1924 ICM - Toronto

1924 International Congress of Mathematicians - Toronto, Canada

The International Congress of Mathematicians was held in Toronto, Canada from 11 August to 16 August 1924. There were 444 full members present in Toronto, 82 Corresponding members, not present, and 100 family members. A total of 544 were present in Toronto. We give below a version of:
  1. Opening session of the Congress
  2. Proceedings of the Congress
  3. Minutes of the International Mathematical Union
Before presenting the material, we give a short Preface.
Preface by EFR and JJOC.

The 1920 Congress ended by accepting an invitation to hold the 1924 Congress in the United States of America. This invitation, made by the American mathematicians at the 1920 Congress was made without the approval of the American Mathematical Society. When it was realised by the American Mathematical Society that mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey were to be excluded in 1924, as they were in 1920, they refused to give the Congress financial backing. The International Research Council refused to end their exclusion policy so John Charles Fields saved the day by inviting the 1924 Congress to Toronto. Some mathematicians, such as G H Hardy, boycotted the Congress because of the exclusion of 'ex-enemy' countries. Applications of mathematics were even more strongly in evidence with only two Sections on pure mathematics topics and five on applications.

1.       Opening session of the Congress.

The Opening Session of the Congress was held at 10.00 on Monday, 11 August in Convocation Hall.

The Chair was taken by Professor J C Fields, Chairman of the Organising Committee. The proceedings opened with an address by The Honourable Dr Henri S Béland, Minister of Health and Minister of Soldiers' Civil Reestablishment, who, on behalf of the Government of the Dominion of Canada, extended welcome to the Delegates and Members thus:
Mr Chairman, Ladies and Gentlemen of the Congress:

Those of us who, a quarter of a century ago, felt that, at not too distant a date, some development would take place, the effect of which could be to concentrate the world's attention on Canada, scarcely dreamed of an event such as this.

We indeed entertained the hope of a sensational, transcending, commercial and economical achievement, something commensurate with the resources which, in a large measure, still lie dormant in the bosom of our land, of our forests, of our lakes and oceans.

Little did we cherish the belief that world-wide renowned scientists would honour Canada by selecting for their convention one of her most charming cities. This, however, has come to pass and, as spoiled children of Fortune, we find that is only natural.

On this memorable occasion it is my privilege, a privilege which, I can assure you, I personally prize very highly, to extend to your distinguished assemblage a cordial welcome in the name of the Government of Canada.

Had not the Prime Minister been unavoidably engaged elsewhere, he would himself have relished the opportunity of greeting you.

It has undoubtedly occurred to you that Canada, being comparatively young, cannot boast of a long list of scientists, or offer for your appreciation many daring feats of engineering. The majesty of our mountains and streams has, however, invited some manifestations in this regard, which have given us reason to be proud.

They will, I trust, reveal to you a stubbornness of study, an exactitude of method, a boldness of conception, that are a credit to those amongst Canadians who have devoted their life to the advancement of the exact sciences.

Your activities, however, are not confined to our planet; they extend far beyond, indeed to other solar systems, to distances which impress our minds with a sentiment of the deepest awe.

You must, sometimes, be carried away into realms of abstraction, the access to which is denied ordinary mortals, and where the souls of Copernicus and Galileo, Descartes, Pascal, Leibniz, Newton and Lagrange fraternise with yours in a communion of supreme delight.

Their work of genius is your work; you carry with you the tradition of all centuries, nursing it gently, adding to it as to a most precious heritage for the benefit of humanity.

I am perfectly aware that a serious accusation has been brought against Science. It has been whispered that, by its discoveries, Science has enhanced the desire and the power for destruction. What an odious calumny! Pasteur, in a remarkable passage, has refuted in advance the sordid allegation. The exclusive object of Science is the improvement of the conditions of humanity, morally, intellectually, economically and socially. Any diversion from that end is the disfigurement of science's divine and celestial rule.

Your task is a noble task. It partakes of heroism and of genius; your altruistic endeavours should be the theme for praise and gratitude.

