**Robert d'Adhémar**, born on the first of November 1874 in Saint Hippolyte-du-Fort (Gard, France), was descended from one of the oldest noble and protestant families from the region of Provence (South of France). His father, Marius d'Adhémar, worked for the French administration as a collector of taxes (receveur de l'enregistrement et des domaines) and, a few years before his son's birth, fought in the Franco-Prussian War of 1870-1871. Robert d'Adhémar's mother was Louise Willelmine Grand d'Esnon. Although Robert was born into a protestant family and brought up as a protestant, he later converted to become a Roman Catholic.

Robert d'Adhémar was awarded his baccalaureate in 1890 in Montpellier (Hérault, France). He then studied at the Lycée Ampère at Lyon, which he entered on 1 October 1891, preparing for the entrance examination for the École Centrale des Arts et Manufactures de Paris. He began his studies at the École Centrale des Arts et Manufactures in 1893, graduating with an engineering degree in 1896. He went on to study mathematics on his own and was, therefore, self-taught in mathematics. In April 1898 he wrote to his friend Robert de Montessus de Ballore telling him about the lectures of Émile Picard that he was attending [2]:-

From 1898 he began teaching at the Saint François boarding school in Evreux, about 90 km to the west of Paris, in fact the letter we just quoted from was sent from Evreux. He obtained his Licence es Sciences in 1899 from the Sorbonne. In 1902, the lectures of Émile Picard edited by Robert d'Adhémar were published under the titleA word in haste to tell you that I will write at length soon to tell you about the course of M Picard that I am attending regularly - tomorrow is the103^{th}lesson. We might make a judgement under these conditions, which was hard afteror4lessons. The course is wonderful, like his books only easier. In short, one learns properly only with really good books. This is to reassure and encourage you.

*Leçons sur les séries à termes positifs, professées au Collège de France*Ⓣ. He was elected to the Société Mathématique de France on the 21 February 1900. His candidature was supported by Émile Picard and Maurice d'Ocagne.

Robert d'Adhémar defended his thesis on 22 April 1904 before a committee consisting of his supervisor Émile Picard, Jacques Hadamard and Édouard Goursat. The first part of the thesis, entitled *Sur une classe d'équations aux dérivées partielles du second ordre, du type hyperbolique, à 3 ou 4 variables indépendantes* Ⓣ, dealt with the partial differential equation (1) with limit condition that arise in the two problems: the interior problem and the exterior problem.

In fact, he improved on a work of Vito Volterra on that subject. In the case of the interior problem, Robert d'Adhémar used his new methods to confirm more quickly the formulas which Volterra had obtained. For this problem, he dealt also with the equation (2).

The thesis was published in 1905 in the *Journal de Mathématiques Pures et Appliquées* (5) 10, pp 131-207. In a lecture to the International Congress of Mathematicians at Heidelberg in August 1904, Hadamard referred to the ideas in Robert d'Adhémar's thesis.

In 1901, Robert d'Adhémar became Maître de Conférences (essentially equivalent to an assistant lecturer) at the Lille Catholic University. He was promoted in November 1904 to substitute professor, then to full professor in 1907. He taught differential and integral calculus. In 1902 he helped his friend, the mathematician Robert de Montessus de Ballore, to join the Catholic University of Lille when he proposed him to fill a vacancy as substitute for the Special Mathematics course. Robert de Montessus was, at this time, teaching in Senlis and d'Adhémar wrote to his friend [2]:-

Moreover, in the same letter, Robert d'Adhémar explained to his friend that the course of Jules Drach at the University of Lille would be of a great interest for him to prepare for the agrégation.I do not write to you to influence you but I think you must have the courage to leave Senlis, as I had the audacity to leave Evreux. ...

Robert d'Adhémar married Jeanne Marie Henriette Duhamel (born the 15 April 1881 and died the 20 August 1965) on 5 February 1904 in Merville. Jeanne Marie Henriette Duhamel was the daughter of a manufacturer who owned a castle in Merville in the north of France. Robert d'Adhémar and his wife lived in Lambersart in the suburbs of Lille.

