Paul Appell's Obituary of Gaston Darboux

In 1920 the International Committee for Weights and Measures published an obituary of Jean-Gaston Darboux written by Paul Appell. We give an English version of this Obituary below.

Jean-Gaston Darboux

By Paul Appell

Jean-Gaston Darboux was born in Nîmes on 13 August 1842; in a house that had once been a cathedral chapel. His father, a haberdasher, an educated man, died in 1849. His mother courageously took over the business, and, seeing that her two sons had happy arrangements for intellectual work, sacrificed everything to enable them to continue their studies.

Having received a Bachelor of Science on 22 July 1859, Gaston Darboux entered the special mathematics class at the Lycée de Montpellier in October. After a single year of work, Darboux appeared, to please his teacher, at the École Polytechnique entrance examinations. Declared admissible, he did not want to undergo the second degree examination, because he already had the vocation of teaching. After another year of specials, in 1861 he was admitted ranked first to both the École Polytechnique and the École Normale Supérieure. He chooses the École Normale Supérieure. This decision had a great impact, which J-J Weiss echoed in the Journal des Débats of 20 November 1861.

This then showed a real vocation for teaching and research, to prefer, rather than the École Polytechnique which ensured for the best of its students the top situations of state engineers, the École Normale which led to positions in secondary education, where the teacher was far from having the freedom and independence of the engineer. Darboux's mother came to Paris herself to present him to Pasteur, the director of scientific studies at the School. He was particularly pleased with the young man's choice, which truly opened a new era in the study of higher mathematics. Darboux was therefore authorised by the Minister to attend, outside the School, the courses which he liked. He was thus able to attend, at the Collège de France, the lectures of Joseph Bertrand, with whom he developed a deep friendship. Later, he won the esteem and friendship of the great mathematicians of the time, Chasles, Hermite, Serret, Bouquet, and Briot.

From that time, even during his stay at the École Normale, Darboux turned to the beautiful geometric questions that had been dealt with by Monge, Gauss, Poncelet, Dupin, Lamé, and Jacobi.

His first memoir, relating to the theory of orthogonal surfaces, was presented by Serret to the Académie des Sciences in August 1864. Soon after, on 20 September 1864, Darboux was placed first in the mathematics aggregation [becoming a qualified mathematics teacher]. Eager to keep him in Paris to allow him to continue his work, recognising the national utility there was in allowing young aggregates to stay in contact with the masters of science who would introduce them to research methods, Pasteur had the Ministry create posts for teaching fellows, given for a few years to the best students leaving the École Normale. Gaston Darboux inaugurated this position with brilliance. He composed a memoir on orthogonal surfaces which contained a large number of new results, and which earned him the title of doctor from the Sorbonne, on 14 July 1866.

As a substitute for Joseph Bertrand at the Collège de France, as a substitute for Bouquet in the chair of special mathematics at the Lycée Impériale Louis-le-Grand, he was successively full professor at the Lycée Louis-le-Grand in 1868 and at the Lycée Descartes in 1870.

On Darboux's work at the École Normale, M Lavisse, Director of the École, discovered a document signed "Pasteur" and drawn from the registers of the École. This document makes a prediction about the great career of the scientist.

He is a student whose work, conduct, distinction of spirit, character, and behaviour, nothing leaves to be desired. This young man will quickly be among the most eminent mathematicians. The spirit of invention was the one quality which one could expect this young master still had to achieve. However, he showed recently, with a very remarkable work presented to the Academy of Sciences and by various notes which he gave to the professors and assistants during the year, on various subjects the study of which he was able to devote himself without ceasing to retain the first rank in his division, in spite of the preoccupations of the preparation for the competition of the aggregation. It is absolutely essential that this young man stay in Paris.

On Darboux's teaching in special mathematics, we have the testimony of Lucien Lévy, now student examiner at the École Polytechnique.

It was in 1871, said Lucien Lévy, that I was a pupil of Darboux at the Lycée Louis-le-Grand, and I still remember, as if it were yesterday, the pleasure with which my comrades and I went to our class. Gaston Darboux knew how to get a huge amount of work out of us, as if he were playing.

The clarity, the clearness of his speech, the personal character of his demonstrations, provoked our admiration, and we worked with enthusiasm, without even remembering that we had exams to prepare and without even knowing the names of our examiners ... Darboux thus developed our critical sense and our reasoning power instead of loading our memory.

In 1872, Darboux was in charge of lectures on differential and integral calculus at the École Normale Supérieure. He became tenured on 18 September 1813. He was, at the same time, substitute professor for Liouville, in the chair of mechanics at the Sorbonne, from 1873 to 1878. It was there that I had the pleasure of having him as entrance examiner, lecturer and professor of mechanics. He then appeared extremely young, to the point that one of the candidates for the School, taking him for a third year pupil, who was trying, as it happened sometimes, to make him pass a bogus exam, refused at the first moment to answer him; telling him that "he didn't fool him".

At the School, he not only sought to develop our critical spirit and our initiative, but he took special care of us, giving each of the duties proportioned to his strength and correcting them with care. Tannery wrote on this subject:- I do not like to speak about those which are too close to us. How can we not remember, however, that the Mathematical Department of the School shone with incomparable brilliance while Darboux directed it.

