Gaston Darboux dans ses belles années :

Formation d’un scientifique engagé

 

This is a presentation that I am going to give on Princeton Research Day (9 May, 2019). If you have any comments, questions or suggestions, please write to hainaw@princeton.edu. 🙂

PART 1

Introduction

“We are the future of the past.”

This is an important fact that we, historians or not, need to keep in mind. The related important question is therefore: What kind of future did people in the past hope for and fight for? To what extent do our lives now agree or disagree with the visions of our ancestors?

My interest in Gaston Darboux, apart from his mathematics that intrigued me since first year in college (analysis, then geometry), stems from this general question. As an international female scholar, what are the historical forces that make my identity here and now possible?

Darboux was, at least in his time, considered a central force in educational and academic reform, in creating equality for internationals and for women. In this introduction I will simply take his pioneering international journal Bulletin de Sciences Mathématiques et Astronomiques (called simply Bulletin Darboux by his contemporaries) and his enthusiastic public support for electing Marie Sklodowska-Curie into the Academy of Science as one example for each, but we will see more in the following parts.

Darboux is a representative figure of a multitude of French progressive savants very engaged in social-political change in the Third Republic. Other examples include Tannery, Poincaré, Appell, Borel, etc. (This extremely vibrant culture of “engaged scientists” seems to be a unique French phenomena.) But not only being representative, he was in various important leadership roles and it’s not exaggerating to say that he influenced every “engaged scientist” of his time.

Discussion of the institutional and social legacy of Darboux is still very sparse, especially in the United States, making [Croizat 2016] an exceptional must-read on this topic. One possible reason is that historians of mathematics are naturally more interested in the mathematical aspects of the savants, and the institutional and social experience of Darboux are deemed secondary. Also, in the sense of academic genealogy, the US academia has much more German heritage than French heritage.

This poses the risk of biasing the history. For example, in the book Mathematics Without Borders: A History of the International Mathematical Union by Olli Lehto [Lehto 1998], a long discussion is devoted to the German-based journal Jahrbuch über die Fortschritte der Mathematik, featuring it as a precursor to international collaboration of mathematicians, but little mention, if at all, is given to Bulletin Darboux, although the latter was much more apparent in its internationalist nature. Studying the institutional and social legacy of Darboux offers an exciting aspect to accurately understanding what historical legacy we have in the equality and inclusion in STEM (science, technology, engineering and mathematics), an important issue in today’s industry and academia.

In the same spirit of [Croizat 2016], we stress the importance of a biographical approach, the usefulness of analyzing the life dynamics of our hero, of appreciating the changes and complexities of his ideas. We attempt to capture the emergence of his engagements in equality and inclusiveness in the his early years after graduating from the ENS: 1866-1874 as called les belles années by Lucien Lévy.

Methodological notes

Besides the biographical approach mentioned above, we also see the value of empathy in historical studies. And, in the case of the present research, we attempt to depict our story in a broad background, where the academic, economic, political and social situations in which our hero found himself are given when possible. The ideal of Michelle Perrot’s “total history” is kept in mind [Perrot 1998]. This background canvas will be in no ways complete, but any such effort of historical reconstruction renders us better understanding of his actions, and in which aspect they were, or were not, pioneering.

Empathy as a methodology also allows us to discuss Darboux’s legacy in equality and inclusion while recognizing his apparent limitations partly due to his time: He obviously endorsed colonialism, and his vision of gender equality is by no ways sufficient in today’s standards. He still accepted the notion of gender roles and seemed to think, probably subconsciously, that women are naturally kind and moral. The ENSJF (Normal school for young girls) initiative, in which Darboux played am important role for more than 30 years, is also known to be a very incomplete reform in educational equality: For example, women teachers were expected to be motherly, modest, etc. [Margadant 1990].

Despite these limitations, we hope it is still possible to see that Darboux was a bold reformer in his time, and his ideas of scientific solidarity beyond national borders and social stereotype already took their roots in his youthful years.