Let me express the hope that your sojourn in Canada may be an agreeable and a fruitful one, that you will carry with you an enduring and favourable impression of our composite population which, I assure you, is greatly honoured by your visit.
Changing to a language more familiar to many of those in the audience, a Canadian language, too, the Honourable Dr Béland continued speaking in French as follows:

If M Frédéric Masson, instructed by his colleagues at the French Academy, to welcome M Henri Poincaré, one of your masters, felt the need to show his shyness in the presence of the great mathematician, what embarrassment should not be mine right now?

I hasten to add, however, that this very natural feeling of fear is mixed with very lively pleasure, because if the task is perilous of appearing before the authorised representatives of the exact sciences, it carries with it a badge of honour, that of welcoming you to Canadian soil on behalf of the Prime Minister and the Government, and express our deepest regret at not being able, like your colleagues in the British Association for the Advancement of Science, to give you the honour of the Federal Capital.

However, knowing the generous spirit of hospitality that is one of the characteristics of the city of Toronto, I imagine that you do not bitterly regret the benevolent shadow of the tower of our imposing parliamentary buildings.

You will search in vain for the treasures of ancient art in America. In some museums no doubt, in some private salons, famous paintings, even groups of sculpture could invite and charm your eyes, but we will have to wait for the pious and persevering work of centuries before we can present to visitors of distinction the wonders of architectural works that abound in Europe.

I believe, moreover, that when you came to Canada you were not attracted by the style of our monuments, our cathedrals or our public buildings, although some of these are worthy of attention, perhaps of admiration.

No, what makes the charm of this country, what makes it almost irresistibly attractive, is its physical beauty, it is these bold strokes of the Creator's brush and chisel: mountains, inland seas, majestic rivers, immense plains, lush forests all well formed to captivate the soul of scholars like you. We particularly feel on this occasion how much we are indebted to the beauties and natural riches of the country since they brought you to our shores. Both mathematicians and poets need inspiration. You will look for yours in the rich and vast fields which are offered like ripe fruits waiting to be picked, in mining engineering, mechanical engineering, civil engineering, in the science of electricity.

It has been said of humanity that it is a perpetual collaboration; this truth is affirmed and demonstrated more in scholars. Indeed, with you, collaboration goes back very far; it finds its manifestations even in the most remote centuries. You claim, and with good reason, the family of Pythagoras and Euclid, Copernicus, and Galileo, Newton, Leibniz, Lagrange, Poincaré, and Bertrand. You apply yourself with tireless zeal and disinterestedness which is too little known in other spheres of human activity, to enrich, for the benefit of humanity, the heritage received from your illustrious predecessors. You climb the starry heavens and you pass with the speed of light next to our planetary sisters, plunging into infinity to scrutinise the worlds, recognise relationships and movements, then return to the earth, such as bees, charged with precious scientific loot.

You move quickly from the abstract to the practical. And after having adorned the intelligence and amazed the imagination, your works are concerned in raising the material level through discoveries, improvements and innovations, the result of which is an increased sum of well-being for humankind.

Your task is a noble task. It has heroism and genius. It commands the admiration of all those interested in the fate of humanity.

The Canadian Government wishes that your conference be both pleasant and fruitful; it hopes that you will bring back a lasting impression of your passage within our peoples, which is greatly honoured by your presence.

The President of the University of Toronto, Sir Robert Falconer, K.C.M.G., in the name of the University welcomed the visitors with the following words: Mr Chairman, Ladies and Gentlemen: I have much pleasure in welcoming, on behalf of the University of Toronto, the members of the International Mathematical Congress to the meetings which are about to be held in this place. This University and City are being honoured in having here the first meeting of the Congress that has been held on this side of the Atlantic. Never before have so many distinguished mathematicians and those interested in the applications of mathematics been gathered together in Canada. A very large number of the celebrated universities of the world are represented in this gathering, and many of the names on the programme are those of persons who have long been distinguished for their contributions to the advancement of the mathematical sciences. The variety of the nationalities is an indication of the breadth of science; the common purpose that brings you together is an indication of the unity of the sciences. Your visit to the Dominion of Canada, and especially to this University, will be a powerful impulse for the development of Mathematics. It will be an encouragement to many individual workers to have the opportunity of meeting others who have been foremost in the advancement of their subject. We hope that you will enjoy your visit socially and will make many acquaintances and friendships which will last long after you have returned to your homes.
The Chairman, speaking for the Royal Canadian Institute and the Organising Committee, then said:
Ladies and Gentlemen:

