Marie-Hélène Schwartz

Quick Info

27 October 1913
Paris, France
5 January 2013
Paris, France

Marie-Hélène Schwartz was the daughter of Paul Lévy and the wife of Laurent Schwartz. She lived through very difficult times but went on to have an outstanding career at the University of Lille. She worked on functions of a complex variable, Ahlfors theory, the Poincaré-Hopf theorem, and finally characteristic classes of singular varieties.


Marie-Hélène Schwartz was named Marie-Hélène Lévy and only adopted the name Schwartz after her marriage to Laurent Schwartz. She was the daughter of the mathematician Paul Lévy and his wife Suzanne Lévy (1892-1973), a daughter of the merchant Paul Lévy (1853-1903) and Berthe Weil (1862-1930). [Suzanne really did have a father and a husband with the same name!] Suzanne's maternal grandfather was Henri Weil (1817-1913), a philologist and member of the Institut de France. Paul and Suzanne Lévy had three children, Marie-Hélène Lévy (the subject of this biography), Denise Lévy (born 3 October 1916) and Jean Claude Lévy (born 10 April 1918). Denise became a professor of German at the lycée Molière in Paris. She married the engineer Robert Piron. Jean Claude studied at the École Polytechnique and became an engineer in the navy.

Marie-Hélène was educated in Paris and spent her final years of schooling at the lycée Janson de Sailly. This famous lycée was founded in 1880 and admitted girls from the 1890s. It had an excellent reputation and was the place where the Paris "high society" sent their children for a top quality education. Perhaps the most famous mathematician to have studied at this lycée was Élie Cartan. Marie-Hélène enjoyed mathematics and slowly got to know another pupil who was in the year below her at the lycée, namely Laurent Schwartz. He writes in [1]:-
Marie-Hélène Lévy, daughter of Paul Lévy, ... was not unknown to me since I had seen her once or twice in the past, our families having known each other for three generations, but her sister Denise, who was part of the same music theory course as me, was more familiar to me. Marie-Hélène had really pleased me the first time I had met her, several years before. One year my senior, she entered the first year preparatory class in mathematics and science for entrance to the Grandes Écoles when I passed into elementary mathematics. Despite and perhaps because of the pleasure of seeing her in my high school, I hardly spoke to her for the year, but I quickly fell in love with her. When I met her I spoke to her with extreme shyness, more and more overcome with emotion and confusion.
The relationship between Marie-Hélène and Laurent Schwartz slowly grew. Marie-Hélène performed well in the entrance examinations for the Grandes Écoles and, in 1934 she began her studies of mathematics at the École Normale Supérieure on rue d'Ulm, the only woman in her class. In April 1935 Marie-Hélène and Laurent became engaged but both sets of parents worried that they were far too young, particularly when she said that [1]:-
... she was a mature girl, and she was not afraid of having a child before taking the aggregation.
In the summer of 1935 Marie-Hélène went with her parents on a holiday in the Dolomites. Laurent Schwartz joined the Lévy family on their vacation and at this time Marie-Hélène and Laurent made plans to marry in December 1935. This, however, was not to happen since in October 1935, with Marie-Hélène continuing her studies of mathematics at the École Normale Supérieure, she developed pulmonary tuberculosis. At first Marie-Hélène did not realise she was seriously ill and tried to carry on with her life but suddenly she developed a very high fever. She had suffered from pleurisy several years earlier and quickly she was sent to the Mont-Blanc sanatorium in Passy, on the plateau d'Assy in Haute-Savoie. There were several sanatoriums in Passy specialising in the treatment of tuberculosis and certain other chronic infectious pulmonary diseases. Laurent Schwartz writes [1]:-
It was obviously a tragedy for both of us, and of course for our families. There was no longer any question of marriage in December.
At the Mont-Blanc sanatorium Marie-Hélène was treated by Jacques Arnaud (1904-1944), one of the pioneers of functional respiratory exploration in France. We note that his death at the age of forty occurred in the performance of his professional duty being arrested and shot by the German occupation troops for refusing to hand over the list of his patients. Arnaud did not hide the seriousness of Marie-Hélène's condition, telling her that she would be at the sanatorium for a very long time, not months but years. She was advised to prepare for a very lengthy stay and, as much as possible, to mingle with other patients in the sanatorium, because a certain collective life enabled them to maintain their balance. She resolved that [1]:-
... she would use all her energy to look after herself, to heal herself and to shorten her forced stay as much as possible. To achieve this, she mingled little with others, bonding only with rare friends. She asked to take her meals in her room, and spent a large part of her day reading or resting, bundled up on the balcony, in the extreme cold. She was also careful to eat all of her rations.
Examinations of her lungs showed that her condition was worsening, and the Lévy family were informed. Marie-Hélène, although not told directly of her worsening condition, was aware of it herself [1]:-
Seeing her future truly compromised, Marie-Hélène took care of herself with an extraordinary will, "like a dragon", said Dr Arnaud.
Laurent Schwartz writes [1]:-
We wrote to each other at length every day without exception throughout her stay in the sanatorium. Our letters were obviously sentimental, even sensual, but I did not omit anything, neither from my mathematical work, nor from my political activity, allowing Marie-Hélène to evolve with me. She was thus passionate about the same great political causes as me. Of course, we read a lot, and these readings fed into our intense correspondence.
Although they both kept the very many letters that they exchanged over this period, they eventually had to be burned during the German occupation of France during the war to prevent them falling into the hands of the Germans. Both being Jewish and having Trotskyist political views, clearly expressed throughout their correspondence, these letters would not only have put them in fatal danger but also put their political friends mentioned in the correspondence in peril. Slowly Marie-Hélène's condition improved but the doctors told her that even if she survived, she would stay in the sanatorium for a very long time, that she would almost certainly not be able to get married and that, if she did get married, she should not have children since pregnancy could cause a relapse. Laurent Schwartz writes [1]:-
From the start, to affirm loudly that I remained united with Marie-Hélène, and in protest against the long engagement that had been forced on us, I had decided to consider us as husband and wife. I addressed all my letters to the sanatorium, day after day, to Mrs Laurent Schwartz. Marie-Hélène asked for nothing better, and the sanatorium authorities considered this an asset for her recovery.
Indeed she did recover, and immediately after she left the Mont-Blanc sanatorium she married Laurent Schwartz on 2 May 1938. Rather charmingly, they never accepted that as the day of their marriage, but always considered they had married years before. Almost immediately after their marriage, Marie-Hélène went to Laon, the capital of the Aisne department of Hauts-de-France, northern France. After graduating from the École Normale Supérieure, Laurent Schwartz had undertaken compulsory military service. He had been assigned first to Ban-Saint-Martin, near Metz, then becoming a second lieutenant assigned to Laon. Marie-Hélène settled down there with her husband and, although they would have liked children, they were told to wait for four years to improve Marie-Hélène chances of avoiding a relapse. In the autumn of 1938 they moved to Châtillon-sous-Bagneux when Laurent was appointed to the Mont Valérien garrison.