PART 2

Bulletin Darboux :

“L’internationale” in the mathematical world

Today, in a world with the Internet, almost every big journal is international, so it is easy to forget the fact that this was hardly the case in the 1800s (and actually well into the 1900s). And when a journal in those times decided that it wanted to be international, it was revolutionary: It took its managers courage, effort, entrepreneurship, international connections, multilingualism, and a truly global vision of science.

This was exactly the case of “Darboux’s journal”, or Bulletin des Sciences Mathématiques et Astronomiques. Still “alive” today, it is the first mathematical journal that declares its mission as being international beyond language barriers, and probably the first truly international journal in natural sciences. This article analyzes the international nature of Bulletin and the internationalist vision of Gaston Darboux, its editor-in-chief.

 

Born International, for a nationalist goal

(This section is mainly a summary of Chapter 5, Section 3 of [Croizat 2016].)

The idea of creating such a journal was that of Michel Chasles, and the initial objective was in fact nationalist: to keep French mathematicians up-to-date with the newest progress in the foreign world, especially in Germany and Italy.

By the end of the 1860s, several bright mathematicians realized that math in France was outdated and declining compared to foreigners. For example, the French world isn’t familiar with non-Euclidean geometry by Riemann and Lobachevsky, and in analysis, while mathematicians in Germany are looking rigorously at the definition of continuity (Richard Dedekind got his idea of the cut as early as 1858), in France the literature still endorses arguments with “aussi petit qu’on le veut” (“as small as one wants”, an heuristic for the infinitesimal) without much scrutiny. [Gispert 1987, 1990]

Chasles was one of the worriers. In 1869, he persuaded the French Ministry of Public Instructions to create the Bulletin. He handpicked his former doctoral student Darboux as the editor-in-chief. The 27-year-old Darboux was energetic, bold, spoke German, and almost always a dissident. He shared Chasles’s opinion that French mathematics had to reform immediately. He had, in fact, long thought that all French geometers of his time are old-fashioned like dinosaurs, and later declared famously:

… let’s try with our Bulletin to awaken the sacred fire and to make French people understand that there are a lot of things in the world they do not suspect, and that if we are still the Grrrande nation, one hardly notices this abroad.

… tâchons avec notre Bulletin de réveiller ce feu sacré et de faire comprendre aux Français qu’il y a un tas de choses dans le monde dont ils ne se doutent pas, et que si nous sommes toujours la Grrrande nation, on ne s’en aperçoit guère à l’étranger.

Letter in July 1872 from Darboux to Jules Hoüel, collected in [Gispert 1987]

[He really spelled “Grrrand” like that (to mock the German pronunciation??)]

His editorial collaborator, Jules Hoüel, astronomer-mathematician based in Bordeaux, was a rare multilingual French scholar of the time. Knowing German, English and Russian, he had translated several important books into French.

We see that the Bulletin was special in that it was born international due to a nationalist goal. To save French mathematics, the journal’s creators decided to face up to the world.

Le Bulletin Darboux in the 1870s

The Bulletin was officially launched in 1870 and appeared monthly. Before 1878, each issue had 32 pages, containing four parts

• Revue Bibliographique (Book reviews)
• Bulletin Bibliographique (List of books recommended to readers)
• Revue des Publications Périodiques (Review of journal articles)
• Mélanges (Featured research articles or summary of an author’s previous research)

Note that there was no peer-review procedure like today. A small editorial team of 8 people, and especially Darboux and Hoüel, wrote all the reviews and edited all the Mélange articles, including all the translations from foreign languages to French.

Apart from the usual challenges of starting a journal: finding contributors, finance, decision on the font and the paper, many problems are unique for a pioneering international journal.

As the editor-in-chief of a new journal, Darboux had to build his international network. He wrote numerous letters to foreign mathematicians, introducing the Bulletin and begging for a resumé and a summary of their works: “in all my letters I have insisted the international character of the Bulletin”. Here is an example of Darboux’s first letter to the German mathematician Lipschitz, written as the chief editor of the Bulletin.

