1920 ICM - Strasbourg

1920 International Congress of Mathematicians - Strasbourg, France

The International Congress of Mathematicians was held in Strasbourg, France from 22 September to 30 September 1920. There were 200 full members, 57 family members, giving a total of 257. We give below a version of:
  1. Programme of the Congress
  2. Internal Rules of the Congress
  3. Opening Session of the Congress
  4. Closing Session of the Congress
  5. Report by the Secretary General of the Congress
Before presenting the material, we give a short Preface.
Preface by EFR and JJOC.

Although the 1920 International Congress of Mathematicians was called 'International', it was a limited definition of International. Mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey were excluded. This decision, based on the countries 'blamed' for World War I being excluded, was supported by most people but we must say that it was strongly opposed by a small number, most notably G H Hardy and G Mittag-Leffler, neither of whom attended. The International Research Council had been founded in Brussels in 1919 and it had decided that the next Congress would be held in Strasbourg and not Stockholm as had been proposed in 1912. This was a highly political decision made to 'celebrate' France regaining Strasbourg from Germany. Strasbourg had been French until the French were defeated in the 1870 Franco-Prussian war. As you will see in the reports of the Congress given below, there was a strong nationalistic thread running though the Congress. The Congress ended by accepting an invitation to hold the 1924 Congress in the United States of America.

1.       Programme of the Congress.

Wednesday, 22 September

9.00. - Official opening session under the chairmanship of E Charléty, Rector of the University of Strasbourg, representing M Alapetite, Commissioner General of the Republic held in the Salle des Fêtes of the University, Palais principal, 1st floor.

11.00. - Visit to the University.

15.30 - First plenary session in the Salle des Fêtes. Constitution of the final Board, appointment of the President, Vice-Presidents, Secretaries, etc.

20.30 - Reception of the Members of the Congress by the Organising Committee in the Salle des Fêtes.

The facade of the University was illuminated by the be the careful elegance of the Force et Lumière Society of Strasbourg.

Thursday, 23 September.

From 9.00 to 12.00. - Ordinary meetings of the various Sections.

8.00 to 12.00 - Visit of the four Museums, in groups, under the direction of members of the Bas-Rhin Science Society.

14.30 - Plenary lecture of Sir Joseph Larmor in the Salle des Fêtes.

16.30 - Tea offered by the Society of Friends of the University, 2, rue Geiler. Speeches by M de Witt-Guizot on behalf of the Society, and Émile Picard, on behalf of the members of the Congress.

20.00. - Lecture by M A Ungerer On the astronomical clock of the Strasbourg Cathedral.

Friday, 24 September.

From 9.00 to 12.00 - Ordinary Sessions of the Sections.

10.00 - Visit to the Mausoleum of the Marshal of Saxony.

11.00 - Visit to the Cathedral.

These two visits were led by members of the Bas-Rhin Science Society.

14.30 - Plenary lecture of Leonard Eugene Dickson in the Salle des Fêtes.

17.30 - Official reception at the Hôtel-de-Ville (tea was served). Address by M H Lévy on behalf of the city of Strasbourg, G Koenigs and C de la Vallée-Poussin on behalf of the members of the Congress. Jeanne Clapier, from the Académie de Vaucluse, recited an Ode Salut à Strasbourg with the most beautiful inspiration.

20.30 - Session organised in honour of the Congress by the Bas-Rhin Science Society in the Salle de l'Aubelle, place Kléber. Programme: Lecture by General Taufflieb, Senator, on: Science in Alsace; Speeches, Concert.

Saturday, 25 September.

From 9.00 to 10.30. - Ordinary Sessions of the Sections.

10.30 - Plenary lecture of Charles de la Vallée-Poussin in the Salle des Fêtes.

From 14.00 to 16.30 - Ordinary Sessions of the Sections.

17.00 - Official reception (with tea) at the General Commissariat of the Republic in rue Brûlée.

Sunday, 26 September.

Excursion to Sainte-Odile.

Monday, 27 September.

From 9.00 to 10.30 - Ordinary Sessions of the Sections.

