1936 ICM - Oslo

1936 International Congress of Mathematicians - Oslo, Norway


The International Congress of Mathematicians was held in Oslo, Norway from 13 July to 18 July 1936.There were 487 full members of the Congress, 182 family members, making a total of 669. We present below:
  1. Preparatory Work for the Congress
  2. Congress Programme
  3. Section Lectures
  4. Opening Session
  5. Closing Session
  6. Speeches
Before presenting the material, we give a short Preface.

Preface by EFR and JJOC.

This Congress is perhaps most famous for being the first at which Fields Medals were presented. This would become an important feature of all futures Congresses. The political situation at this time was very worrying for many and this resulted in a comparatively low attendance. The Italian government did not allow Italians to attend in protest to the sanctions Norway had imposed on Italy following their invasion of Ethiopia. No mathematicians from the Soviet Union attended. Notice that the number of plenary lectures at this Congress were 19, each of 45 minutes. This was a slight decrease from the previous Congress. An invitation for the 1940 Congress to be held in the United States was fully supported by the American Mathematical Society, unlike the invitation which had been given in 1920 for the holding the 1924 Congress in the United States.

1.       Preparatory Work for the Congress.

At the closing session of the Zurich Congress on 12 September 1932, the late Professor Alf Guldberg, on behalf of the mathematicians of Norway, had the honour of inviting mathematicians to Oslo for the next International Congress of Mathematicians. To the great pleasure of the mathematicians of Norway this invitation was accepted, and the closing session approved the plan that the next Congress would be held in Oslo in 1936.

Already in the spring of 1932, a Norwegian Organising Committee had received the offer of the necessary financial support from several of the contributors mentioned below [in fact we have omitted the list], so that one had - before accepting the invitation to Zurich - the certainty of being able to carry out the Congress project from an economic point of view.

The municipality of Oslo offered Congress participants a dinner on 15 July and the Oslo Tramway Company granted holders of the Congress badge free travel on all of the Company's tram and bus lines. The Norwegian State Railways granted a 20% reduction for the outward journey to, and return journey from, the Congress.

The following shipping companies granted a reduction to the delegates. "Fred Olsen & Co.", Oslo (Newcastle, Rotterdam, Antwerp). The company "Sondenfjelds-Norske Dampskibsselskab" (Kiel, Hamburg).

The first invitation circular was sent out in October / November 1935 to mathematicians, academies, universities, graduate schools and mathematical societies, numbering around 6000 copies. Then the final programme was sent to those who answered the first call.

2.       Congress Programme.

Monday, 13 July.

20.00: Reception offered to the members of the Congress by the Rector of the University of Oslo in the Aula. The Rector was represented by Poul Heegaard, Dean of the Faculty of Sciences.

Tuesday, 14 July.

8.50-10.00: Opening session in the presence of His Majesty the King in the University Aula. Address by Carl Stormer, President of the Organising Committee, and welcoming speech by Halvdan Koht, Minister for Foreign Affairs. Election of the President and Vice-Presidents of the Congress. Distribution of Fields medals.

10.15-11.00: Lecture: C Stormer, Program for the quantitative discussion of electron orbits in the field of a magnetic dipole, with application to cosmic rays and kindred phenomena.

11.15-12.00: Lecture: R Fueter, Die Theorie der regulären Funktionen einer Quaternionenvariablen.

14.00-16.30: Section Lectures.

17.30: His Majesty the King received the members of the Congress at the Royal Palace.

Wednesday, 15 July.

9.00-9.15: Inauguration of a Sophus Lie bust, donated to the University of Oslo and presented by lawyer Georg Lous on behalf of the Donors Committee.

We decided to send the following congratulatory telegram to Professor Friedrich Engel, Giessen: "The plenary session of the International Congress of Mathematicians, assembled for the unveiling of a bust of Sophus Lie, sends you its cordial congratulations thanking you for your precious work for editing the master's works."

9.15-10.00: Lecture: E Cartan, Some insights into the role of Sophus Lie's group theory in the development of modern geometry.

10.15-11.00: Lecture: C L Siegel, Analytische Theorie der quadratischen Formen.

10.15-11.00: Lecture: O Veblen, Spinors and projective Geometry.

11.15-12.00: Lecture: J Nielsen, Topologie der Flächenabbildungen.

15.00-18.00: Sections Lectures. Meeting of the C. I. E. M.

20.00: Dinner offered by the City of Oslo to ordinary members of Congress at the Hotel "Bristol"

Thursday, 16 July.

9.15-10.00: Lecture: E Hecke, Neuere Fortschritte in der Theorie der elliptischen Modulfunktionen.

10.15-11.00: Lecture: O Neugebauer, Über vorgriechische Mathematik und ihre Stellung zur griechischen.