In the letter above:

…if I have taken the liberty to bother you, please excuse me, because I don’t have other desire than to serve the science and to make your research known in a manner exact and complete.

He wrote hundreds of letters like this in the early years of the Bulletin. Lipschitz replied promptly and became a major point of contact in Germany for the journal, but there are people who ignored the letters or replied coldly.

Other international problems include: deciding on the sex of nouns when translating English terms (e.g. “quantic” used by Arthur Cayley, today called “algebraic form”) to French, spelling Italian names correctly, and obtaining Russian letters to print the title of works by Lobachevsky. When the publisher, Gauthier-Villars, decided to mold the letters themselves because no printing house wanted to do it just for a single journal, they realized that they couldn’t find a Russian in Paris, and had to ask the embassy…

All these problems show that Bulletin was really pioneering in its international vision and forced the French academic world to get out of its comfort zone.

Wartime memories and Darboux’s internationalism

If the original goal of the Bulletin was to help France catch up, Darboux himself had a higher goal as we have already seen in the letter to Lipschitz: to accelerate the progress of science by building an international platform. His internationalist ideals could have come from Louis Pasteur, his director of studies at ENS, but were definitely deepened by the international friendship fostered through the Bulletin.

Darboux’s internationalism is most clearly seen during the Franco-Prussian war (1870-71). In the heat of tension he tried his best to minimize the war’s impact on the continuation of the Bulletin.

On November 2, 1870, well into the Siege of Paris, he wrote to Hoüel:

Don’t forget our Bulletin

if you have the heart for the work.

N’oubliez pas notre Bulletin

si vous avez le cœur au travail.

collected in [Gispert 1987]

And on November 8:

In the Academy [of Science] we have made the communications on the flour, on the balloons and on our Bulletin.

On a fait à l’Académie des communications sur la farine, sur les Ballons et sur notre Bulletin.

collected in [Gispert 1987]

In end January-early February 1871, he received a letter from Klein in Germany, he answered him politely, and argued with Hoüel that it was not the fault of Klein that France finds itself in a terrible war.

But probably the most telling story is one concerning Norwegian mathematician Sophus Lie. Lie befriended Felix Klein in Germany and they visited Darboux in Paris in spring 1870. As the war broke out, Lie decided to go to Italy, but was arrested for being a German spy in Fontainebleau. The mathematical letters sent by Klein were thought by the police to be top military secrets! It was only after the intervention of Darboux that he was released from prison. [Baas 1994]

From these discussions and the previous ones (“the Grrrand nation”) we see both the patriotism and internationalism in Darboux, which signifies the multiple dimensions, the complexity, of his beliefs and values. However, from his actions, we could conclude that he was primarily pacifistic and pioneered enormously in fostering the international academic community, starting in les belles années.

Influence…

… in France

The Bulletin excellently achieved its goal of going international. In the first volume (1870), in the section of bibliography list, only 10% of the listed books are French, 53% are German, 15% are English, 10% are Italian. There are also books in Scandinavia, in the United States, in Netherlands, in Russia. [Gispert 1987] The percentages are similar in other sections.

It did shock the French mathematical world and woke up French scholars and forced them to see the world. As [Gispert 1987] puts it:

The French mathematicians discovered in this year [1870], if they read the Bulletin and particularly the bibliographical review, lots of researches and new problems: the ideas of Riemann in analysis as in geometry, the non-Euclidean geometry, the Italian works of geometry, etc.

Darboux himself also got valuable inspirations from the foreign works. His most well-known paper today, Mémoire sur les fonctions discontinues [Darboux 1875], was clearly inspired by German mathematicians like Weierstrass and Schwarz to bring more rigor into analysis. This paper, in turn, influenced Borel and Lebesgue to develop new analysis based on measure theory.

The long-term success of Bulletin in France can be seen in a letter by Darboux in 1881, written with confidence, 11 years after its creation:

I believe that we give our readers a sufficiently exact idea of the movement and the progress of the diverse branches of the mathematical science.