10.30 - Plenary lecture of Vito Volterra.

14.30 - Boat trip on the Rhine, visit to the ports of Strasbourg and Kehl The excursion was offered free of charge by the Directorate General of Ports.

Tuesday, 28 September.

From 9.00 to 12.00 - Ordinary Sessions of the Sections.

14.30 - Plenary lecture by Niels Erik Norlund in the Salle des Fêtes.

17.00 - Official closing session, in the Salle des Fêtes, under the chairmanship of M Alapetite, Commissioner General of the Republic.

19.00 - Banquet offered by the Organising Committee.

Wednesday, 29 September.

Excursion to Saverne (Hohbar).

Thursday, 30 September.

Excursion to the Linge (Turckheim, Kayserberg, Trois-Épis, etc.).

2.       Internal Rules of the Congress.
  1. -The General Sessions will be chaired by the President of the Congress or by one of the Vice-presidents.

  2. -The first meeting of each Section will be chaired by one of the Introducers appointed by the Organising Committee. At this first meeting the Section will appoint one or more Secretaries, who will be responsible for collecting the discussions throughout the duration of the Congress. At each meeting the Members of the Section will elect the President for the following meeting.

  3. - The order of the Communications registered at each meeting will be fixed by the Organising Committee, which will keep in this choice the largest possible account of the wishes expressed by the different Sections.

  4. - The presentation of a Communication should not exceed twenty minutes. During the discussion, a speaker may not speak for more than ten minutes, or more than once on the same subject, except by special permission of the President.

  5. - The Conferences and Communications presented at the Congress will be brought together in the volume of the Proceedings of the International Congress of Mathematicians at Strasbourg. The manuscripts must be delivered by the Authors into the hands of the Drafting Committee (composed of Picard, Koenigs, Galbrun, and Villat) at the latest on the same day that the Communication will be placed on the agenda of a meeting.

  6. - Manuscripts must be very legible, typed as much as possible with the typewriter (with the exception of the formulas), and necessarily with a typewriter if they are written in a language other than French.

  7. - Authors are requested to submit a very short summary of their Communications, to the Editorial Board at the latest on the day before the day on which these Communications will be made in the session.

  8. - The Editorial Committee recalls that it reserves the right to print only a summary of certain Communications.

  9. - Authors who request major changes to their manuscripts during printing must bear the costs of the above modifications.
3.       Opening Session of the Congress.

This session took place on 22 September 22, at 9.00, in the large Salle des fêtes of the palais of the University, in front of an audience comprising both the members of the Congress and a number of Alsatian notables from Strasbourg and the region.

The meeting was chaired by S Charléty, Rector of the Academy of Strasbourg, representing M Alapetite, Commissioner General of the Republic, who was detained elsewhere by the duties of his office. M S Charléty delivered a welcoming speech on behalf of the Government and on behalf of the University.

Then the following spoke:

Henri Levy, Deputy Mayor, who greeted the Congress members on behalf of the city of Strasbourg;

Émile Picard, Perpetual Secretary of the Academy of Sciences, on behalf of the Academy of Sciences and the French National Committee of Mathematicians;

Henri Villat, Professor at the University of Strasbourg, on behalf of the Faculty of Sciences of Strasbourg and on behalf of the Organising Committee of the Congress.

G Koenigs, Secretary General of the Congress, read out the list of official delegations.

W-H Young who spoke on behalf of the English members of the Congress.

C de la Vallée-Poussin, who spoke on behalf of Belgium.

N-E Norlund, who spoke on behalf of Denmark.

L-E Dickson, who spoke on behalf of the United States of America.

G Remoundos, who spoke on behalf of Greece.

V Volterra, who spoke on behalf of Italy.

T Takagi, who spoke on behalf of Japan.

F Störmer, who spoke on behalf of Norway.

F-M Da Costa-Lobo, who spoke on behalf of Portugal.

P A Typpa, who spoke on behalf of Serbia.

L Crelier, who spoke on behalf of Switzerland.

B Bydzowsky, who spoke on behalf of Czechoslovakia.