Robert d'Adhémar became an officer in the general staff of the French Army in Italy during World War I. He wrote to Robert de Montessus from the Italian front on 25 May 1918 [2]:-

He left the Lille Catholic University, being given leave during the academic years 1920-1921 and 1921-1922, then was appointed as professor at the engineering school Institut Industriel du Nord (now a day École Centrale de Lille) in 1922.My dear friend, I spent one month in Alsace, and I was called urgently to Italy. My training in Alsace was too short ... It was also lovely. I visited all the batteries in an area, and heard the shells whistle, accompanied by a charming man, Gal Jaquet. Here we organize a large ... firing between France and Italy. I deal with the artillery and I have a lot of work under a blazing sun, surrounded by roses. The front has nothing in common with the French front.

It was in 1901 that Robert d'Adhémar's first publications were published, namely the mathematical papers *Sur une intégration par approximations successives* Ⓣ and *Sur une classe d'équations aux dérivés partielles du second ordre* Ⓣ. In the same year his 40-page paper on the history of mathematics *L'oeuvre mathématique du XIXe siècle* Ⓣ also appeared. His first book, however, was on the philosophy of science and religion, topics which occupied him in the early part of his career. The Preface to the book *La philosophie des sciences et le problème religieux* Ⓣ (1904) begins as follows:-

He divides science into three parts, mathematics, physics/chemistry, and biological sciences but, in this book, considers mainly the philosophy of mathematics and physics. The final chapter is on science and religion. He continues this discussion of the ideas in this book in his second bookThe philosophy of science has completely changed its point of view in France in the last ten years of the19^{th}century. I would like to show the major importance in this movement of ideas and to perceive what may be their distant consequences.

*Le triple conflit : science, philosophie, religion*(1905).

His next book *Les variations des théories de la science* Ⓣ (1907) continued to investigate similar subjects. He writes in the Introduction:-

He goes on to say that religious thought varies both with the times and with the individual thinkers.I do not wish to speak ill of my contemporaries. And yet we must admit that when it comes to religious things, most of them lose their composure. But, addressing them, we say that the Catholic Church is the greatest in the history of religion and the Catholic faith lives in a very large number of intellectually elite men of high morals. ... we will be booed three times, held to be of unsound mind and narrow heart.

Although he had been writing philosophy book, he continued to publish mathematical papers such as *Sur une équation aux dérivées partielles du type hyperbolique* Ⓣ (1905) and historical works such as *Trois maîtres: Ampère, Cauchy, Hermite* Ⓣ (1905). His first mathematics book *Les équations aux dérivées partielles à caractéristiques réelles* Ⓣ was published in 1907. This was quickly followed by the books *Exercices et leçons d'analyse. Quadratures. Équations différentielles. Équations intégrales de M Fredholm et de M Volterra. Équations aux dérivées partielles du second ordre* Ⓣ (1908) and *L'équation de Fredholm et les problèmes de Dirichlet et de Neumann* Ⓣ (1909).

In collaboration with Robert de Montessus, he wrote the two volume book* Calcul numérique* Ⓣ (1911). The first volume covered arithmetic and algebraic operations and the second volume studied integration. This book gave numerical methods for solving non-linear equations. Perhaps his most famous book was the two volume *Lecons sur les principes de l'analyse par R d'Adhémar, professeur a la Faculté Libre des Sciences de Lille* Ⓣ. The first volume *Séries.- Déterminants.- Intégrales.- Potentiels. Equations intégrales. Equations différentielles et fonctionnnelles* Ⓣ was published in 1912 with the second volume *Fonctions synectiques, méthodes des majorantes. Equations aux derivées partielles du premier ordre. Fonctions entières* Ⓣ being published in the following year.

His later books were: *Henri Poincaré* (1914); *Résistance des matériaux* Ⓣ (1921); and *Statique cinématique* Ⓣ (1923) which was intended as an introduction to mechanics for engineers. He wrote several works on ballistics such as *La balistique extérieure* Ⓣ, Gauthier-Villars (Paris, 1934) and *Théorie du mouvement gyroscopique des projectiles* Ⓣ (1939).

**Article by:** Hervé Le Ferrand, Université de Bourgogne, and *Edmund Robertson*, University of St Andrews.