Je crois que nous donnons à nos lecteurs une idée suffisament exacte du mouvement et du progrès des diverses branches de la Science mathématique.

cited in [Gispert 1987]

… and abroad

In 1876, the Bulletin published a 6-year collection with a list of all its authors and contributors during the previous 11 volumes: there are more than 2000 authors listed, spanning from the United States to Russia, and everywhere in Europe. In a world without Facebook, le Bulletin Darboux accomplished a mission impossible.

There are many stories with the Bulletin, new mathematics evolved and mathematicians connected through the platform. Many of them are discussed in the great work [Croizat 2016], and I will tell one that I know well.

Richard Dedekind published his theory of algebraic numbers as an appendix to Dirichlet’s Lectures on Number Theory in 1871. Disappointed that it received little notice in Germany, he decided to go for the French audience under the suggestion of Lipschitz, and published a summary in the Bulletin in 1876. This work, Sur la théorie des nombres entiers algébriques, becomes a classic in algebraic number theory and is still printed today. Although it also didn’t stir up much follow-up in France (being too ahead of its time indeed), it is the only comprehensive introduction of Dedekind’s ideal theory, and later it was this paper that inspired Emmy Noether to develop her ring theory [Dedekind 1996]. The most important Dedekind paper was published in French and in the Bulletin.

Epilogue for Part 2

Darboux remained an internationalist for his life, and believed that science should be shared with the whole world. In 1904 he gave a speech on the unifying power of science in Saint Louis, US:

The science is like the universe. The phenomena that it studies do not know the borders of the nations, nor the political divisions between the peoples.

La science est une comme l’Univers. Les phénomènes qu’elle étudie ne connaissent, ni les frontières des états, ni les divisions politiques établies entre les peuples.

Collected in [Darboux 1912].

But Darboux himself was a unifying power. Among his 7 doctoral students, 4 were French and 3 were foreigners: Stieltjes (Dutch), Țițeica (Romanian) and Zaremba (Polish). He hosted numerous foreign scholars visiting Paris, helping them connect with French savants.

His international vision, crystallized in Bulletin, clearly inspired Klein and Cantor to launch the International Congress of Mathematicians, and still inspiring today’s academic world.

In Darboux’s scientific jubilee in 1912, there was an appreciating speech by Schwarz, representing all foreign mathematicians, that I think can perfectly conclude this article:

Your example clearly shows that the competition that exists between the scientists of all countries does not make them enemies, but brings them closer all the more intimately by the treasures discovered by each of them, which immediately become the good for all.

Votre exemple montre clairementque l’émulation qui existe entre les savants de tous les pays, ne les rend pas ennemis mais, les rapproche d’autant plus intimement par les trésors découverts par chacun d’eux, qui deviennent aussitôt le bien de tous.

Collected in [Darboux 1912].

 

PART 3

Darboux as human in les belles années :

A working-class scholar ?

Since the 1980s historical studies are pointing out the importance not to separate people’s public and private lives. This is unfortunately not well done in the History of Math community. This part, therefore, concerns the more personal side of Gaston Darboux in les belles années, and in particular a little family forming in great hardship. This aspect, which should have been standard in any Darboux biography, is surprisingly untold by all the memorial texts written by Darboux’s contemporaries shortly after his death. It only begins to surface with [Gispert 1987], [Brasseur 2015] and [Croizat 2016].

I argue that the young Darboux was in a special socio-economical position for a mathematician, closer to the modest working class than to the “industrial bourgeois” where most savants and educational policy makers found themselves. This socio-economical standing, together with his experiences within family and community, could have contributed to his progressive values, his sensitivity to inequality. Although this analysis is by no means conclusive, I believe it should not be omitted if we are to understand his later social and political engagements.