10.15-11.00: Lecture: C W Oseen, Probleme der geometrischen Optik.

11.15-12.00: Lecture: V Bjerknes, New Lines in Hydrodynamics.

11.15-12.00: Lecture: H Hasse, Über die Riemannsche Vermutung in Funktionenkörpern.

15.45-24.00: Excursion on the Oslo Fiord with the Stavangerfjord transatlantic liner from the "Norske Amerikalinje". In the morning and throughout the morning the trip was quite uncertain; however at the departure time of the boat "Vippetangen" the sun dissipated the mist and the excursion on the Oslo Fjord until the Faerder lighthouse at the mouth of the fjord with the return to Oslo, was favoured by magnificent weather.

At 18.00 dinner was served for around 700 delegates in four dining rooms. Professor Carl Stormer, in an address, greeted His Royal Highness the Crown Prince, Honorary President of the Congress, and Her Royal Highness the Crown Princess, who had honoured the Congress with their presence on board the boat. His Royal Highness the Crown Prince responded with a speech in honour of mathematicians and mathematics. Professor Edgar B Schieldrop, on behalf of the mathematicians from Norway, paid tribute to the foreign delegates. Professor Émile Borel, Paris, replied on behalf of the hosts. With the help of loudspeakers all the speeches were transmitted to all the dining rooms.

Friday, 17 July.

9.15-10.00: Lecture: G D Birkhoff, On the Foundations of Quantum Mechanics.

10.15-11.00: Lecture: L J Mordell, Minkowski's Theorems and Hypotheses on Linear Forms.

11.15-12.00: Lecture: L V Ahlfors, Geometrie der Riemannschen Flächen.

11.15-12.00: Lecture: J G van der Corput, Diophantische Approximationen.

15.00-18.00: Sections Lectures.

Saturday, 18 July.

9.15-10.00: Lecture: S Banach, Die Theorie der Operationen und ihre Bedeutung für die Analysis.

10.15-11.00: Lecture: M Fréchet, Mélanges mathématiques.

10.15-11.00: Lecture: N Wiener, Gap Theorems.

11.15-12.00: Lecture: O Ore, The Decomposition Theorems of Algebra.

14.00-17.00: Section Lectures.

17.15: Closing session of the Congress.

3.       Section Lectures.

The following sections were formed:

I. Algebra and number theory. - II. Analysis. - III. Geometry and topology. - IV. Calculation of probabilities, mathematical statistics, insurance mathematics and econometrics. - V. Mathematical physics, astronomy and geophysics. - VI. Rational and applied mechanics. - VII. Logic, philosophy and history. - VIII. Pedagogy.

Various arrangements made for the ladies were made according to the following programme:

Tuesday, 14 July, 10.00-14.00: Visit by coach to the Museum of Peasant Civilisation in Bygdoy as well as to the Viking ships. Lunch at the restaurant "Dronningen".

Wednesday, 15 July, 10.00-12.00: Visit to the National Museum of Painting and Sculpture. 18.00-22.00: Excursion to Frognerseteren. Dinner at 19.00.

Friday, 17 July, 14.30-18.00: Excursion by coach to "Skaret". Tea at Mrs C O Lovenskiold's.

Saturday, 18 July, 10.00-12.00: Sightseeing by coach around Oslo and its suburbs.

During the excursion on 17 July, a contribution of gratitude among foreign ladies produced a sum which would benefit a student at the University following the decision of the university authorities.

4.       Opening Session Protocol.

The Opening Session was held in the University Aula, on Tuesday, 14 July at 9.00.

Professor Carl Stormer, president of the Organising Committee, opened the Congress with the following speech:
Your Majesty, Ladies and Gentlemen.

I have the honour, on behalf of the Organising Committee, to welcome you all to this conference.

It is a great joy for Norwegian mathematicians to see that so many of our colleagues have responded to our call to come to Oslo to take part in the work of the Congress, renew old friendships and create new ones despite the obstacles of different countries, nations and races.

About 500 mathematicians came here from almost every country in the world.

We hope that the fatigue of the journey that so many of the members of this Congress had to undergo in order to take part in it, will be offset by the results which will emerge for them from the rich scientific program of this Congress.

And we will do our utmost to ensure that both active members of the Congress and those of their family who have accompanied them keep a pleasant memory of their stay in Oslo.

Perhaps more than in any other field of culture the results acquired by the sciences are international. The scientific discoveries made by the scientists of one country can be immediately used all over the world. This particularly applies to mathematics. Mathematical truths are indeed universal and its means of expression international. As a result, collaboration across borders should be more natural for mathematicians than for all other scholars. We also see that our congresses have always had a success which clearly shows the desire for international collaboration of mathematicians.