We give below the text of the speech of Émile Picard.

Address by Émile Picard.
Ladies and Gentlemen,

On behalf of the French National Committee for Mathematics and the Organising Committee for this Congress, I thank the Commissioner General for agreeing to be represented at this inaugural session. In welcoming the friends of our country, who have responded to our call, the Commissioner General and the Rector of the University have shown the interest that the government of the Republic takes in the progress of science. When we proposed to meet in Strasbourg, we thought of paying homage to the noble land of Alsace, returned to this French homeland, to which its ancient origins are attached and sympathies which have always remained alive through the ups and downs of its history. We also wanted to honour the University of Strasbourg, which, since the sixteenth century, has counted so many distinguished masters. The eminent men who teach there today play with dignity the role imposed on them by the tragic events of recent years, making them the pioneers of the generous and human culture that was always French culture. We ask the Council of the University to accept the expression of our gratitude for the gracious hospitality it offers us in this palace. How can we not remember in this place the admirable conduct of so many professors of our teaching in the war which has just ended; their patriotic faith contributed to the common victory, which allows us today to meet in the city of Strasbourg. I would like to pay special tribute to one of the youngest masters of this University, who bears the glorious traces of his heroism on his face.

We are also very grateful to the Local Committee, which, under the active direction of Henri Villat, had the heavy responsibility of regulating our sessions and organising receptions and walks, whose charm will temper the austerity of our work. Our colleagues from Strasbourg indeed considered that they had a duty to make known to our hosts something of this district of Alsace, whose name has become a symbol. We hope that all the members of the Congress will take away a touching memory of it.

Finally, it is particularly pleasant for me to thank the Mayor and the President of the Strasbourg Chamber of Commerce, as well as the representatives of many Alsatian companies and other generous benefactors of this Congress, whose donations are extremely precious to us and will allow publications testifying to the scientific activity of this meeting.

In a recent article, full of penetrating remarks on the teaching of mathematics in various countries, a professor of this University evoked the memory of two mathematicians who taught there formerly: Sarrus, whose name will remain in the history of the calculus of variations, and Arbogast, who appears as a precursor of Functional Calculus. I will add to these two names of mathematicians that, perhaps unexpected name, of Pasteur. Didn't the young scientist, who came here in 1849 to teach chemistry, be somewhat of a geometer? Pasteur's famous memoirs on hemihedry and rotational polarisation, which date from this time, are geometry: very picturesque geometry, moreover, where certain microscopic mushrooms are skilful mathematicians, since they know how to distinguish, for nourishment, between a right crystal and a left crystal. It was through geometry that Pasteur entered the study of fermentations. Strasbourg can be proud to have counted this great man among its masters.

Gentlemen, it is one of the objects of congresses, like the one we are inaugurating today, to establish personal relationships between researchers who cultivate the same or neighbouring sciences. After the appalling turmoil of recent years, which has broken so many ties, reconciliations are necessary between scholars who esteem themselves and who, without any ulterior motive, have no other concern than the selfless worship of truth. This is particularly useful to mathematicians who have sometimes shown some tendency to isolate themselves in very limited parts of their science. Broad sketches, showing the present state of some great questions, must be one of the attractions of meetings like ours, and can exert the happiest influence. Mathematicians sometimes pass for somewhat original characters, buried in their symbols and lost in their abstractions. It is important that the educated public, sometimes too exclusively literary in training, have a fairer opinion in this regard. No, mathematics is not the strange and mysterious science that so many people imagine; it is an essential piece in the construction of natural philosophy.

Any physical theory, sufficiently developed, necessarily takes a mathematical form; it seems that the actions and reactions between the mind and concrete things have led little by little to form models into which reality, at least partially, can be inserted. Certainly, many concepts created by mathematicians have not yet found applications in the study of physical phenomena, but the history of science shows that it was reckless to assert that such and such a notion will not be used one day. Geometers like to recall the words of the great mathematician Lagrange, who, one day comparing mathematics to an animal of which we eat all the parts, said: "Mathematics is like pork, everything is good."

The profession of a prophet is always dangerous. Some believe, however, that the applications of mathematics will be mostly studied in the coming years and that pure theory will be somewhat overlooked by the younger generations. The time we live in is becoming singularly harsh in all areas for the workers of intelligence, and the most optimistic sometimes wonder with concern whether civilisation, as we are used to envisioning it, will not undergo an eclipse. So we must not tire of repeating that theoretical speculation is ultimately the real source of all progress in the applied sciences. If unfortunately unselfish research ceases to be possible, the scientific capital accumulated in previous ages would quickly run out, and one would not continue long to live on the scent of an empty vase, as Renan said for another object. Whatever happens, one will always find among mathematicians incorrigible idealists, who, like the woman of the Gospel, believe they have chosen the best part by scrutinising the properties of space, and by analysing in its most hidden corners the subtle idea of a function; it will not be taken from them. It is in the hope that pure mathematics and applied mathematics will continue a fruitful collaboration that we begin the work of this Congress, where many Communications have been promised to us, and where eminent mathematicians will kindly give us some plenary lectures on the progress and trends of the science that is dear to us. May all those who will thus contribute to the splendour of this meeting please receive in advance the thanks of the Organising Committee.
4.       Closing Session of the Congress.

This session took place on 28 September at 17.00, in the Salle des Fêtes of the University, under the chairmanship of M Alapetite, Commissioner General of the Republic, assisted by S Charléty, Rector of the University.

M Alapetite opened the session with a speech in which he appreciated the importance and scope of the Congress, and congratulated the members of the Congress on the results of their work.

Émile Picard, President of the Congress, delivered the speech which will be found below.

G Koenigs, Secretary General of the Congress, read the Report which will be found below.

G Greenhill replied by expressing the sentiments of the members of the Congress, on behalf of England.

A Demoulin then spoke on behalf of Belgium.

M N E Norlund, spoke on behalf of Denmark.

J Rey-Pastor, spoke on behalf of Spain.

T Buck, spoke on behalf of the United States of America.

P Zervos and N Hatzidakis, spoke on behalf of Greece.

J A Barrau, spoke on behalf of the Netherlands.

J Boccardi, spoke on behalf of Italy.

A V E Guldberg, spoke on behalf of Norway.

F-M Da Costa Lobo, spoke on behalf of Portugal.

A Myller, spoke on behalf of Romania.

D Riabouchinski, spoke on behalf of Russia.

H Cramer, spoke on behalf of Sweden.

G Du Pasquier, spoke on behalf of Switzerland.

B Bydzowsky, spoke on behalf of Czechoslovakia.

At 19.00, a Banquet, offered to the members of the Congress and their families by the Organising Committee, brought together, in the restaurant of the Baeckehiesel, the members of Congress themselves, and a certain number of chosen guests; this banquet, chaired by M Alapetite, was enlivened with the most frank and cordial gaiety.

Address by Émile Picard.
Monsieur the Commissioner General,

On behalf of the members of Congress, I thank the French Government, of which you are the representative here, for the interest it has taken in this international meeting. We are happy to salute in this closing session the eminent administrator who, in his brilliant career, has always shown himself to be up to the most delicate situations, and who here worthily continued the task started by his illustrious predecessor, whom the confidence of the Parliament, and, one can say it, of the country has just raised to the Presidency of the Republic.

Ladies and Gentlemen,

When the meeting in Strasbourg of the International Congress of Mathematicians was definitively announced last December, some timid people told us that the enterprise was premature. The question was far from new, however. The resumption of international relations had been studied at length in London and Paris in October and November 1918 in two inter-academic conferences, which included representatives of the powers then at war with the Central Powers. In these meetings, it was strongly insisted on this point that the previous wars had not destroyed the mutual esteem of the belligerent scholars for each other, and that, after a few years, peace could have erased the traces of the past. "But today, concluded unanimously the delegates of the Allied countries, the conditions are quite different. Unnamed crimes will leave a stain on the history of guilty nations, that signatures at the bottom of a peace treaty cannot wash away. So we will have to abandon the old international associations and create new ones with the possible help of neutrals. These are the principles which guided the decisions taken first in London and Paris, confirmed and clarified in a new conference held in Brussels last year. An International Research Council was created, to which would be attached, by adhering to certain general ideas, but retaining a large independence, from International Unions relating to the different areas of science. The question of International Congresses would come under the corresponding Union. Finally, neutral nations would be asked to join the International Research Council as well as the various Unions.