Military service being over in September 1939, Laurent was immediately mobilised as World War II broke out. They moved first to Ballancourt, then to Biscarrosse, Landes, where they were living when France capitulated to Germany on 22 June 1940. For their safety, Marie-Hélène and Laurent were evacuated to Aire-sur-l'Adour before German troops arrived in Biscarrosse. Laurent was demobilized on 15 August 1940 and the family went briefly to Toulouse to join up with the Laurent's parents. There they met Henri Cartan and Marie-Hélène took the opportunity to ask him for his advice about how she could try to restart her academic studies. Cartan advised that they move to Clermont-Ferrand where the French University of Strasbourg had moved after the German invasion, which would benefit both her and her husband. At Clermont-Ferrand, Marie-Hélène began research and published her first paper Exemple d'une fonction méromorphe ayant des valeurs déficientes non asymptotiques in 1941.

When 1942 arrived and four years had passed from Marie-Hélène leaving the sanatorium, she had now reached the time when the medics had told her she could try for a child. Laurent Schwartz writes [1]:-
Marie-Hélène had suffered so much from the obligation to wait four years before having a baby that she now deeply desired this child. The idea of waiting until the end of a war that dragged on seemed unbearable to her.
Believing that the situation in Vichy France was relatively stable, Marie-Hélène was pregnant by July 1942 but their position took a sudden turn for the worse with the German invasion of Vichy France on 11 November. Both Marie-Hélène and Laurent were now in extreme danger, not only being Jewish but also being active Trotskyists with contacts to others in the organisation. From this time on they had several successive homes near Clermont-Ferrand, Boisséjour, Ceyrat, and Vernet-la-Varenne. Soon they had to adopt false identities, Laurent becoming Laurent-Marie Sélimartin and Marie-Hélène adopting the name Marie-Hélène Lengé. Their son Marc-André Schwartz was born on 17 March 1943.

