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The Belgian Centre for Mathematical Research
Founded in 1948
The Belgian Centre for Mathematical Research was founded in 1948 by Lucien Godeaux. After it had operated for ten years, Godeaux wrote the article 'Le Centre Belge de Recherches Mathématiques', Bulletin de la Fédération des Sociétés Scientifiques 3 (1960), 161-168. It is available on the web at
https://orbi.uliege.be/bitstream/2268/318049/1/465472B_20_68.pdf
We give below an English translation of Lucien Godeaux's article.
Lucien Godeaux was president of the Belgian Centre for Mathematical Research from its founding until 1966. The article we reproduce gives details of the colloquia organised by the Centre up to 1959. We end this article by giving some titles of Colloquia organised by the Centre after Godeaux wrote the article Le Centre Belge de Recherches Mathématiques.
https://orbi.uliege.be/bitstream/2268/318049/1/465472B_20_68.pdf
We give below an English translation of Lucien Godeaux's article.
Lucien Godeaux was president of the Belgian Centre for Mathematical Research from its founding until 1966. The article we reproduce gives details of the colloquia organised by the Centre up to 1959. We end this article by giving some titles of Colloquia organised by the Centre after Godeaux wrote the article Le Centre Belge de Recherches Mathématiques.
1. The Belgian Centre for Mathematical Research.
When in 1947, Mr C Huysmans, Minister of Public Instruction, proposed the creation of interuniversity research centres, the Professors of Mathematics of the Universities of Brussels and Liège agreed to present a project of which we reproduce the essential passages:
The Professors of Mathematics of the Universities of Brussels and Liège have the honour to propose the constitution of a Centre for Research in Mathematics in Belgium. They hope that their colleagues at the Universities of Ghent and Louvain, those at the Polytechnic Faculty of Hainaut and the Military School will join them once the Centre is constituted.This proposal was approved by the Minister and a substantial credit was granted. We would like to pay tribute to Minister Huysmans and Mr J Kuypers, Secretary General of the Ministry of Public Education, who, by this gesture, showed the interest they had in disinterested research.
The following is planned:
1° The organisation of colloquia where questions of mathematics would be presented and discussed, each colloquium being devoted to a specific question.
2° The publication of a series of updates of the questions studied in the colloquia.
The creation of colloquia responds to a real need. If university professors sometimes have the opportunity to meet and discuss among themselves, it is not the same for young researchers: Tutors, Managers, Assistants and Researchers attached to the Fonds National de la Recherche Scientifique (F.N.R.S.). It is important to put them in contact, in order to coordinate research and to direct it ...
On the other hand, the publication of updates would be useful to researchers. By update, we mean the presentation of the state of a question, for example of a question that has been the subject of discussions in colloquia. Accompanied by a precise bibliography, such a presentation would possibly indicate the research that remains to be carried out in the field considered and the links with other questions ...
It would be childish to insist on the need to have a good range of mathematicians in the country, if we want it to participate successfully in the current development of physical-chemical sciences and applied sciences.
The Belgian Centre for Mathematical Research was thus created; it brought together the professors of Mathematics from the higher education establishments listed above, to which were later added the professors from the State Agronomic Institutes.
A provisional committee was appointed with the mission of drawing up the statutes. There were many tentative steps, but finally a general assembly held on 17 November 1948, voted on the statutes, drawn up by the Secretary of the Provisional Committee, Mr F Bureau. The Centre was established as a non-profit association and the statutes were published as an appendix to the Belgian Official Gazette of 25 June 1949. The Executive Committee, appointed for three years, was composed of: Mr L Godeaux, president (Liège); Messrs Casteels (Ghent), Bruwier (Mons), Bouckaert (Leuven), vice-presidents; Mr Bureau, secretary (Liège); Mr Van Den Dungen, treasurer (Brussels); Messrs Errera (Brussels), Ballieu (Leuven), Backes (Ghent), Risack (Ecole Militaire), members.