This programme has largely been carried out today. We have a large number of countries joining the International Research Council. The Astronomical Union, the Geodetic and Geophysical Union, the Chemical Union, still others, finally the Mathematical Union were founded. We who are here on this Wednesday asked the neutral countries to join this last Union, and we have no doubt that they will answer our call. It is in accordance with this general plan that the current Congress was convened, the genesis of which I thought it my duty to retrace for you.

Gentlemen, the world of 1920 is very different from that at the beginning of 1914 and there are few scientists who are today disposed to isolate themselves in an ivory tower; although academics, we remain men. You have just seen that the problem of international relations has been taken up with hard work. In each area of science, any Scientific Congress, attached to the International Research Council, and which will meet for the first time in the coming years, will be essentially new, I mean that it will not fit into any series already started.

With particular regard to our Congress, we have never concealed that we intended to give it a particular meaning, by bringing it together in Strasbourg. We were therefore extremely touched by the eagerness with which our foreign friends answered our call. Arriving in this city, they let themselves, like us, be filled with the Alsatian atmosphere, and many, I am sure of it, gave themselves up to reflections, that, far from here, they would not have had. More intimate bonds have been formed, which will remain precious. We will thus continue, between friendly peoples, our scientific work, bringing to this collaboration our various qualities, without anyone pretending to exert an unbearable hegemony and without worrying about certain threats, that with a shamelessness which does not surprise us, we have dared to utter.

As for certain relationships, which have been severed by the tragedy of recent years, our successors will see if a sufficiently long time and sincere repentance can one day allow them to be resumed, and if those who have excluded themselves from the meetings of civilised nations are worthy of entering. For us, too close to the events, we still make ours the beautiful word pronounced during the war by Cardinal Mercier, that, to forgive certain crimes, it is to make oneself their accomplice.

From all points of view, the Congress which is about to end has succeeded beyond our expectations. Our various sections have heard communications of great importance and the Plenary Lectures which have been given to us have been absolutely brilliant. The most varied subjects of Analysis, Geometry, Mechanics and Mathematical Physics, as well as questions concerning teaching and the history of sciences, were tackled. The theory of relativity, so fashionable today, could not fail to be the subject of some discussion. Some cannot speak without passion of this doctrine which has become, for them, like a kind of religion. The future will say whether the general theory of relativity is something other than a purely formal and mathematical construction, or whether psychologists are right, who consider that hypotheses, incapable of being grasped by intuition, are not likely to be the basis of an explanation of the physical world. One consequence of theory, however, may interest us here, is that we age less quickly when we move quickly. It is therefore good to travel a lot, a result conducive to the success of International Congresses.

I have only one pleasant duty left to accomplish. I already thanked in advance, during the inauguration session, some of the organisers of this Congress, in particular the members of the Local Committee and its tireless President, Henri Villat. Today, in closing, I would like to express the gratitude of all to the workers who worked so hard from the start, and to our dedicated Secretary General, Gabriel Koenigs. He never doubted success: let him be in the spotlight, after all his trouble.
5.       Report by G Koenigs.

Report by the Secretary General of the Congress.
Gentlemen,

The Secretary General's duty is to bring you here, in the shortest possible terms, a precise report on the genesis of this Congress, on its holding and also to pay a public tribute to the contributions, so devoted, to which it owed its brilliant success.

The President of the Congress has just told you, with his high authority, what the scientific ties of this Congress were and, one might add, its moral directives.

To follow up on the projects previously drawn up in Paris and London by the Inter-allied Research Council, a Congress was convened in July 1919 in Brussels under the auspices of the Inter-allied Academies. The creation of various international unions such as the Astronomical Union, the Geodetic Union, etc. was continued there.

