Four Luxembourg Mathematicians, Professors at the University of Liège

Lucien Godeaux gave the paper Quatre Mathématiciens Luxembourgeois, Professeurs à l'Université de Liège, at the Luxembourg Congress of the 72nd Session of the French Association for the Advancement of Science in July 1953. It was published in the Proceedings of the Congress. We give below an English translation.

Four Luxembourg Mathematicians, Professors at the University of Liège, by Lucien Godeaux.

Since its foundation in 1817, the University of Liège and the Grand Duchy of Luxembourg have maintained close relations. While Liège has had and still has a large number of Luxembourg students, several of its Professors were born in the Grand Duchy and received their initial training there. We would like to recall here the memory of four of them, who taught Mathematics with real success and all four belonged to the Royal Academy of Belgium. They are: Antoine Meyer, Jean-Baptiste Brasseur, Mathias Schaar and Joseph Neuberg.

Antoine Meyer was born in Luxembourg in 1801 to parents of modest means. After brilliant studies at the Athénée in his hometown, he enrolled at the University of Liège, giving lessons for a living. It was under the same conditions that he spent a stay in Paris to complete his training. On his return, in 1826, he was appointed professor at the Collège d'Echternach and two years later moved to the Military School in Breda. In 1831, we find him as a professor at the Collège de Louvain, then at the Gaggia Institute in Brussels. In 1832, he was awarded a Doctorate in Physical and Mathematical Sciences by the University of Liège and in 1834, he was appointed professor of Mathematics at the Military School, which had just been created. In this establishment, he had been forced to use a textbook whose many imperfections he soon realised. He refused to continue his teaching under such conditions and was forced to resign in 1836. Without any fortune, he thus gave a fine example of independence. For two years he was unemployed, but in 1838 he was appointed professor at the University of Brussels, at the same time as he assumed the functions of calculator at the Ministry of War. Finally, in 1849, he was appointed professor at the University of Liège and in charge of the courses of Mathematical Analysis and the Calculus of Probabilities.

From this moment on, Meyer was able to devote himself solely to his teaching and research. These focused on various points of mathematical analysis - he was responsible, among other things, for an elementary exposition of the theory of definite integrals - and especially for the Calculus of Probabilities. At the time of his death in 1857, he had just written a voluminous memoir on this discipline; this work was published by one of his students, F Folie, and translated into German by E Czuber (Teubner, 1879).

Antoine Meyer had been elected Correspondent of the Royal Academy of Belgium in 1846.

Antoine Meyer's memory has remained vivid in Luxembourg; he was in fact one of the first to write in the Luxembourgish dialect. He is notably responsible for a collection of tales and fables in which, following Le Roy, he even sings in verse the beauties of the number π. In the Liber Memorialis of the University of Liège published in 1869 by Alphonse Le Roy, it is said that Meyer was helped in his task by a friend: M Henri Gloden, perhaps an ancestor of our amiable President!

It is with particular pleasure that we will speak of Jean-Baptiste Brasseur, born in Esch-sur-Alzette in 1802; it was he who created at the University of Liège the Course of Higher Geometry of which we are currently the holder.

Brasseur's middle school studies were made difficult by the closure of educational establishments during a period troubled by political events. In any case, he enrolled at the University of Liège in 1824, where he notably followed Dandelin's course on Analytical Geometry and was proclaimed Doctor of Physical and Mathematical Sciences in 1829. After a stay in Paris, he returned to Liège and was given charge, in 1832, of the courses on Descriptive Geometry and Analysis Applied to Geometry. During the reorganisation of the University in 1835, he was relieved of the latter course but the course on Applied Mechanics was placed in his remit.

Brasseur's research in Geometry is marked by a certain elegance, combined with great simplicity of means. In short, starting from Descriptive Geometry, he recreated Projective Geometry by a method that was somewhat intuitive. He did not publish his most important research until the end of his life, but he had been presenting it for several years in a free course that he had created and which was to become the current course in Higher Geometry. The work of the first three holders of this course: F Folie, C Le Paige and F Deruyts were to constitute, with that of Brasseur, the heritage of the Liège School of Geometry. We find, in these works, a certain continuity that marks Brasseur's influence on the development of geometry in our country.