For the first time an International Mathematical Congress meets in America, and a Canadian city has the privilege and honour of being chosen as the place of meeting. Mathematics on this continent has no such retrospect as in Europe. American mathematical achievements are of comparatively recent date, and Canada's place in the world of mathematics is a very modest one.

We in Canada derive our earlier scientific traditions from Great Britain. More recently we have begun to feel the influence of continental Europe. The founding of the Johns Hopkins University in 1876 marked a new era in the history of universities and science in America. It meant the recognition of the place of research in the university. It meant acceptance of the fact that one of the functions of a university is to train men for research. It meant that the professor was to be encouraged to engage in research. The founding of the American Journal of Mathematics in 1878 was a natural sequence to the founding of the university. This provided a means of publishing the output of American mathematicians and stimulated their productive activity. The character of this output was largely determined by the mathematical training furnished in the universities on this side of the Atlantic. The defective teaching of the calculus here made itself felt, more particularly on the side of analysis. During the first couple of decades of its existence, too, a considerable proportion of the more important papers which appeared in the Journal were of European origin.

Among the papers published in the early numbers of the Journal, we may here point out, was a series of communications on the solution of algebraic equations by Professor George Paxton Young of the University of Toronto. With these papers, we may say, that Canadian mathematics sprouted. The tree is not yet large. May its growth be stimulated by this Congress!

The gradual reform in the teaching of the calculus has had its influence in improving the quality and increasing the quantity of the American mathematical product. I know of no more striking illustration of the dependence of man on his environment than that afforded by the history of mathematics on this continent. In less than two generations, America has passed from near sterility in mathematics to a comparatively affluent productivity. This transition I would attribute primarily to the change in the teaching of the calculus.

The sterilising of one or more generations by the false teaching of a subject is a tragedy of the first order. To those who have called a halt to such teaching, who have made correct texts possible, who have helped remedy the evil, we owe a debt of gratitude which it is not easy to repay. Such benefactors are in attendance at this Congress. We have them with us here to-day.

It would not be easy to differentiate between the influence of the Johns Hopkins University and that of immediate European contact on the development of the other great American universities. One might, however, indicate that the founding of Clark University in 1889, as a purely graduate institution of a highly specialised character, was a direct outcome of the spread of the Johns Hopkins idea.

More important than the event just mentioned, in promoting the growth of the research spirit in general and the progress of mathematics in particular in this part of the world, was the founding of the University of Chicago in 1892. Two years later the New York Mathematical Society extended the range of its activities by becoming the American Mathematical Society. This marked an epoch in the history of mathematics in America. An event of capital importance was the appearance of the first number of the Transactions of the Society in the year 1900.

In later years the evolution of the Annals of Mathematics illustrates the growing need of increased facilities for the publication of research work in mathematics. The founding of the Mathematical Association of America, too, is evidence of the spread of the mathematical interest.

May we hope that the present Congress will do much to further the cause of mathematics on this continent. As constituted it brings together the theoretical man and the applied scientist, the mathematician whose occupation it is to spin fine webs and elaborate beautiful configurations in the realm of the subjective and the applied man who takes all the risk of assuming that over against the subjective network prepared by the mathematician there is something corresponding in the external universe.

May we hope, too, that the Congress will not be without its influence on the layman to whom science must ultimately look for its material support and that on seeing the practical man standing side by side with the theoretical man, he will realise that practice cannot be divorced from theory and that the pure scientist does his share in contributing to the well-being of the community.