In [1] Laurent Schwartz recounts a highly dangerous experience Marie-Hélène suffered while they were in Ceyrat:-
In June an event occurred which nearly cost us dearly. I went to Paris for three days to meet different members of our family who had stayed there and to have contacts with Trotskyist friends. ... During this absence of three days, the police appeared one morning at seven o'clock in our small apartment in Ceyrat. Marie-Hélène received them in her dressing gown. She led the two policemen into the main room, both an office and bedroom, and told them that I was in Paris, that I had crossed the demarcation line regularly (I had a very fragile throat ... and I had a pass to consult in Paris, where naturally I did not consult anyone) ... They had a search warrant and began to look at the mathematics books and search the desk drawers ... The search continued through the kitchen where they obviously noticed the ladder that allowed entry through a trap door into the attic. Marie-Hélène had the guts, with a twinge of heart, to invite them to come upstairs. A few days earlier, it was strewn with prohibited works including Marx's 'Das Kapital' ... and books by Lenin and Trotsky, among others. We had everything hidden under a double floor. ... These books were so well hidden that they never found them.
Marie-Hélène was summoned to the police station where the commissioner asked her a question about Gérard Bloch, telling her that he had just been arrested in Lyon. Bloch was a leading Trotskyist but fortunately was also a young and brilliant mathematician whom Marie-Hélène had known since childhood since she had taken piano lessons with his mother. Realising that Bloch must have been followed when he had visited them earlier, she claimed that he had come to discuss mathematics with them. Given the Trotskyist connections and their Jewish background, it must have been a mixture of skill and luck which saw Marie-Hélène and her husband survive the war. After the Allied invasion of France in June 1944 the German occupiers were driven back, and by August of that year the Vichy regime had fallen. In September 1944 Marie-Hélène and her husband returned to Paris, living in an apartment at 2 rue de Monticelli.

After a year in Grenoble, the family moved to Nancy when Laurent was appointed there in the autumn of 1945. On 30 July 1947 Marie-Hélène had her second child, a daughter Claudine Schwartz. She undertook research on a problem suggested by Georges Valiron and received helpful suggestions from André Lichnerowicz. In 1949 she published two papers: Sur les surfaces de Riemann possédant des points critiques arbitrairement rapprochés ; and Sur les indices de ramification de M Nevanlinna . Both were presented by Jacques Hadamard. In 1950 another paper appeared, namely Applications intérieures régulières dans les variétés à n dimensions followed by Compte-rendu de travaux de M Heins sur diverses majorations de la croissance des fonctions analytiques ou sous-harmoniques (1952) which she had presented to the Séminaire Bourbaki in December 1949.

She submitted her thesis Formules apparentées à celles de Gauss-Bonnet et de Nevanlinna-Ahlfors pour certaines applications d'une variété à n dimensions dans une autre in May 1953 and it was examined by Georges Valiron, chairman, Henri Cartan and André Lichnerowicz. Laurent Schwartz writes [1]:-
If someone had told her in 1935, when she entered the sanatorium, that she would overcome so many obstacles, not to mention a world war, she would have thought it a joke.
Marie-Hélène published her thesis in two papers, the first two chapters of her thesis were published as Formules apparentées à la formule de Gauss-Bonnet pour certaines applications d'une variété à n dimensions dans une autre (1954), while the third chapter was published as Formules apparentées à celles de Nevanlinna-Ahlfors pour certaines applications d'une variété à n dimensions dans une autre (1954). In the first of these papers she writes:-
I would like to express here my gratitude to M Valiron without whose encouragement I would not have undertaken this work and to M Lichnérowicz who was kind enough to take an interest in it and give me the benefit of his advice.
After her thesis was accepted, Marie-Hélène taught as an assistant at the University of Paris, and was then appointed to the University of Reims Champagne-Ardenne. In 1964 she was appointed to the Faculté des Sciences de l'Université de Lille where she remained until her retirement in 1981. At Lille [7]:-
... in addition to teaching first-year courses in large lecture halls to young students who did not always appreciate her pedagogy, Mme Schwartz taught advanced courses and had a small group of very successful doctoral students. She wrote several book-length lecture notes for these courses, on analytic functions and sheaf theory in 1966, on differential manifolds and transversality in 1973, on singular vector bundles in 1982, and on analytic subsets of analytic manifolds in 1988. Fibered spaces had been the subject of her research for a long time. As early as 1956, she had given a three-month set of lectures in Bogotá on 'Espacios fibrados'. The lecture notes, in Spanish, that she wrote for this course can be found in Paris, both in the library of the Institut Henri Poincaré and in the mathematics library of the Université Pierre et Marie Curie. All the above courses were only mimeographed and remained unpublished, but between 1960 and 1992 she published a number of papers on differential geometry and analytic spaces, their singularities and their characteristic classes, that were later recognised to be fundamental, and she continued to work and to publish after her retirement in 1981.
This quote refers to book length lecture notes by Marie-Hélène which include: Fonctions analytiques et théorie des faisceaux. Fasc. I-III : cours de D.E.A., Lille 1965-66 (1966); Lectures on stratification of complex analytic sets (1966); Classes obstructrices d'un sous-ensemble analytique d'une variete analytique (1988); and Classes de Chern des ensembles analytiques (2000). The publisher's information about the last mentioned book is as follows:-
Chern classes are among the main invariants of complex analytic manifolds. The present work of Marie-Hélène Schwartz deals with the generalization of this idea to the case of singular complex analytical sets. The problem then becomes considerably more difficult. To deal with it, she uses a decomposition, called Whitney stratification, of a complex analytic space into analytic submanifolds which satisfy certain incidence properties and she invents several very interesting techniques which allow her to define Chern classes by means of the index of reference fields that satisfy certain conditions with respect to the strata of the Whitney stratification. This work takes up ideas that the author presented in 1964. The definition of Chern's classes given by Marie-Hélène Schwartz is very useful both from a conceptual point of view and from a practical point of view. The techniques she introduces in this text have a scope beyond the simple definition of Chern's classes and help to understand the structure of singular analytic sets.
Jean-Paul Brasselet gives a summary of Marie-Hélène's mathematical journey in [4]:-
From the study of the functions of a complex variable to the characteristic classes of singular varieties, Marie-Hélène Schwartz's mathematical journey has followed a well-defined route, braving all the difficulties encountered along the way. This presentation is not intended to write all of Marie-Hélène Schwartz's work but to show how her results follow this route. We can in fact distinguish in her mathematical journey four periods whose themes successively cover the functions of a complex variable, Ahlfors theory, the Poincaré-Hopf theorem for singular varieties and radial fields, and finally the characteristic classes of singular varieties.
It is remarkable that Marie-Hélène, who was not given much chance of surviving when in her early 20s, should live to her 100th year. She had many heartaches during her long life, living through terrible times during World War II, then suffering the dreadful loss of her son Marc-André Schwartz who committed suicide in 1971.