Baron Ch de la Vallée Poussin was elected Honorary President by acclamation. One of the first acts of the Centre was to publish his work "Le Potentiel logarithmique: Balayage et Représentation conforme", the printing of which had been delayed by post-war difficulties. The Centre was pleased to be able to pay this tribute to the illustrious Belgian mathematician.
The Centre's activity consisted of organising:
1° National Colloquia,
2° International Colloquia,
3° Computing centres in higher education establishments (the Centre was involved in equipping the computing laboratories of the Universities of Louvain, Brussels and Ghent).
4° Lectures given by foreign mathematicians passing through Belgium or near our borders.
5° Facilities given to young researchers to attend lectures given outside the establishments to which they are attached.
There were a few National Colloquia. The first was organised in Liège in 1949. Messrs Hirsch and Godeaux presented the theory of correspondences between two algebraic curves, the subject of a work currently being published in the Mémorial des Sciences mathématiques. But it was mainly the International Colloquia that were the focus of the Centre's concerns. The first, devoted to Algebraic Geometry, took place in Liège in December 1949. The aim was to show the different methods used in Algebraic Geometry and the applications of this geometry to other questions.
The participants were: Mrs Dubreil-Jacotin (Poitiers), Messrs Severi (Rome), Van der Waerden (Amsterdam), Dubreil (Paris), Samuel (Clermont-Ferrand), François Châtelet (Besançon), Garnier (Paris), Segre (Bologna), Libois (Brussels), Bureau (Liège), Godeaux (Liège).
On the proposal of M Guy Hirsch, a Colloquium on the Topology of fibered varieties took place in Brussels in June 1950. The speakers were MM Hopf (Zurich), H Cartan (Paris), Ehresmann (Strasbourg), Koszul (Strasbourg), Eckmann (Zurich), Leray (Paris), Guy Hirsch (Brussels).
With M Simonart, we organised in Louvain, in April 1951, a Colloquium on Differential Geometry. We heard talks there by Messrs Bompiani (Rome), Favard (Paris), Terracini (Turin), Schouten (Amsterdam), Vincensini (Marseille), Haantjes (Leiden), Lichnerowicz (Paris), Hlavaty (Bloomington); Kuyper (Wageningen), Simonart (Louvain), Van Bouchout (Louvain), Backes (Ghent), Godeaux (Liège), Rozet (Liège), Debever (Brussels).
The first Colloquium on Algebraic Geometry was far from having exhausted the vast domain of this theory. A Second Colloquium on Algebraic Geometry was held in Liège in June 1952. We heard Messrs Chisini (Milan), Gauthier (Nancy), Villa (Bologna), Kähler (Leipzig), Dolbeault (Paris), Gröbner (Innsbruck), Gaeta (Saragossa), Burniat (Brussels), Nollet (Liège), Godeaux (Liège).
The following Colloquia were to deal with questions of Mathematical Analysis. First, in Brussels, in March 1953, there was a Colloquium on functions of several variables, where Messrs Behnke (Munster), Bergman (Stanford), H Cartan (Paris), Lelong (Lille), Martinelli (Genoa), Roquette (Munich), Saxer (Zurich), Serre (Paris), Severi (Rome), Stein (Munster) spoke.
Then, with the help of Messrs Lepage and Gillis, two Colloquia on partial differential equations were organised: the first in Louvain in December 1953 where Mrs Fourès-Bruhat (Marseille), Messrs Lichnerowicz (Paris), Delsarte (Nancy), Doetsch (Freiburg), Lepage (Brussels), Gillis (Brussels), Sauer (Munich) spoke. The second was held in Brussels in May 1954 and Messrs Picone (Rome), Schwartz (Paris), Lions (Paris), Leray (Paris), Brelot and Choquet (Paris), de Rham (Lausanne), Garnir (Liège), Fantappiè (Rome) spoke.