With regard to the International Mathematical Union, the mathematicians present in Brussels did not consider themselves to be either numerous enough or sufficiently accredited to achieve its definitive constitution. At that time, in fact, the National Mathematics Committees had not been set up anywhere, the assistance of which was to be the natural basis of the Union. We therefore decided in Brussels to constitute only a provisional Union; we carefully drafted its statutes, in accordance with the regulations of the Research Council to which we unite, we appointed a provisional office and finally we expressed our wishes.

The first of these wishes was that an International Congress of Mathematicians would be held in the fall of 1920 in the city of Strasbourg, despite certain pre-war commitments.

It was also decided that each of us would cause in our country the constitution of a National Mathematics Committee. These various Committees were to send to Strasbourg, the day before the Congress, delegates with the mission of definitively constituting the International Mathematical Union.

This whole programme has been completed.

From the winter of 1919 our French National Mathematics Committee was formed under the auspices of the Academy of Sciences of the Institut de France and with the assistance of the French Mathematical Society. Similar Committees were then organised in England, Italy, Belgium, the United States, and these Committees sent here duly accredited delegates. They also came from Czechoslovakia, Greece, Portugal, Serbia, Japan, and Poland. On 20 September 1920 we were then able to hold, in a room of the University of Strasbourg, the planned meeting of the allied or associated delegates. The provisional statutes drawn up in Brussels were definitively adopted there, a definitive office was set up, which, with certain additions, confirms in its functions the provisional office in Brussels; it is composed of the following:

Honorary Presidents: Professors Jordan, Lamb, Picard, and Volterra.

President: Professor de la Vallée-Poussin.

Vice-Chairs: Professors Appell, Bianchi, Dickson, Larmor, and Young.

Secretary General: Professor Koenigs.

Secretaries: De Donder, Hatzidakis, Petrovic, Pompeiu.

Treasurer: Demoulin.

Immediately it was formed, the International Mathematical Union made two decisions. The first concerns mathematical bibliography; the directors of the mathematical journals will be invited to require the authors of articles to print the writing of a short summary of the memoir made by the author himself.

The second decision concerns the date and place of the next Congresses. According to the constitution of the International Mathematical Union, it is indeed to it that this initiative belongs.

It was decided that the International Congresses of Mathematicians would take place every four years, therefore in 1924, 1928, etc. As for the meeting place, two proposals were simultaneously put forward by the Belgians and the Americans, some proposing Brussels and the others New York or its surroundings. It was agreed that the 1924 Congress would be held in New York and the next in Belgium.

The next day, 21 September, information was given to all the neutrals present about the final constitution of the International Mathematical Union and its statutes. They have been advised that they are free to join us and we have every reason to hope that most of the neutral nations will, as with us, constitute National Committees with sufficient authority to represent them legally within the Union.

Thus is accomplished the work that we had in view in Brussels and which our French heart rejoices all the more since it was carried out in the University of Strasbourg.

As for its constitution, in December 1919, the French National Committee chaired by Émile Picard and of which Gabriel Koenigs is the Secretary general and Henri Galbrun the Secretary, had taken in hand the organisation of the International Congress of Mathematicians. The young elite of mathematicians that France had sent to the University of Strasbourg could not fail to make the most eager reception at the request of the French National Committee. These gentlemen immediately constituted a local committee which had all the latitude to organise itself first and to then organise on the spot the multiple elements necessary for the holding of a Congress.

The President of this Local Committee is Henri Villat, the Secretary René Thiry, the Treasurer Georges Valiron.

The Congress was held on non-communal but individual invitations, addressed by the French National Committee itself, which also centralised all the proposals for Lectures and Communications.