A conference was held in her honour at Lille on 17-18 April 1986. The proceedings were published as [3]. Another two-day meeting was held in Paris to honour her 80th birthday in October 1993 at which Marie-Hélène delivered the main lecture. After her death in 2013, an issue of the Gazette des Mathematiciens was devoted to papers written in her honour, for example [4], [5], [6], [8], 9].

We end with Yvette Kosmann-Schwarzbach's summary of her contribution [7]:-
She played a remarkably modest but efficient role as the wife of a great mathematician who conducted manifold political and social activities, so her own achievements tended to be overshadowed by his enormous mathematical talent. But her pioneering role in the field of analytic geometry is now well established.

References (show)

  1. L Schwartz, Un mathématicien aux prises avec le siècle (Odile Jacob, 1997).
  2. L Schwartz, A Mathematician Grappling with His Century (Birkhäuser, 2001).
  3. M-H Schwartz, Journées de géometrie en l'honneur de Marie-Hélene Schwartz: 17 et 18 avril 1986 (Université des sciences et techniques, Lille, 1986).
  4. J-P Brasselet, Hommage à Marie-Hélène Schwartz: un aspect de l'oeuvre mathématique de M-H Schwartz, Gazette des Mathematiciens 138 (2014), 61-71.
  5. B Callenaere and M-T Pourprix, Hommage à Marie-Hélène Schwartz: témoignages lillois, Gazette des Mathematiciens 138 (2014), 56-57.
  6. E Ghys, Hommage à Marie-Hélène Schwartz: Madame Schwartz, Gazette des Mathematiciens 138 (2014), 57-58.
  7. Y Kosmann-Schwarzbach, Women mathematicians in France in the mid-twentieth century, BSHM Bulletin: Journal of the British Society for the History of Mathematics 30 (3) (2015), 227-242.
  8. F Laudenbach, Hommage à Marie-Helene Schwartz: depuis L'Aquila 1966, Gazette des Mathematiciens 138 (2014), 55-56.
  9. J-C Thomas, Hommage à Marie-Hélène Schwartz: une rencontre déterminante avec une mathématicienne d'exception, Gazette des Mathematiciens 138 (2014), 59-60.
  10. L Schwartz, La pensée mathématique de P Lévy, La Jaune et la Rouge (November 1973).

Additional Resources (show)

Other websites about Marie-Hélène Schwartz:

  1. Mathematical Genealogy Project
  2. MathSciNet Author profile
  3. zbMATH entry

Written by J J O'Connor and E F Robertson
Last Update September 2020