Ladies and Gentlemen, Delegates, Members of the Congress, I extend to you on behalf of the Royal Canadian Institute and the Organising Committee a most cordial welcome to our country, Canada, and to the city of Toronto, Mesdames et Messieurs, je vous souhaite la bienvenue!
Replying on behalf of the delegates and members of the Congress, Professor Charles de la Vallée Poussin, President of the International Mathematical Union, responded thus:
Ladies and Gentlemen,

The last International Congress of Mathematicians, the first that followed the war, met in Strasbourg. The choice of this city had obvious moral significance. When in 1920 I came to this city to take part in the Congress, I found in the Alsatian metropolis the same feelings which had moved me the previous year at the inauguration of the French University of Strasbourg. It was not just a scientific congress that was about to open; it was a symbol and it was a feast, that of the deliverance of Alsace and also, as I said then, that of the liberation of science that sacrilegious hands had enslaved for too long with criminal designs.

But that does not prevent the Strasbourg Congress from being above all an important scientific event. It brought together members from almost all countries and the very large volume of documents that we owe to the care of M Villat is the undeniable and lasting testimony of his fruitful activity. It was during this Congress that the International Mathematical Union received its final status and that I myself had the honour of being chosen for its president. This honour, ephemeral like most human greatness, because it expires tomorrow, calls me to speak at this beautiful meeting today, a bit like the swan who is said to sing only one time and who dies after his first speech.

It is up to the International Mathematical Union in principle to organise international congresses and the determination of the place of the current congress was the first item on the agenda at the Strasbourg meeting. As you can read in the minutes of this meeting, written by the Secretary-General, M Koenigs, member of the Institut de France, two proposals had been presented, one to hold the congress in Belgium and the another near New York.

It was the American proposal that won and, while being Belgian myself, I think there is every reason to rejoice.

First of all, both from a moral and a geographical point of view, Brussels is too close to Strasbourg. The choice of this centre as the seat of the congress would have seemed to be inspired too exclusively by the same concerns. It would have been to sacrifice the international and universal character of the congress to the demands of an undoubtedly legitimate feeling, but to which the choice of Strasbourg had given full and entire satisfaction. I would even add that the choice of Brussels, far from fortifying the lesson of things given by the Congress of Strasbourg would, on the contrary, have blunted its true meaning. After Strasbourg, it was first of all necessary to affirm the international and exclusively scientific character of the congress.

Now which country could satisfy this desire better than America? To hold the congress in the new world was to immediately give it an extension which precedents had not known. It was to give legitimate satisfaction to the natural desires of American scholars. They who had come, so many and so many times, to Europe had the right to think that their turn had come to receive Europeans at their home. It was a fitting tribute to the importance of the work accomplished by American science, already so rich in the present, and richer still by the marvellous perspectives that the future opens before it.

And for us, inhabitants of the old world, was it not a rejuvenation that we tore ourselves away in some way to come into contact with new ideas and forget, if only for one day, the difficulties facing us there? We who crossed the ocean to find ourselves here, will we regret breathing a more serene atmosphere? Shall I tell you the singular, unexpected, even a little disturbing impression that I myself experienced when I heard myself, here for the first time, referred to by the beautiful name of European of which we could be so proud and which unites us all here with each other more than a thousand leagues from the shores of the Mediterranean?

So let us rejoice to be here and that our thanks go first to the noble and great country whose generosity made this Congress possible. Each of the nations represented here was keen to express their thanks themselves through the voice of their delegates. But the success of the conference exceeded the committee's forecasts. The number of delegates is too great to allow everyone to speak. We had to delete the part of the agenda devoted to their responses. But their feelings are the same for everyone, and they are also the same as mine, they will allow me at this moment to formulate them on their behalf.

