics.