Jacques' mother was Dorothée (or Dora) Gittler and the family home was 16 Rue du 22 Novembre, just round the corner from where Armand had his business. This house, along with others on that side of the road, had been built around 1912 when it was a new residential area. The road had been named "Neue Strasse" from 1912 to 1918 and renamed "Rue du 22 Novembre" after Strasbourg returned to France following World War I. Jacques had a sister Jeannette, who had been born on 30 August 1916. Jacques and Janette were very close as they were growing up. Let us note that, although Jacques Feldbau is considered to be a French mathematician, in fact the family were German speaking and German was Jacques' first language. This is not surprising since at this time the majority of the families in Strasbourg were German speaking.
The family moved from Rue du 22 Novembre to 8 Rue des Pontonniers as Jacques was growing up and this reflects the fact that they were well-off and living a comfortable life. This Strasbourg address would remain Feldbau's home address for the rest of his life. On 1 October 1920 Feldbau began his primary school education in the Gymnasium Fustel de Coulanges. At this time girls were only educated for the first few classes, and his sister Janette attended the same school from October 1922 to July 1924. Feldbau remained at this school until 10 July 1925. He had been an excellent pupil although, probably because he was bored with the elementary material he was taught, he was somewhat restless. Feldbau was eleven years old in 1925 and he spent the school year 1925-26 at the rabbinical school in Paris. On 1 October 1926, having returned to Strasbourg, he re-entered the Gymnasium Fustel de Coulanges for his secondary education.
Feldbau was awarded his Premier Baccalauréat on completing Class 1e and in the following year La Tribune juive notes on 22 July 1932 that Jacques Feldbau passed the baccalaureates in mathematics and philosophy. He then spent the two years 1932-33 and 1933-34 at the Gymnasiums Kleber preparing to take the entrance examinations in mathematics for the École Polytechnique and the École Normale Supérieure. He was taught in the Mathématiques (spéciales) préparatoires class by a teacher M Roy and in the Mathématiques spéciales class by M Picardat. However, he was not considered for entry to the École Normale supérieure since one of the entrance examinations was on a Saturday and he refused to take this because of his Jewish faith. As a consequence, he enrolled at the University of Strasbourg in the autumn of 1934.
In his first year at university, he attended courses on differential and integral calculus given by Henri Cartan and on mechanics given by René Thiry. He performed well in the examinations in June 1935 and continued to his second year of study taking courses on general physics and on higher analysis. This analysis course was given, at least in part, by André Weil. In 1936-37 he continued to study for the Agrégation, the examination which was required to qualify as a secondary school teacher. It appears that he did not satisfy the examiners for his oral and so he went to the École Normale supérieure where he spent the academic year 1937-38 as a guest student. Only the best students not studying at the École Normale supérieure were invited to spend a year there as guests in order to get the best level of instruction to sit the Agrégation. There were four examinations, elementary mathematics, special mathematics, differential and integral calculus, and rational mechanics. Feldbau took the first of these on 30 May 1938 and, being one of the 51 best students, he continued to take two further written papers on descriptive geometry and calculating, and two oral examinations, one on elementary mathematics and the other on special mathematics. Of the 51 students who were allowed forward to take these examinations, Feldbau was ranked eighth. La Tribune Juive notes on 12 August 1938 that it has pleasure in announcing that Jacques Feldbau of Strasbourg has successfully passed the Agrégation in mathematics. The report states that he was ranked seventh in the written tests but had to miss an oral examination which was held on Saturday.
Feldbau had been particularly inspired to undertake research in topology because of the course he attended given by André Weil. After the award of his agrégation he returned to Strasbourg to begin work on his doctoral dissertation. He asked Weil about possible topics for his dissertation and Weil suggested that Feldbau speak to Charles Ehresmann who had just been appointed as a lecturer at Strasbourg.
Perhaps before we continue to relate the events which followed the outbreak of World War II, we should look briefly at Feldbau's character and interests. One of his friends, Georges Cerf, said that Feldbau was (see ):-
... a tall, well-built young man, who enthusiastically took part in all sports, was enraptured by music and, thanks to his sincerity and his goodness and his cheerful character, only had friends.He was an excellent pianist, and the large range of sports he was involved in (at surprisingly high levels) included swimming, football, skiing and cycling.
As Feldbau began his postgraduate studies, life in Strasbourg was not easy for Jews. Many German Jews had fled there to escape the Nazi anti-Semitic policies and the local people accused the Jewish inhabitants of encouraging a war against Germany. By the time that Feldbau began research in the autumn of 1938 the situation had become nasty. An incident that took place in November 1938 is related in . The "Maison Kammerzell" put up a sign which read, "Dogs and Jews are forbidden". Feldbau tore the sign down and a scuffle with some guests at the Maison resulted. Feldbau and some fellow students were then approached by the police and arrested. Around this time the same group of students were involved in an incident with a pro-Nazi bookshop, but it is uncertain whether Feldbau was one of the students who damaged the store. However, on the mathematical side Feldbau's work was progressing well and he wrote the paper Sur la classification des espaces fibrés Ⓣ which was published by the Academy of Sciences in 1939. This paper, read in May 1939, introduced the important notion of a fibre bundle for the first time. It contains an important theorem, namely the classification of fibre bundles over spheres.
Not only was Feldbau's mathematics progressing well, but so were his sporting activities. In July 1939 he became the French university champion at the 200 metres butterfly in the Tourelles swimming pool in Paris. In August 1939, Russia and Germany signed a secret pact, the so-called Ribbentrop-Molotov pact, to divide Poland between them. The two-pronged German attack on Poland began on 1 September 1939 and, on the following day, Britain, France and several other countries, declared war on Germany. Over the following months France was not involved in any fighting, but spent time strengthening the Maginot line, designed to protect the country from an invasion by Germany. Feldbau had already completed military training as an officer cadet earlier in 1939, this having been postponed earlier when he was a guest student at the ENS. With the outbreak of war, France mobilised and Feldbau was posted to the airbase at Tours where he had already undertaken training. He was based at the Châteauroux officers' school from October 1939 and, in early 1940, he was involved in the fighting, flying around 20 missions against the advancing Germans. He did not find this easy, however, saying later:-
You do not know how terrible it is when you get the order to bomb.The war had changed dramatically for France on 10 May 1940 when the German army crossed the Dutch and Belgium borders. Five days later German forces crossed into France and quickly headed for the coast. German forces entered Paris on 14 June and a couple of days later France requested armistice terms but fighting continued. The armistice was signed on 22 June and within a couple of days all hostilities in France had ended. Feldbau was demobilized and became a high school teacher in Châteauroux, a small town in central France, taking up this position in the autumn of 1940.
The armistice had divided France into two regions, one under German military occupation and the other, known as Vichy France, nominally under French control but with a government which cooperated with the Germans. Châteauroux, where Feldbau became a teacher, was in Vichy France. However, on 3 October 1940 the Vichy government passed anti-Semitic laws dismissing Jewish teachers. On 21 November Feldbau was still in Châteauroux when he wrote to Georges de Rham (see for example ):-
I have the reprints that you had the kindness to send me, they arrived safe and sound and I am very grateful to you.Although he was in Châteauroux, Feldbau must have kept in contact with his Strasbourg colleagues since he clearly knew exactly what was happening. Clermont-Ferrand is where the University of Strasbourg moved in September 1939 before the German armies invaded France so by the time Feldbau is writing this the University of Strasbourg had been located there for over a year. In December 1940, dismissed from his teaching position in Châteauroux, Feldbau arrived in Clermont-Ferrand. His family joined him there in April 1941. Laurent Schwartz writes :-
These are more useful to me since almost all my books have remained in Strasbourg and must be considered as lost.
MM Ehresmann and A Weil are at present in Clermont-Ferrand (Puy de Dôme). M Ehresmann is a professor at the Faculty of Science, while M Weil is waiting to depart to America.
I am mainly interested in topological questions (fibrations, absolute parallelism on spheres, homotopy of the orthogonal group, etc.) and would be happy to stay in contact with the Swiss school, which is interested in the same questions.