It is therefore in their name as in mine that I address the expression of our gratitude to the Canadian government, enlightened enough to know the importance of science, generous enough to be its patron, and who has made available from the organising committee the considerable sums required by the circumstances. We thank in the person its representative, Minister Béland, who was kind enough to himself bring to this assembly the testimony of his very high benevolence. It is in their name as in mine that I address my thanks to the Royal Canadian Institute, the University of Toronto, to its president, and, in particular, to Professor Fields. It was he who, after taking the initiative in transferring the congress to Toronto, accepted the chairmanship of the organising committee and assumed most of the heavy task that was necessary to ensure its success. Since the meeting of the International Research Council in 1922 in Brussels where this project began, M Fields has known no peace or rest. I will not tell you how many times he has crossed the Atlantic, how many times he has visited countries and cities, met with mathematicians, and asked for collaborations. I will not calculate all the steps he has taken or the kilometres he has travelled, I would fear by proclaiming the total to scare him himself, because I am sure he never has counted.

But the goal is achieved, fully achieved, and we who have not been troubled, we will be in the spotlight. The Congress promises to be magnificent by the number of its members, by the importance and the interest of the promised communications. It is to Mr Fields and his staff at the Royal Canadian Institute that we owe this result. It is to them that we must be here, in the attractive setting of monuments and greenery that is the University of Toronto, in a setting so well suited to our needs, where nothing has been spared for ensuring maximum comfort for our people, maximum ease and attractiveness for our work.

And now here is this enchanting setting where everything still seems young brings me back, far beyond the war, to the years of my youth. This beautiful city at the edge of its immense lake evokes for me the memory of another extended city, too, on the banks of an admirable lake, and I think of the very first Congress, that of Zurich in 1897, like this one here, all framed with fresh landscapes and young also with hopes.

How easy it would be and how vain it would be to insist on the resemblances and on the contrasts that this rapprochement suggests. I only want to remember two things. First I note that the object of a mathematical congress was defined, in that of Zurich, with perfect precision and clarity which has not been surpassed. This object remained ours: personal relationships between mathematicians, reports and lectures, organisation of congresses, bibliography, etc. Then I take from the welcome speech that Hurwitz addressed to the delegates the following few thoughts, because they are still suitable today and can serve as a conclusion to my speech.

The great ideas which fertilise mathematical science are born in the isolation and the silence of the scholar's quiet room; no other science, except perhaps philosophy, requires solitary reflection to the same degree. However mathematicians are people like any other and that is why they need the society of their peers. May a frank and cordial fraternity animate our meetings, charm our mutual relationships; may the representatives of the various nations, in love with the same ideal, feel comforted by the awareness that united in their aspirations, they work to bring people together and prepare peace between nations.

This was the meaning of Hurwitz's words. Alas! War broke out seventeen years later, which proves that peace and war cannot be decided at congresses of mathematicians. However the words of Hurwitz are not false and whatever appearance of emptiness that events give them, I want to make them mine at the moment, but by completing them with a last thought.

The peace we dream of among the peoples is the very peace that reigns here among us. This is based on justice, good faith and love of the truth. Mathematicians find one of their great enjoyments is in admiring the work of others and their greatest desire is to give back to each one what is due to him. It is probably a pipe dream to want nations to be as disinterested as mathematicians, but, whatever we want, peace with all that it entails for humanity of hope of happiness and promises of progress, that peace can only be based on justice. May our meetings be frank and cordial and be able to serve both as a lesson and as an example to the world!
Professor G Koenigs, assisted by Professor W H Young, read a provisional list of delegates to the Congress.

The General Session.

Following the Opening Session a General Session of the Congress was held for the election of Officers. On the nomination of Professor de la Vallée Poussin, Professor J C Fields was elected President of the Congress, and the following Vice-Presidents were elected: Professors B Bydzovsky, F M Da Costa Lobo, L E Dickson, Senator F Faure, Professors H Fehr, L E Phragmén, S Pincherle, E Schou, C Servais, C Stormer, W van der Woude, W H Young, and S Zaremba.

Professors J L Synge and L V King were elected General Secretaries of the Congress.

Following the General Session a group photograph of the members of the Congress was taken in front of the Physics Building.

