Fall 2024
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By Jari Taskinen
Alexander Grothendieck (1928 – 2014) is considered by many one of the greatest mathematicians of the last century. Besides being a mathematical genius, he was a German Jew who survived World War II. The story could be considered a wonderful example of how practical Christianity contributed to the progress of science.
Grothendieck’s survival, and indeed his basic mathematical education, depended on the courage and endeavors of French Christians living, and risking their own lives, in the town of Le Chambon-sur-Lignon in the Vivarais Plateau of south-central France.
There are many accounts of the bravery of the people of Le Chambon (1), as well as of Grothendieck’s mathematics (2). What I find interesting is how the two stories intertwine.
Alexander Grothendieck (1928 – 2014) is considered by many one of the greatest mathematicians of the last century. Besides being a mathematical genius, he was a German Jew who survived World War II. The story could be considered a wonderful example of how practical Christianity contributed to the progress of science.
Grothendieck’s survival, and indeed his basic mathematical education, depended on the courage and endeavors of French Christians living, and risking their own lives, in the town of Le Chambon-sur-Lignon in the Vivarais Plateau of south-central France.
There are many accounts of the bravery of the people of Le Chambon (1), as well as of Grothendieck’s mathematics (2). What I find interesting is how the two stories intertwine.
In 1990, the State of Israel recognized the inhabitants of Le Chambon as “Righteous Among the Nations.” |
Grothendieck’s family background was unconventional. He was born in Berlin in March 1928 to Sascha (Alexander) Shapiro, a Russian Jew and anarchist who had escaped to Germany after fighting in the Russian Revolution, and Hanka Grothendieck, a German journalist who also sympathized with anarchist ideas. As the Nazis gained power in Germany in the early 1930s, his parents were among those who saw what was to come and decided to move to Paris.
Hanka sent her son to a foster home with the family of Pastor Wilhelm Heydorn and his wife Dagmar in Hamburg. Alexander lived there for five years, and he had the opportunity to attend school. As the situation for Jews got more and more difficult in Germany, he was sent to France, where he again met and lived with his mother. After the start of the war, Hanka and Alexander were interned in the Rieucros camp for “undesirable foreigners” near the town of Mende in Southern France.
In 1942 Alexander was again separated from his mother, and he ended up in Le Chambon-sur-Lignon, a town which at the time was in the area of Vichy France (ruled by the pro-German but nominally independent Vichy regime). Alexander’s father was interned and killed in Auschwitz in 1942, but Hanka survived the war.
Why Le Chambon? Le Chambon-sur-Lignon is situated in an isolated, hilly part of south-central France. The region is also known as the Protestant Mountain because it was settled by the French Huguenots who had fled there to avoid religious persecution. This history of persecution led the inhabitants of the region to oppose the Vichy government and its anti-Jewish policies. The descendants of the Huguenot refugees recognized a shared destiny in the persecuted Jewish minority, and these sympathies inspired the people of the region to hide Jews and others whose lives were in danger.
The rescue efforts eventually became well organized. They were not restricted to the Protestant inhabitants: many Catholics also participated. The rescue operation was led by Pastor André Trocmé, assisted by his wife Magda and another pastor, Edouard Theis. Pastor Trocmé contacted the American Friends Service Committee, a Quaker organization in Marseille that was providing relief supplies to the 30,000 foreign Jews and others held in internment camps in southern France.,
Trocmé found out that the Quakers might be able to get internees released from the camps, but they needed a place to go afterwards. He assured the Quakers that Le Chambon would take in refugees. In addition to those who arrived in Le Chambon as a result of this organized rescue effort, individual Jews and others in danger also found their way to the town, having heard of the Vivarais Plateau as a possible safe place. Many of the incoming refugees were born abroad and did not have French citizenship, and the majority of them were children. After arrival they were dispersed among the isolated villages and farms in the surrounding hilly region.
The town of Le Chambon was raided many times by the Vichy police. However, the residents were often warned by sympathetic officials, and the Jews were sent into hiding in the forests until the raid was over. When Vichy France was finally occupied by the Germans in November 1942, the situation became more difficult. Pastors Trocmé and Theis were arrested, although they were released after a month. Eventually, they went into hiding, and Magda Trocmé stepped in to lead the rescue operation. An estimated 3,000 to 3,500 Jews were saved there during the war, as were others such as members of the French Resistance. The exact number is not known, because no records were kept, for obvious reasons. Some of the refugees were also guided by the people of Le Chambon to the safety of Switzerland, following the route the Huguenots had used centuries before.
In 1990, the State of Israel recognized the inhabitants of Le Chambon and those of nearby villages collectively as “Righteous Among the Nations.” French President Jacques Chirac officially recognized the heroism of the village during a visit there in July 2004.
The Protestant churches in the area had long been interested in offering at least a basic education for all people, including farmers, workers, and their families, so that everybody would be able to read the Bible. Pastor Trocmé had founded an international private school in Le Chambon in the 1930s called the Collège Cévenol, which continued instruction even during the chaotic wartime conditions. Grothendieck was one of the students, and he completed his Baccalauréat in 1945.
After the war, Grothendieck studied mathematics in Montpellier. In 1948, he moved to Paris, where he got in contact with the most important French mathematicians of the time. Laurent Schwartz was at that time writing his fundamental work on distribution theory, which is a branch of functional analysis providing a rigorous mathematical framework for the Dirac delta-function and other distributions, used by physicists since the invention of quantum mechanics. Grothedieck’s first great mathematical contributions were on the topic of functional analysis, where he developed the theory of locally convex spaces, used in Schwartz’s distribution theory, and also Banach space operator theory.
Grothendieck’s Ph.D. thesis “Produits tensoriels topologiques et espaces nucléaires” (3) and the article “Résumé de la théorie métrique des produits tensoriels topologiques” guided international mathematical research for the next four decades. He moved from functional analysis to algebraic geometry in 1954, influenced by Jean-Pierre Serre. His pioneering works in the fields of algebraic geometry are considered even more important, and they earned him the Fields medal, the “Nobel prize in mathematics,” in 1966. Grothendieck worked in the prestigious IHES, Institute des hautes études scientifiques, in Orsay near Paris. Later on, his interest in mathematics faded and was replaced by pacifist activities. In 1973, he moved back to southern France, where he lived near Montpellier for the rest of his life.
It is hard to say if the practical Christianity that was essential for his survival during the war had any influence on his way of thinking, although some signs of this can perhaps be found in the pacifist pamphlets he wrote in his later years.
The author of this essay contributed to Grothendieck’s mathematics by publishing in 1986 (4) the solution to one of the functional analytic problems left open in Grothendieck’s thesis (3). This paper was one in a series produced by many mathematicians, which helped to complete, by the end of the last century, the functional analytic tradition and theory started by the work of Schwartz and Grothendieck.
References
1. United States Holocaust Memorial Museum, “Le Chambon-sur-Lignon”, Holocaust Encylopedia, https://encyclopedia.ushmm.org/content/en/article/le-chambon-sur-lignon.
2. W. Scharlau, “Who is Alexander Grothendieck”, Notices of the AMS 55, 8 (2008), 930-941.
3. A. Grothendieck, “Produits tensoriels topologiques et espaces nucléaires” Memoirs of the American Mathematical Society 16 (1955)
4. J. Taskinen, “Counterexamples to ‘problème des topologies’ of Grothendieck”, Ann.Acad.Sci.Fenn. Ser A I Math. Dissertationes (1986) no. 63.
Jari Taskinen is Senior University Lecturer at the Department of Mathematics and Statistics of the University of Helsinki, and an active member of the Finnish Free Evangelical Church of Helsinki (in Finnish, Helsingin Vapaaseurakunta). Married with three children, he is also a music coordinator and leader of a houseband.
Hanka sent her son to a foster home with the family of Pastor Wilhelm Heydorn and his wife Dagmar in Hamburg. Alexander lived there for five years, and he had the opportunity to attend school. As the situation for Jews got more and more difficult in Germany, he was sent to France, where he again met and lived with his mother. After the start of the war, Hanka and Alexander were interned in the Rieucros camp for “undesirable foreigners” near the town of Mende in Southern France.
In 1942 Alexander was again separated from his mother, and he ended up in Le Chambon-sur-Lignon, a town which at the time was in the area of Vichy France (ruled by the pro-German but nominally independent Vichy regime). Alexander’s father was interned and killed in Auschwitz in 1942, but Hanka survived the war.
Why Le Chambon? Le Chambon-sur-Lignon is situated in an isolated, hilly part of south-central France. The region is also known as the Protestant Mountain because it was settled by the French Huguenots who had fled there to avoid religious persecution. This history of persecution led the inhabitants of the region to oppose the Vichy government and its anti-Jewish policies. The descendants of the Huguenot refugees recognized a shared destiny in the persecuted Jewish minority, and these sympathies inspired the people of the region to hide Jews and others whose lives were in danger.