It is useful to start from Lucien Lévy’s actual comment on the beautiful years:

Beautiful years 1866 to 1874, during which you worked out the program of your entire mathematical life! Beautiful years during which you also associated your life with the partner …

Belles années que ces années 1866 à 1874, pendant lesquelles vous élaboriez le programme de toute votre vie mathématique ! Belles années pendant lesquelles vous aviez aussi associé à votre vie la compagne …

In the second part of the quote, Lévy was talking about Célina Carbonnier (1848-1911), Darboux’s partner for more than 40 years. (Lévy was a student of Darboux at Lycée Louis-le-Grand during the years 1871-72 and probably had seen the Darboux-Carbonnier couple in those years.)

Célina was born to a tailor on Christmas 1848 in Beauvais, a town 70 km from Paris once known for its textile industry, but refused to embrace the innovations of automated machines towards the mid-19th century, and became a “sleeping town”. It was probably the need to support her family in poverty that in her teenage years Célina left for Paris with her little sister Clara and worked there as a milliner. The trip could well take 10 hours because Beauvais refused to left the railway pass through.

She met Gaston Darboux by 1866, they fell in love and by 1869 the Darboux brothers (Gaston and Louis) and the Carbonnier sisters were living together in a little apartment at rue d’Assas 48 that might also served as Célina’s atélier. It was a district where many working class people lived.

The living conditions of such home/atélier could be terrible:

…without air, the small room frequently served as the only lodging for a family of several persons. Whether in one or two rooms, furnished or not, their housing was ‘deplorable’, ‘malsain’, ‘insalubre’, ‘humide’; it often had blackened walls; it might be too small for the number of persons living there; it might be unlit except by one small window or skylight; while it was almost invariably either too cold or too hot.

[Fuchs 1998]

We may choose not to believe that the Darboux-Carbonnier partners lived in exactly such a condition, but we know Darboux was not rich either. His mother, running a little mercer shop in Nîmes since her husband died when Gaston was 7, apparently wasn’t able to support them financially. Darboux wrote to Jules Hoüel that he had a small room and “a huge mess of books”. In spring 1870, when Sophus Lie visited, he was surprised by how modestly they were living and announced to Klein that Darboux “married a poor girl”. [Stubhaug 2006]

But they must have been pretending to be married at the time Lie first visited, as they were apparently expecting their first child. In the “normal” world of “respectable” savants, having a child before marriage was at least an embarrassing mistake. However, from the aspect of working class in Paris, it was reasonable and even a common practice: single mothers in poverty received public welfare, and most of them were afraid that the aid will be terminated after marriage [Fuchs 1988]. We don’t know if the partners received aid, but we know it was common in their district. We see Darboux’s unique position between the scholar circle and the circle of have-nots.

Therefore, the hectic first months of creating Bulletin was also the months when they were expecting the baby, which also coincided with the Franco-Prussian war.

On September 11 the baby was born. Gaston Darboux went to register the birth with his brother Louis and and their neighbor Jacques Chaudet, a shoemaker living in the same building. 6 days after the birth, Paris was sieged. The food source was cut. Gradually they had to eat from horse, donkeys, cats, dogs and “things unnameable”, probably rats. Darboux wrote to Hoüel: “the women queued 6-7 hours [for food] without complaining”. In January 1871, the coldest winter in many years, rue d’Assas was bombarded by Prussians.

 

When the siege finally ended, the have-nots started a revolution, known as the Paris Commune (18 Mar. – 28 May 1871).

Among other remarkable events during the Commune, recorded in any specialized document, we highlight that women played an important role in the fighting and the political constitution of the Commune. The Commune anthem, La Marseillaise de la Commune was written by a woman, Mme Jules Faure. [Fauré 1997]

Like many savants in Paris (and a semi-working class himself), Darboux sympathized with the communards and was extremely shocked by “the bleeding week” when the Commune was violently suppressed. He wrote to Hoüel thereafter: “You must be asking yourself if I still exist.” “I threw my arms into the sky and cried out that it was the end of the world.” “I hope the next year will not be 10 times worse than this one.” [cited in Gispert 1987]

But Paris swiftly recovered into the third republic, so did the little family, though they still lived in poverty until 1881. They pretended to be married in Paris and talked little about personal matters in letters. When they finally really got married in July 1872, it was a great secret. Before they went to Beauvais to register, Darboux wrote to Hoüel “I will leave for a day or two to have myself relaxed.” [cited in Croizat 2016]