There were only three graduate students for the whole illustrious faculty of Clermont-Strasbourg: Jacques Feldbau, a student of Ehresmann, Gorny, a Polish refugee in France and a student of Mandelbrojt, both brilliant, and myself. We could hardly imagine a better pedagogical situation. Feldbau had been an auditor at the ENS - he had not succeeded in entering the ENS because, as a practising Jew, he had refused to pass one of the exams on a Saturday. He had passed his agrégation in 1938 and, like me, he had arrived in Clermont in 1940. He taught me a lot of algebraic topology and we became very friendly. I had studied algebraic topology in a brochure on homology written by Ehresmann, and Feldbau taught me cohomology, invented by Kolmogorov.During the sessions 1941-42 and 1942-43 Feldbau was enrolled as a doctoral student in mathematics. He worked mainly with Ehresmann but also with André Weil for a month before he left for America in January 1941. Despite the extraordinary difficulties imposed by the war, mathematics flourished in Clermont-Ferrand during these years. To earn money to live Feldbau gave private mathematics lessons but he also learned Russian, played the piano, learned the profession of a metal lathe operator, and made new friends with whom he often went for long bicycle rides in the mountains. However, he also took an active role in the French Resistance. He joined the French underground movement as part of the Organisation of Jewish Combat Fighters; he joined the underground French Fighters and Partisans; and was a member of La Sixieme (the Sixth).
In collaboration with his thesis advisor Ehresmann, Feldbau published the joint paper Sur les propriétés d'homotopie des espaces fibrés Ⓣ in 1941. After this, in order to protect his Jewish identity, Feldbau published his mathematics under the pseudonym Jacques Laboureur. Two papers published under this name are: Les structures fibrées sur la sphère et le problème du parallélisme Ⓣ (1942) and Propriétés topologiques du groupe des automorphismes de la sphère Sn Ⓣ (1943). Both were published in the Bulletin of the French Mathematical Society. By June 1943 he had completed research for his doctoral thesis and intended to write it up over the summer and defend his thesis before the end of the year. A friend wrote about him around this time:-
Everything was effortless for him. He spoke several languages, he was a man of great intelligence and humanity. He also had a tremendous amount of humour.However, the situation in Clermont-Ferrand had changed since German troops had occupied the town in November 1942. On 24 June 1943 two Gestapo agents were shot in Clermont-Ferrand and reprisals were expected. Feldbau decided to go underground and left the student accommodation where he was living. However, on the morning of 25 June he returned to his room to pick up manuscripts which formed part of his thesis. German soldiers and Gestapo agents had raided the building during the night and were interrogating the students when Feldbau arrived. He was arrested immediately.
Taken to the La Malcoiffée prison in Moulins, Feldbau gave lessons in astronomy, mathematical games and topology to fellow prisoners. From there he was taken to the concentration camp at Drancy near Paris, a standard holding place for French Jews who were being sent to the extermination camps in Poland. On 7 October 1943 he was taken in a cattle truck, with over a thousand other prisoners, to the Auschwitz concentration camp in Poland. They arrived at the camp on 10 October and about half were immediately taken to the gas chambers. Feldbau was put to work as the secretary in the surgical block of the infirmary. He continued to give mathematics and physics lessons to the other prisoners. To take their minds off the terrible situation they were in, a number of mathematicians in the camp, led by Feldbau, set and solved mathematical problems each day.
On 18 January 1945 the Russian army was approaching Auschwitz and the Germans decided to evacuate it. The prisoners, who were extremely malnourished and poorly clothed, were marched through snow in extreme cold for long distances. Feldbau is said to have discussed Fermat's Last Theorem with a fellow mathematician as they marched. Many died of exhaustion and those who could not keep up were shot. After three days they were put into open rail trucks and taken to Flossenburg, where those who survived arrived on 30 January. They remained there for several weeks and then they were taken to the Ganacker concentration camp. By this time Feldbau was very weak and he died of exhaustion in the concentration camp on 22 April 1945, two days before the liberation of the camp and fifteen days before the war ended.
Some results which were to form part of his thesis had not been published before he died. The 17-page paper Sur la loi de composition entre éléments des groupes d'homotopie Ⓣ containing these results was published in 1958. For a discussion of this paper and the other papers that Feldbau wrote, see .
Article by: J J O'Connor and E F Robertson
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