The rescue efforts eventually became well organized. They were not restricted to the Protestant inhabitants: many Catholics also participated. The rescue operation was led by Pastor André Trocmé, assisted by his wife Magda and another pastor, Edouard Theis. Pastor Trocmé contacted the American Friends Service Committee, a Quaker organization in Marseille that was providing relief supplies to the 30,000 foreign Jews and others held in internment camps in southern France.,
Trocmé found out that the Quakers might be able to get internees released from the camps, but they needed a place to go afterwards. He assured the Quakers that Le Chambon would take in refugees. In addition to those who arrived in Le Chambon as a result of this organized rescue effort, individual Jews and others in danger also found their way to the town, having heard of the Vivarais Plateau as a possible safe place. Many of the incoming refugees were born abroad and did not have French citizenship, and the majority of them were children. After arrival they were dispersed among the isolated villages and farms in the surrounding hilly region.
The town of Le Chambon was raided many times by the Vichy police. However, the residents were often warned by sympathetic officials, and the Jews were sent into hiding in the forests until the raid was over. When Vichy France was finally occupied by the Germans in November 1942, the situation became more difficult. Pastors Trocmé and Theis were arrested, although they were released after a month. Eventually, they went into hiding, and Magda Trocmé stepped in to lead the rescue operation. An estimated 3,000 to 3,500 Jews were saved there during the war, as were others such as members of the French Resistance. The exact number is not known, because no records were kept, for obvious reasons. Some of the refugees were also guided by the people of Le Chambon to the safety of Switzerland, following the route the Huguenots had used centuries before.
In 1990, the State of Israel recognized the inhabitants of Le Chambon and those of nearby villages collectively as “Righteous Among the Nations.” French President Jacques Chirac officially recognized the heroism of the village during a visit there in July 2004.
The Protestant churches in the area had long been interested in offering at least a basic education for all people, including farmers, workers, and their families, so that everybody would be able to read the Bible. Pastor Trocmé had founded an international private school in Le Chambon in the 1930s called the Collège Cévenol, which continued instruction even during the chaotic wartime conditions. Grothendieck was one of the students, and he completed his Baccalauréat in 1945.
After the war, Grothendieck studied mathematics in Montpellier. In 1948, he moved to Paris, where he got in contact with the most important French mathematicians of the time. Laurent Schwartz was at that time writing his fundamental work on distribution theory, which is a branch of functional analysis providing a rigorous mathematical framework for the Dirac delta-function and other distributions, used by physicists since the invention of quantum mechanics. Grothedieck’s first great mathematical contributions were on the topic of functional analysis, where he developed the theory of locally convex spaces, used in Schwartz’s distribution theory, and also Banach space operator theory.
Grothendieck’s Ph.D. thesis “Produits tensoriels topologiques et espaces nucléaires” (3) and the article “Résumé de la théorie métrique des produits tensoriels topologiques” guided international mathematical research for the next four decades. He moved from functional analysis to algebraic geometry in 1954, influenced by Jean-Pierre Serre. His pioneering works in the fields of algebraic geometry are considered even more important, and they earned him the Fields medal, the “Nobel prize in mathematics,” in 1966. Grothendieck worked in the prestigious IHES, Institute des hautes études scientifiques, in Orsay near Paris. Later on, his interest in mathematics faded and was replaced by pacifist activities. In 1973, he moved back to southern France, where he lived near Montpellier for the rest of his life.
It is hard to say if the practical Christianity that was essential for his survival during the war had any influence on his way of thinking, although some signs of this can perhaps be found in the pacifist pamphlets he wrote in his later years.
The author of this essay contributed to Grothendieck’s mathematics by publishing in 1986 (4) the solution to one of the functional analytic problems left open in Grothendieck’s thesis (3). This paper was one in a series produced by many mathematicians, which helped to complete, by the end of the last century, the functional analytic tradition and theory started by the work of Schwartz and Grothendieck.
References
1. United States Holocaust Memorial Museum, “Le Chambon-sur-Lignon”, Holocaust Encylopedia, https://encyclopedia.ushmm.org/content/en/article/le-chambon-sur-lignon.
2. W. Scharlau, “Who is Alexander Grothendieck”, Notices of the AMS 55, 8 (2008), 930-941.
3. A. Grothendieck, “Produits tensoriels topologiques et espaces nucléaires” Memoirs of the American Mathematical Society 16 (1955)
4. J. Taskinen, “Counterexamples to ‘problème des topologies’ of Grothendieck”, Ann.Acad.Sci.Fenn. Ser A I Math. Dissertationes (1986) no. 63.
Jari Taskinen is Senior University Lecturer at the Department of Mathematics and Statistics of the University of Helsinki, and an active member of the Finnish Free Evangelical Church of Helsinki (in Finnish, Helsingin Vapaaseurakunta). Married with three children, he is also a music coordinator and leader of a houseband.