At home Gaston and Célina talked as equals, she giving him counsels in his work and communicating with him “her sentiments of kindness and of humanity”. [Darboux 1912]

In 1873 they were expecting a second child, Darboux told Hoüel, “… I said to you an heir, but it may be an heiress, doesn’t matter, she is welcome.” [cited in Croizat 2016]

Later into the 1890s, the Darboux-Carbonnier couple was engaged in la Societé des Amis des Sciences, an aiding institution for poor scientists and their families, to “free them from worrying about the future” (words by Émile Picard in memory of Darboux in 1917). [Darboux 1912, Picard 1917]

We believe that these experiences – his partner and mother as courageous working women, and the hard life in the siege-commune years, forecast Darboux’s later social engagements, with the Normal School for young girls, with the support of the election of Marie Sklodowska-Curie into the Academy, with Societé des Amis des Sciences just said.

And by the way, the little family lived the modest way for their entire lives, in an apartment on the 5th floor of rue Gay-Lussac 36 between 1875 and 1911 despite Darboux receiving an enormous number of titles and awards during the years, which surprised his biographer Ernst Lebon: “Nobody with this kind of [social] status live such a modest way like him” ! [Lebon 1913]

Conclusions

We want to conclude with several statements.

• Pushing for equality and inclusion in science was an important but understudied aspect of Darboux’s life.
• He influenced generations of engaged scientists and was central in the French circle of engaged scientists around 1890s and early 1900s.
• “The beautiful years” profoundly shaped his values on social issues.
• Our study is relevant today, as we are still fighting for equality and inclusion in STEM. It’s important to know what legacy we have, and to learn from their examples if possible.

REFERENCES

[Baas 1994] Sophus Lie. Modelling Identification and Control, Vol. 15, No. 1, 3-7.

[Brasseur 2015]  Dictionnaire des professeurs de mathématiques en classe de mathématiques spéciales.

[Croizat 2016] Gaston Darboux : naissance d’un mathématicien, genèse d’un professeur, chronique d’un rédacteur. Doctoral thesis Université Lille 1.

[Darboux 1912] Eloges Académiques et Discourses.

[Darboux 1875] Mémoire sur les fonctions discontinues. Annales scientifiques de l’É.N.S. 2e série, tome 4 (1875), p. 57-112

[Dedekind 1996] Theory of Algebraic Integers. Translation and Introduction by John Stillwell. Cambridge: Cambridge University Press.

[Fauré (dir.) 1997] La Révolution avec ou sans la femme ?; La Commune de 1871. Encyclopédie politique et historique des Femmes, PUF, 1997.

[Fuchs 1988], Morality and poverty: public welfare for mothers in Paris, 1870-1900, French History Vol 2 No 3, pp 288-3.

[Gispert 1987] La correspondance de G. Darboux avec J. Hoüel. Chronique d’un rédacteur (déc. 1869-nov. 1871), Cahiers du séminaire d’histoire des mathématiques, Volume 8 (1987), p. 67-202

[Gispert 1990] Principes de l’analyse chez Darboux et Houël (1870-1880) : textes et contextes. In: Revue d’histoire des sciences, tome 43, n°2-3, 1990. pp. 181-220;

[Lebon 1913] Savants Du Jour: Gaston Darboux. 

[Lehto 1998] Mathematics Without Borders: A History of the International Mathematical Union. New York: Springer-Verlag

[Lipschitz 1986] Briefwechsel mit Cantor, Dedekind, Helmholtz, Kronecker, Weierstrass und anderen. Springer-Verlag.

[Margadant 1990] Madame le professeur : women educators in the Third Republic. Princeton: Princeton University Press.

[Perrot 1998] Les femmes ou les silences de l’histoire. Paris: Flammarion.

[Picard 1917] La vie et l’œuvre de Gaston Darboux. Annales scientifiques de l’É.N.S. 3e série, tome 34 (1917), p. 81-93