2.       Proceedings of the Congress.

Monday, 11 August

14.30. Sections I, II, III (a), 111(6), IV(a), IV(b), V, and VI, having been separately installed by the Introducers, papers were read and discussed.

16.30. The members of the Congress were entertained at a Garden Party at the York Club by Professor and Mrs J C McLennan.

20.30. Professor Carl Stormer delivered his lecture on "Modern Norwegian Researches on the Aurora Borealis."

Tuesday, 12 August.

9.00 Sections I, II, III (a), III (b), IV(a), IV (b), V, and VI met separately. Papers were read and discussed.

14.30. Professor F Severi delivered his lecture on "géométrie algébrique".

16.30. The members of the Congress were entertained at a Garden Party at Government House by His Honour Henry Cockshutt, Lieutenant- Governor of Ontario and Mrs Cockshutt.

20.30. The members of the Congress were entertained at a Conversazione in Hart House by the University of Toronto and the Royal Canadian Institute.

Wednesday, 13 August.

9.00. Sections I, II, III (a), IV (a) and V met separately. Papers were read and discussed.

11.30. Professor É Cartan delivered his lecture on "La théorie des groupes et les recherches récentes de géométrie différentielle".

15.00. The honorary degree of D.Sc. was conferred by the University of Toronto on the following delegates to, and members of, the Congress: Sir William Bragg, Professor Charles de la Vallée Poussin, Professor G Koenigs, The Honourable Sir Charles A Parsons, Professor F Severi, Professor W Stekloff. Following the conferment, the members of the Congress were entertained at a Garden Party given by the University of Toronto.

20.30. Professor W H Young delivered his lecture on "Some characteristic features of Twentieth Century pure mathematical research".

Thursday, 14 August.

The members of the Congress crossed to Niagara, where, on the invitation of the Hydro-Electric Power Commission of Ontario, they inspected the generating station at Queenston. They then proceeded to Niagara Falls, where they were entertained at Luncheon in the Clifton Inn as the guests of the Power Commission. After viewing the Falls, and taking the trip along the Gorge Route, the party returned by boat to Toronto.

Friday, 15 August.

8.30. A General Assembly of the International Mathematical Union was held in Convocation Hall.

10.00. Sections I, II, IV(a), and V met separately. A joint session of Sections III (a) and III (b) was held. Papers were read and discussed.

14.00. Professor L E Dickson delivered his lecture "Outline of the theory to date of the arithmetics of algebras".

15.00. The-joint session of Sections III (a) and III (b) was continued.

15.15. Professor S Pincherle delivered his lecture on "Sulle operazioni funzionali lineari".

16.30. The members of the Congress were entertained at a Garden Party at the Grange by the Council of the Art Gallery.

19.30. The members of the Congress attended a soirée at the Hunt Club.

Saturday, 16 August.

9.00. Sections I, II, and V met separately. Sections III (a) and III (b) held a joint session. Sections IV (a) and IV (b) held a joint session. Papers were read and discussed.

14.00. Professor de la Vallée Poussin, on behalf of the members of the Congress, laid a wreath at the foot of the Soldiers' Memorial Tower.

14.30. Professor Le Roux delivered his lecture "Considérations sur une équation aux dérivées partielles de la physique mathématique".

17.00. Closing Session in Convocation Hall.

The Chair was taken by Professor J C Fields, President of the Congress, who spoke as follows:
A Congress such as this brings together many eminent men from many different lands, to benefit by the interchange of ideas and to come into personal contact. The policy of the present Congress was to accentuate more than has been done at previous Congresses the side of applied mathematics. I think that you will agree with me that the results justified the policy.

We have been accustomed here in Canada to look to Europe for our intellectual inspiration, and the presence of so many distinguished scientists from the other side of the Atlantic cannot but act as a great stimulus to the intellectual activities of our country. We have been carrying on a campaign for some years past with the object of impressing our Governments and the people with the importance of science, for to the layman the scientist must ultimately look for the material resources necessary to the support of research. We have not been altogether unsuccessful in our efforts, and I am sure that the movement will be greatly helped by the meeting which has been in session during the past week. While we have gained by the presence of so many distinguished visitors, we will hope that they have profited by learning something of Canada. We would wish that a larger number could take the Western Excursion and inform themselves more fully in regard to the physical features of Canada and its natural resources.