The local committee had the heavy burden of ensuring the material service by providing the members of the Congress with accommodation, by arranging suitable premises for the plenary sessions and those of the Sections, by regulating the functioning of the latter, by arranging excursions for the members of the Congress, arranging walks and visits to museums and monuments whose beauties or memories make the glory of Strasbourg. Finally, or rather, first of all, we had to think that none of this could be done without money and that the contributions requested from members of the Congress would not suffice, under penalty of being prohibitive, to cover the expenses of Congress. These expenses do not consist solely of costs for receptions, banquets, postage, circulars and allowances to auxiliary staff. We must also think about the impression of the Communications made at the Congress and the work presented there.

Nothing less than the admirable skill and devotion deployed by the Board of the Local Committee was needed to overcome these difficulties.

René Thiry organised with meticulous care and perfect order the distribution of accommodation, and all the members of the Congress are deeply grateful to him for the concerns which, thanks to him, have been avoided on this subject. He was strongly assisted in this task by the Syndicate of Initiative and Propaganda, whose assistance made it possible to establish a reception for members of the Congress when they left the station and which also greatly facilitated the question of accommodation.

We owe a special mention to Professor Delcourt who so beautifully organised the evening offered by the Committee to the members of the Congress on the first day of the Congress.

The Commissioner General, for his part, was kind enough to offer a lunch to the members of the Congress who, through me, expressed their gratitude to him. Thanks again to the Society of Friends of the University, and to the Strasbourg Municipality, who both agreed to give receptions in our honour.

What thanks should we not also owe to G Kern, the distinguished President of the Society of Sciences, Agriculture and Arts of the Bas-Rhin, who had the gracious care to receive within his Society the members of the Congress who had the honour to meet there with the elite of the Strasbourg Society. We cannot forget either the splendid concert which was given to us by artists of choice, or the choir of young singers whose characteristic costume and large black bow will always symbolise Alsace in its most charming patriotic way.

In organising large excursions, General Fetter and Colonel Holtzapfell have very kindly worked to make them as easy and as inexpensive as possible. They are entitled to all our gratitude.

But the one to whom our recognition is particularly acquired is the President of the Local Committee, Henri Villat. What must be said about him is too true for his modesty to be offended.

If the Congress was able to find the necessary financial resources, we owe it is to his persevering efforts, to its tireless efforts. He was able to find in himself, in his patriotic and scientific faith, the strength to makes it work, the word that persuades. I asked him the other day how he had been able to get so many successful memberships. "I talked about Science and France," he replied. And this answer gives a singular moral value to the enumeration that I owe you and whose length you are going to undergo.

To all these patriotic and generous donors, I say from the bottom of my heart: thank you!

Henri Villat himself told me that he would never have reached such a high figure without the advice or the discreet personal action of many devoted intermediaries who assisted him in his tireless propaganda. We extend our sincere thanks to all, and in particular to Émile Schwoerer, Correspondent of the Institut de France, whose activity has been particularly effective.

And now, Gentlemen, I would fail in my duties if I did not renew in a special way, on behalf of the members of the Congress, all our thanks to Commissioner General Alapetite who, after having granted the Congress a significant subsidy, has received multiple testimonies of his benevolence and who was kind enough, despite his heavy workload, to agree to chair this closing meeting.

Let us also renew our thanks to the Municipality of Strasbourg which, after having granted us a subsidy of 5,000 francs, has not ceased to give us its support. Our thanks to the Rector of the University, who liberally made available to us the spacious premises of the University of Strasbourg and so happily opened our Congress on 22 September.

Finally, our thanks to all those who we do not forget, but whose long list of names we cannot read here, and whose assistance has been precious to us.

However, I would like to say a special word to the ladies of Strasbourg who have helped their husbands in their arduous task or who have created an atmosphere of friendship around the Congress favourable to its success. Thank you to these good and valiant French women.

Gentlemen,

The French and their friends came to Strasbourg, met there with the Alsatian soul, they experienced the extreme sensitivity it manifests in contact with everything related to the great homeland, France, and its glory. Strasbourg, for its part, understood the gesture of these friendly mathematicians who, by making Strasbourg the seat of the first international post-war Congress and by organising it there according to the wish of its heart, undoubtedly had the deep desire to give:
in Alsace a testimony of deep affection,
to others an example to follow,
and still others a lesson to ponder.