At the Sorbonne, where the students of the École Normale followed his course, he inaugurated the teaching of rational mechanics, combining intuitive methods based on geometric reasoning and the direct view of things, with the highest analytical methods, waves with the Lagrange equations, the canonical equations of Hamilton, and the integration methods of Jacobi. But his real vocation was higher geometry. He was substitute for Chasles from 1878 to 1881, then he became professor of higher geometry, on 8 April l881, in the chair which he was to keep until his death.

This chair was created to allow Chasles to exhibit his beautiful work on Projective Geometry, the results of which, based on intuitive methods requiring no borrowing from mathematical analysis, had quickly become classic. Darboux then developed teaching in the new way in which Bonnet had already taken it, the way of general geometry, considered as an application of analysis, whose founders were Euler, Monge and Gauss; it was in this chair, where he was the professor for 37 years, that he founded this brilliant School of Geometry, whose disciples are now widespread in all countries, and that he developed the methods and results that make of him a creator, and which will preserve his name from being forgotten.

On 18 November 1889, the Assembly of the Faculty of Sciences of the Academy of Paris presented Darboux for the triennial functions of Dean. The Assembly regularly renewed these powers with almost unanimous support, and Darboux would have remained Dean until his death, if he had not resigned a year before the expiration of the fifth period, to devote himself entirely to his new functions as perpetual secretary of the Academy of Sciences. The role of dean, in the old Faculties before 1870, was very peaceful, of a completely paternal character: he confined himself to presiding over a few meetings of the Council, to appointing the juries for examinations, to ensuring the meagre expenses of the few laboratories; but, for the past forty years, especially since the appointment of Darboux, thanks to his initiative and his activity, these functions have become very burdensome. It was under the deanship of Darboux that the new University of Paris was created, that the Sorbonne was rebuilt on the spot, under the direction of Louis Liard and by the architect Henri Paul Nénot. I do believe that when Darboux became dean, plans were made and adopted, the question of reconstruction already decided. If it had not been, Darboux was of the opinion, instead of fitting out the Sorbonne like a liner where no place is lost, to branch outside. This is what the Faculty did under the direction of Darboux, by creating teaching for the School of Physics, Chemistry and Natural Science on rue Cuvier, the Institute of Applied Chemistry on rue Michelet; the laboratory for the evolution of plants on rue d'Ulm, the plant biology laboratory in Fontainebleau, the maritime Zoology laboratories in Roscoff, in Banyuls, in Wimereux, and the Nice Observatory, founded by the generosity of Raphaël Bischoffsheim.

Darboux had been elected a member of the Institute on 3 March 1884. He became Perpetual Secretary of the Academy of Sciences on 21 May 1900, as successor to Joseph Bertrand. His tireless activity and his enlightened dedication helped the Academy in its task and facilitated the accomplishment of its multiple missions: scientific missions, administrative missions, management of income, capital, buildings, and inheritances.

As Perpetual Secretary, Darboux delivered very remarkable obituaries, and published important books on The International Association of Academies, the Carte du Ciel, the Unity of Science, Fulton and the Academy of Science, the Spirit of Geometry and the Subtle Spirit, the School of Sèvres, the role of learned Societies, etc.

Darboux was delegated by the French Government to the International Geodetic Association in 1903. He was appointed a member of the Bureau des Longitudes in 1907. Finally, he was appointed a member of the International Committee for Weights and Measures in 1908. There has rendered important services with his long experience of administration and by his high scientific qualities. In particular, he traced the role of the Académie des Sciences in its relations with the Bureau regarding the definition of the standard length (Le Temps, 1916).

As for the scientific activity of Darboux, I can not do better than to refer to the address of Henri Poincaré, delivered on behalf of the Section of Geometry of the Academy of Sciences, to the scientific jubilee of Darboux, in 1912.

Mathematics, says Poincaré, when addressing Darboux, has a secret harmony which is a source of beauty, and which ensures, for those who live in its intimate trade, incomparable joys; but it is not always easy, in a short and quick presentation, to give a large audience a taste for it, as it should be. I cannot even promise to be brief; but it is not my fault, it is yours if you have made too many discoveries that it is impossible to ignore.

Poincaré then reviews Darboux's works on mathematical analysis, on partial differential equations, on algebraic integration of first order differential equations, on singular solutions, on analytical geometry and on infinitesimal geometry.

Darboux died in 1916, in the middle of the war, before having seen the victory of his country which he helped to prepare, and in which, had a deep faith.

For more complete information concerning Gaston Darboux, you can consult:

The book Savants du Jour: Gaston Darboux by Ernest Lebon, (Gauthier-Villars, January 1910).
Academic praise and speeches. Volume published by the Scientific Jubilee Committee of M Gaston Darboux; (Hermann bookstore, 1912).
The academic praise of Darboux, delivered by the Perpetual Secretary, Émile Picard, at the solemn session of the Academy of Sciences, in December 1916.
A Notice on Gaston Darboux, published by Émile Picard, in the Yearbook of the Bureau des Longitudes, for 1918.

Last Updated July 2020