The Calculus of Probabilities and Statistics are becoming more and more important; it was therefore useful to organise a Colloquium on these subjects. With M Gillis, we organised a Colloquium on Mathematical Statistics, in which Messrs G Darmois (Paris), Blanc-Lapierre (Algiers), de Finetti (Rome), van Dantzig (Amsterdam), Hemelrijk (Amsterdam), Barlett (Manchester), Dugué (Paris), Francks (Brussels), Gillis and Miss Huyberechts (Brussels), Breny (Liège) participated.
In May 1955, a Colloquium on questions of reality in Geometry was held in Liège. The papers on this difficult question were given by Messrs Montel (Paris), Marchaud (Paris), Haupt (Erlangen), Vincensini (Marseille), Fenchel (Copenhagen), Brusotti (Pavia), Galafassi (Pavia), B Segre (Rome), Santalo (Buenos-Ayres).
At the initiative of Messrs Errera and Teghem, we organised a Colloquium on the theory of numbers, in Brussels, in December 1955. Messrs Mordell (Cambridge), Pisot (Paris), Richert (Göttingen), Ricci (Milan), Poken (Amsterdam), Errera (Brussels), Roth (London), Erdős (Budapest), Davenport (London), Delange (Clermont-Ferrand), Van der Corput (Berkeley), Teghem (Gembloux).
At the beginning of the volume is reproduced the memoir of M de la Vallée Poussin on The Riemann function ζ(s) and the number of prime numbers less than a given limit.
The role played by Topology is increasingly important, so we held a Colloquium on Algebraic Topology in Louvain in June 1956. The speakers were Messrs Hilton (Manchester), Thom (Strasbourg), Eckmann (Zurich), Mac Lane (Chicago), Adams (Cambridge), G W Whitehead (Cambridge, Mass.), Vesentini (Milan), Deheuvels (Lille), Dedecker (Liège), Papy (Brussels), Guy Hirsch (Ghent).
In December 1956, we had a Colloquium on Algebra in Brussels, where we heard Mrs Dubreil-Jacotin (Paris), Messrs Dubreil (Paris), Krull (Bonn), Croisot and Lesieur (Besançon and Poitiers), Higman (Oxford), Krasner (Paris), Green (Manchester), Lombardo-Radice (Palermo), Ballieu (Louvain), Samuel (Clermont-Ferrand), Witt (Hamburg), Waelbroecks (Brussels), Tits (Brussels).
With the help of M Teghem, a Colloquium on the theory of sequences was organised in Brussels in December 1957. The lectures were given by Messrs Karamata (Geneva), Meyer-König and Zeller (Stuttgart), Favard (Paris), Vermes (London), Teghem (Brussels), Aljancic (Belgrade), Schmetterer (Hamburg), Sonnenschein (Brussels), Orlicz (Poznań), Ricci (Milan), Zamanski (Paris), Knapowski (Cambridge).
The Centre did not organise a Colloquium in mid-1958, because the Polytechnic Faculty of Hainaut organised a Congress on Engineering Mathematics in Mons, to which the Centre also gave its patronage.
In December 1958, a Colloquium on Global Differential Geometry was held in Brussels, where Messrs Lichnerowicz (Paris), Thom (Strasbourg), Miss Libermann (Rennes), Messrs B Segre (Rome), G Walker (Liverpool), Kuiper (Wageningen), Reeb (Grenoble), Vranceanu (Bucharest), Ehresmann (Paris), Dedecker (Liège), Van de Ven (Leiden), Tits (Brussels), Papy (Brussels) attended.
Finally, in June 1959, at the initiative of M Géhéniau, a Colloquium on the Theory of Relativity was held, where Messrs Hlavaty (Bloomington), Synge (Dublin), Joshua Goldberg (Pittsburgh), Just (Berlin), Ehlers (Hamburg), Schücking (Hamburg), Debever (Brussels), Libois (Brussels), Géhéniau (Brussels), Tits (Brussels) spoke.
In December 1959 a third Colloquium on Algebraic Geometry was held. The following ones will be devoted, in 1960, to questions of mathematical analysis.
Each of the Colloquia gave rise to a volume containing the text of the lectures. The volumes relating to the last two are still in the process of being published, but we now have a series of thirteen volumes which seem to be quite appreciated abroad. The first eleven volumes were printed by Maison Thone in Liège and put on sale at Librairie Masson in Paris. The last volumes were printed by Maison Ceuterick in Louvain and put on sale at Librairie Gauthier-Villars in Paris.
Apart from the Colloquia which have just been mentioned, the Centre has organised others which have not given rise to publications (except in the form of hand written manuscripts not put on the market). Let us mention:
A Colloquium on Recent Developments in Quantum Field Theory (Brussels, 1949) organised by M Géhéniau and where presentations were made by Messrs Serpe, Schönberg, Géhéniau and Van Hove.
A Colloquium on the theory of partial differential equations (Brussels, 1951) organised by M Lepage and where Messrs Leray, Lichnerowicz, Van Hove and Gillis spoke.
A Colloquium on Geometry held in Liège in 1952 and where Messrs Lepage and Jongmans spoke.
A Colloquium on the theory of particles organised in Brussels by M Géhéniau (1953) where Messrs Vigier, Jean, Serpe, Benoist, Prentski, Libois, Géhéniau, Janssens, Debever and Demeure spoke.
This list shows that most of the important questions in mathematics have been reviewed and the volumes of the Colloquia constitute good documentation for our young mathematicians. There is also a result of another order achieved by our Colloquia: it is that they have aroused among most Belgian mathematicians a kind of friendly emulation which can only be fruitful for the future.
It is also important to see what the opinion of foreigners has been on our Colloquia.
Here, the answer is simple. In several countries, Colloquia similar to ours have been organised and the International Mathematical Union has followed the same path for some years.
The opinion that we have gathered on several occasions in international meetings is that the era of the great international Congresses is over. In these Congresses, the authors had from ten to twenty minutes to present their research and their presentations were inevitably difficult to understand for those of their listeners who were not well informed about the question dealt with. Many believe that it is better to reserve these communications for the publications of the Academies and to devote international meetings to general presentations. In our minds, the Colloquia with a limited objective should be multiplied, but the large Congresses should be preserved and devoted to lectures, showing the links between the different theories of mathematics.
We will allow ourselves to reproduce a passage from the speech given by M Paul Montel, Member of the Institute, Associate of the Royal Academy of Belgium, at the meeting of Latin-speaking Mathematicians, in Nice, in September 1957.
The Congresses have been increasingly overwhelmed by the increase in the number of researchers, the multiplication of disciplines and their fragmentation which have transformed them into towers of Babel, as the Academies of Sciences tend to become. Then were born the Colloquia devoted to well-defined parts of mathematics, like those so varied and very renowned that M Godeaux and his colleagues organise in Belgium or like the one that was just held, last month, in Helsinki, by the initiative of M Rolf Nevanlinna, on the theory of functions of complex variables.We still have to talk about one last activity of the Centre: the invitation of foreign mathematicians to give lectures in the Universities or at the Belgium Mathematical Society. One could wonder if we are not following in the footsteps of the cultural agreement commissions. This is not the case. First of all, there are countries whose Mathematical School is flourishing and with which we do not have a cultural agreement. Then, it takes a certain amount of time to obtain from a cultural agreement commission the authorisation to invite a foreign scholar, the request necessarily having to go through a Faculty. However, it happens that we are not informed of the passage of a mathematician until a few weeks in advance. For example, it happened that an Italian mathematician was invited to give lectures in Holland and had to go through Belgium. We stop him on the way. In addition, an exchange professor called by one of our universities may be invited, through us, to give lectures in another university.
Under these conditions, we have decided that each higher education institution and the
The Committee of the Centre has thought of a new activity; it would consist of inviting a foreign mathematician to give, no longer lectures, but lessons in an inevitably limited number. This comes up against a difficulty: These lessons would have to be given over a limited period of time and in a specific University. But then the professional responsibilities of the professors of the other Universities would risk preventing them from attending all the lessons. An experiment has also been carried out. We had invited M Lichnerowicz to give a course of six lessons at the University of Louvain. These six lessons were given in one week and only our colleagues from Louvain and a few from Brussels were able to attend all the lessons.