The teaching of Applied Mechanics was also marked by Brasseur's methodical spirit. It was he who created the laboratory from which the remarkable work of V Dwelshauwers-Dery on the steam engine was to emerge.

Brasseur had belonged to the Royal Academy of Belgium since 1847, when he was elected Correspondent. He became a full member in 1855. With Meyer, he was one of the founders of the Royal Society of Sciences of Liège.

Mathias Schaar was born in Luxembourg in 1817; he was successively professor at the University of Ghent (1854-1857), at the University of Liège (1857-1864), where he succeeded Antoine Meyer, then again at the University of Ghent until his death in Nice in 1867. Schaar's work mainly concerned the theory of Euler functions and that of quadratic residues. They took him to the Royal Academy of Belgium, where he was elected Correspondent in 1848 and Full Member in 1851.

According to P Mansion, who was his student at the University of Ghent, Schaar introduced into the courses of Higher Analysis, the theory of analytic functions following the ideas of Cauchy.

Schaar was in delicate health and died young; he had trained himself, studying the works of Gauss and those of Cauchy. Perhaps, of all the Luxembourgers who taught Mathematics in the Belgian Universities, he was the most original and the most profound in his works.

The fourth of the Luxembourg geometers of whom we wish to speak was our Master at the University of Liège. Joseph Neuberg was born in Luxembourg in 1840 and was successively a student at the Athénée of this city, then at the Ecole Normale Supérieure annexed to the University of Ghent, from which he left in 1862. He did not enter higher education until 1880; Before that, he taught secondary education successively in Nivelles, Arlon and Bruges, that is to say in small provincial towns without scientific libraries. From 1880, he was successively in charge of the courses of Infinitesimal Analysis, Projective Geometry, Complements of Descriptive Geometry, Analytical Geometry and Mathematical Methodology at the University of Liège. Neuberg was, with Lemoine and Brocard, the creator of the geometry of the triangle and the tetrahedron. We know, in this geometry which is ultimately elementary, the treasures of ingenuity that these geometers expended to demonstrate, in a simple and elegant form, numerous properties. Neuberg had a large share of it. He also dealt with many other questions; he studied in particular certain complexes of lines and the systems of articulated rods have repeatedly caught his attention. In 1891, he was elected Correspondent of the Royal Academy of Belgium and in 1897 a full member; he was director of the Classe des Sciences in 1911, the same year he stopped teaching and was admitted as an emeritus.

In 1824, Adolphe Quetelet had founded the Correspondance Mathématique et Physique, nine volumes of which were published. Later, in 1874, Catalan wanted to revive this journal and created the Nouvelle Correspondance Mathématique. This was replaced in 1880 by Mathesis, which appeared without interruption until 1915, under the direction of P Mansion and J Neuberg. Mathesis was aimed at secondary education and students in special schools; in fact, its programme went somewhat beyond this framework. One only has to browse through its collection to realise the enormous amount of work that its editors must have put into writing it. But, on the other hand, what inestimable services has this journal rendered to Mathematics! Let us add that Mathesis reappeared in 1922 under the direction of Neuberg and Mineur. Currently, the journal is successfully directed by M R Deaux, Professor at the Polytechnic Faculty of Hainaut, in Mons.

When we had Neuberg as a professor, from 1907 to 1911, he gave three hours of consecutive lessons three times a week, without any apparent fatigue, to large audiences (several hundred students). At that time, there was no provision for tutorials for students in Mathematics; Neuberg found the time to fill this gap by giving us a one-hour lesson each week devoted to exercises. He was a tireless worker.

What was striking about Neuberg was his prodigious memory. We met him one day, in 1926, a few months before his death. We were accompanied by an engineer who had been the Master's student in 1902. Neuberg, pointing a finger at this engineer in a gesture that was familiar to him, said to him: "It's Germay or Germeau". The first name was correct!

Neuberg died peacefully one morning in March 1926; the night before, he had personally posted corrected proofs of Mathesis.

Last Updated March 2025