I wish to express to the following bodies and individuals the thanks of the Congress for their kind and generous assistance in making this Congress a success. [List omitted.]"
The Session then closed.

20.00. A dinner for the members of the Congress and their wives was held in Hart House. Professor J C Fields presided.

On the night of 17 August a number of members of the Congress left Toronto on a transcontinental excursion to Vancouver and Victoria, which had been arranged through the courtesy of the Canadian National and the Canadian Pacific Railways for overseas members of the Congress and of the British Association for the Advancement of Science, whose Sessions, held also in the buildings of the University of Toronto, had in part coincided with those of the Congress. The excursion returned to Toronto on 3 September. Other members took shorter trips before returning to their home countries.

3.       Minutes of the Session of 15 August 1924 of the International Mathematical Union.

On 15 August 1924, on the occasion of the International Congress of Mathematicians held in Toronto, the Statutory Assembly met under the Presidency of M de la Vallée Poussin, President of the Union.

The meeting took place in the aula of the University of Toronto, kindly made available to us. The following countries, forming part of the Union, were represented: Belgium, Canada, Denmark, United States, France, Great Britain, Holland, Italy, Norway, Poland, Portugal, Sweden, Switzerland, Czechoslovakia.

Several scientists from the following countries who have not yet joined the Union were also present: Spain, Georgia, Russia, India.

The Secretary read out the minutes of the session of 20 August 1920 held in Strasbourg, where the International Mathematical Union was created.

These minutes are adopted. The Treasurer then spoke about the Financial State of the Union. The Treasurer's accounts are approved. The rate for one member joining remains fixed at one hundred and twenty-five francs.

The Treasurer having complained of the delay brought about by the acceding countries in paying their contributions, it was decided that, for their attention, the sums due will be claimed from the latecomers.

Thanks are voted to the Treasurer for his management.

The Board is then renewed, under the statutory conditions. According to article 6 of the Statutes, the Board of the Union is elected for eight years, but exceptionally, the mandate of the President and three Vice-Presidents (designated by lot) appointed at the foundation of the Union, expires at the end of the first General Assembly following that of their election.

The lot designates as outgoing Vice-Presidents Bianchi, Dickson and Larmor.

Professor Pincherle is elected President.

Professors Bliss, Fehr and Holmgren were elected Vice-Presidents.

It should be said that in these various votes, each country affiliated to the Union had a number of votes equal to that which the Statutes assigned to it. A scientist from each country, designated by his compatriots, deposited the required number of ballots.

Then the following were appointed Honorary Presidents, in addition to those already in existence, Professors de la Vallée Poussin, outgoing President, Fields, Dickson and Mittag-Leffler.

The Assembly then dealt with the question of Bibliography. A Special Bibliography Commission was established, which will include, in addition to the President, Archibald, Bortolotti, Fréchet, Van der Woude, and Young. Regarding the choice of the seat of the future Congress in 1928, the provision of which belongs to the Assembly, it decides to postpone this choice to the year 1926 and to defer to the Board for this task.

At the end of the session, the United States deposited in the hands of the President a vow concerning the intervention of the International Research Committee in the admission of Countries into the Union. Denmark, Holland, Italy, Sweden, Norway, and Great Britain join this wish.

The President will be responsible for transmitting it to the Executive Bureau of the International Research Committee.

Secretary General: G Koenigs. The President: de la Vallée Poussin.

State of the Board of the International Mathematical Union.

Honorary Presidents: Lamb, Émile Picard, Volterra, de la Vallée Poussin, Dickson, Fields and Mittag-Leffler.

President: Pincherle.

Vice-Presidents: Appell, Young, Bliss, Fehr, Phragmén.

Secretary General: G Koenigs.

Treasurer: M Demoulin.