Let us add to conclude that the Executive Committee of the Centre is appointed by the General Assembly for three years. It must include two professors from each of the Universities, a professor from the Polytechnic Faculty of Hainaut and a professor from the Military School. The Committee is currently made up of: M L Godeaux (Liège), president; Messrs Vanderlinden (Ghent), Lepage (Brussels), Bouckaert (Louvain), vice-presidents; M P Gillis (Brussels), secretary; M Ballieu (Louvain), treasurer; Messrs Backes (Ghent), Franckx (Military School), Rozet (Liège) and Derwidué (Mons), members.
We have just presented the work accomplished by the Belgian Centre for Mathematical Research during its first ten years of existence. It would probably have been possible to do better: that will be the work of our successors.
2. Some later Colloquia.
1959.
Third Colloquium on Algebraic Geometry: held in Brussels from 17 to 19 December 1959. The following papers were presented: C Marchionna-Tibiletti, Groupe concentré d'intersections de courbes et hypersurfaces algébriques. Applications. B Segre, L'unirationnalité de certaines variétés algébriques du point de vue de la géométrie différentielle et de la topologie. L Roth, Sur les variétés algébriques qui admettent des groupes continus d'automorphismes. E Marchionna, Sur la postulation des variétés algébriques et questions connexes. P Du Val, Application des idées cristallographiques à l'étude des groupes de transformations crémoniennes. D Gallarati, Les variétés algébriques à courbes sections canoniques. C F Manara, Questions d'existence de variétés algébriques. Louis Nollet, Un problème concernant les surfaces algébriques douées de torsion. P Burniat, Surfaces algébriques régulières de genre géométrique et de genre linéaire . L Godeaux, Quelques résultats sur les surfaces de genres zéro possédant des courbes bicanoniques irréductibles. M Baldassarri, I teomeri di Lefschetz e la teoria délia coomologia dei fasci sulle varietà algebriche.
1960.
Colloquium on Functional Analysis: held in Louvain on 25, 27, and 28 May 1960. The following papers were presented: Jean Leray, Prolongements de la transformation de Laplace. Lucien Waelbroeck, Les espaces à bornés complets. Gottfried Kôthe, Une caractéristique des espaces bornologiques. J Sebastiao e Silva, La définition du spectre d'un operateur et les opérateurs à spectre élémentaire non borné. Lucien Waelbroeck, Les espaces à bornés complets. J Sebastio e Silva, Les espaces à bornés et la notion de fonction différentiable. A C Zaanen, A note on the Daniell-Stone integral. Hèinz Kônig, Lineare dissipative Système. Guido Stampacchia, Sur les espaces de fonctions qui interviennent dans les problèmes aux limites elliptiques.
1961.
Colloquium on Numerical Analysis: held in Mons on 22, 23, and 24 March 1961. The following papers were presented: G Lemaître, F L Bauer, L Collatz, G Fichera, C Lanczos, R de Possel, R Sauer, E Stiefel, A van Wijngaarden, L Derwidué, N Forbat, E D Franckz, J Charles and E G Gennart, J Meinguet.
F G Tricomi writes in a review:
1961.
F G Tricomi writes in a review:
It is evidently impossible to report here on all these 14 articles, nor would it be very useful to report only the titles. I will therefore limit myself to saying something about those among them that seem to me to be of greater interest from a general point of view, that is, not only for those who are interested in some special branch of Numerical Analysis.
A first of these articles is that of R Sauer relating to the concept of convergence in Numerical Analysis which, among other things, deals with the extension (due to H J Stetter) to partial differential equations of the methods of G Dahlquist for the study of the convergence of finite difference procedures applied to ordinary differential equations.
Also it seems to me of that an article of general interest is that of L Collatz on certain homogeneous boundary value problems (or initial value problems) for differential equations (ordinary or partial differential equations) having a monotone character; that is (roughly) such that if, in the indefinite equations and in the accessory ones, the signs of equality are changed into suitable signs of inequality; it can be asserted that the corresponding solution is certainly positive (or negative) in a certain field. Indeed, from this fact, one can easily deduce some increases (or "decreases") for the solutions of the corresponding non-homogeneous problems.
Finally, I point out the article by F L Bauer on a formula of numerical quadrature of Römberg, which seems particularly suitable for use in modern programming calculators, and that by N Forbat on variational methods for the approximation of eigenvalues, in a very general class of order .
Some articles are written in a truly abominable French. I am aware of the linguistic difficulties created by the growing internationality of the sciences, but there is also the possibility of having our writings in foreign languages reviewed by a local colleague before they go to print.
Second Colloquium on Differential Geometry: held in Liège on 19, 20, and 21 December 1961.
1962.
Colloquium on the Theory of Algebraic Groups: held in Brussels from 5 to 7 June 1962. The following papers were presented: A Weil: Sur la théorie des formes quadratiques. A Borel, Ensembles fondamentaux pour les groupes arithmétiques. M Kneser, Schwache Approximation in algebraischen Gruppen. J-P Serre, Cohomologie galoisienne des groupes algébriques linéaires. F Bruhat, Sur les sous-groupes compacts maximaux des groupes semi-simples p-adiques. I Barsotti, Analytical methods for abelian varieties in positive characteristic. P Cartier, Arithmétique des groupes algébriques. R Steinberg, Générateurs, relations et revêtements de groupes algébriques. T A Springer, Quelques résultats sur la cohomologie galoisienne. J Tits, Groupes semi-simples isotropes.
1964.
Second Colloquium on Functional Analysis: held in Liège from 4 to 6 May 1964. The following papers were presented: L Amerio, Solutions presque périodiques d'équations fonctionnelles dans les espaces de Hilbert. A Martineau, Equations différentielles d'ordre infini. K Maurin, General eigenfunction expansions and unitary representations of topological groups. A Robertson, Hypercomplete spaces. H Schaefer, On the role of order structures in spectral theory. C Foias, Modèles fonctionnels, liaison entre les théories de la prédiction, de la fonction caractéristique et de la dilatation unitaire. A Pietsch, Dualnukleare lokalkonvexe Râume. E Magenes, Problèmes de traces et problèmes aux limites pour équations linéaires elliptiques et paraboliques. L Waelbroeck, Les semi-groupes différentiables. J Leray and Yujiro Ahya, Systèmes linéaires, hyperboliques non stricts. J Leray and L Waelbroeck, Norme formelle d'une fonction composé (préliminaire à l'étude des systèmes non linéaires, hyperboliques non stricts). L Schwartz, Sous-espaces hilbertiens et noyaux associés; applications aux représentations des groupes de Lie.
1964.
Colloquium on Topology: held in Brussels from 7 to 10 September 1964. The following papers were presented: H Hopf, Einige persönliche Erinnerungen aus der Vorgeschichte der heutigen Topologie. Ch Ehresmann, Cohomologie à valeurs dans une catégorie dominée. S Eilenberg and J C Moore, Homological algebra and fibrations. E Spanier, Duality in topological manifolds. E Thomas, The Steenrod squares in the mod two cohomology algebra of an H-space. P J Hilton, Exact couples for iterated fibrations. V K A Guggenheim, Cohomology theory in the category of Hopf algebras. J F Adams, A spectral sequence defined using A-theory. G Hirsch: Homologie des espaces fibrés et groupes d'homotopie de . P Dedecker, Algèbre homologie non abélienne.
1969.
Colloquium on the Mathematical Theory of Optimal Control: held in Brussels on 23, 24, and 25 April 1969.
1969.
Conference on nonlinear differential equations, their stability and their periodicity: held in Mons on 27, 28 and 29 May 1969.
1970.
Third Conference on functional analysis: held in Liège from 14 to 16 September 1970.
Last Updated March 2025