Obviously a mathematician who makes a discovery can share it with the whole world by publishing it, but by making it known orally in a congress he has more favourable means of reaching a specially interested public. This is evidenced by the very large number of lectures that will take place at this congress.

And yet it may be that the most important work of a congress like this is not that which results from these lectures, but from the friendly conversations between mathematicians from different parts of the world. The direct exchange of ideas in the form of a conversation has an importance which, although we cannot yet find a trace of it in the proceedings of the congress, will nevertheless be manifested in the mathematical literature of the years which follow.

It is especially for young mathematicians that such meetings are important, thanks to the orientation it gives them and to the stimulus they acquire when hearing encouraging words from old and famous colleagues.

We all know that in our time we specialise in everything and we know very well the danger which results from it, but it is precisely there that the Congress will have a great importance, by making known the manner of formulating and solving the problems in other branches of mathematics. In this way, the Congress will help give members of the Congress a broader view of the place of their work in the whole of the mathematical sciences.

And rightly in our time it is of particular importance to be able to bring together so many eminent scholars from around the world. There has hardly ever been in history such a need for free intellectual exchange between different peoples, at the same time that the danger of vast and threatening political and social problems stands as an obstacle to this international collaboration. What is of the utmost importance is that it is precisely in this area of mathematics that all, regardless of race or nationality, have only one goal: to expand our knowledge and reach the most absolute truths.

We so often hear people asking what is the use of this or that scientific discovery. But it is not considerations of utility which lead mathematicians to deal with its problems. Mathematics is a field apart, so full of wonderful surprises for those who enter it, that these considerations of utility become secondary compared to the joy of discovery that one feels in solving problems, and to see the light of truth shine on areas of wonderful beauty. And, like the Norwegian poet Bjornstjerne Bjornson wrote in 1902 on the occasion of the jubilee of Abel:
Impassible as time
the science of numbers is.
Its combinations are
in an eternal aurora
purer than snow;
subtler than air,
yet stronger than the world,
which without scales weigh,
and without beams, illuminate.
Let us always keep this noble enthusiasm for our science and keep the pure from any mixture of motives foreign to it.

It was at the last international congress of mathematicians in Zurich that the Norwegian mathematicians resolved to issue the plan that the next congress would meet in Oslo. It was our colleague, the late Alf Guldberg, who took the initiative, and who has since worked tirelessly to ensure the success of the Congress, and above all to establish it on a solid economic basis. We had hoped that Guldberg could open Congress as president. But, as all members of Congress know, his untimely death snatched him from his work.

No one better than us who had to finish his work, can know what a loss it was for the Congress to be forced to take over from our eminent friend, who knew so well how to make friends and knew the art of socialising with his fellow men.

By recalling here the name of Alf Guldberg, I also wish to mention that for our University old traditions are attached to this name of Guldberg. It was a hundred years ago that Alf Guldberg's uncle, Cato Maximilian Guldberg, was born, who for years occupied the place of professor in applied mathematics, and whose name, as we all know, is attached to the famous law of chemical mass action.

As chairman of the Organising Committee, I make it my duty and my pleasure to thank here all those who, by financial donations or in other ways, contributed to making this Congress possible.

First of all, I would like to thank Your Majesty for having brought this opening meeting to the fore by your presence here today.

I would then like to extend our thanks to the Norwegian government for its economic support, and to the municipality of Oslo for its hospitality; to the University which made its premises available to us, and to the Oslo Tram Company, which offered free transport for all members during the Congress, to banks which, by means of monetary donations, showed their interest in the Congress, and especially the Norwegian Life Insurance Companies, without the generosity of which it would have been almost impossible for us to hold this Congress.

With these words I would wish you, Dear Colleagues, welcome to this meeting here in Oslo, and in doing so I would express the hope that, both scientifically and personally, a happy outcome will arise from our association during these days.

Your Majesty, Ladies and Gentlemen, I have the honour to declare by this that the International Congress of Mathematicians in Oslo in nineteen hundred and thirty-six is open.

Halvdan Koht, Minister of Foreign Affairs, then spoke and said:
Your Majesty, Ladies and Gentlemen,

In the name of the Norwegian Government I have the honour and great pleasure to wish you all heartily welcome to the capital of Norway and to our national University.

We Norwegians are perhaps excessively proud of having produced in our country some of the great mathematical geniuses of the world. But when, as an historian, I have tried to define the qualities that might have made the Norwegian nation in some particular way useful to the rest of humanity, I have found them in mathematics and music.

You know, even better than I do, that since the days of Pythagoras these two arts have been closely connected, and I remember very well what a vivid impression I gained in this respect when, thirty four years ago, another assembly of eminent mathematicians had gathered here in Oslo and in this University in order to celebrate the centenary of our great Abel. On that occasion a great English mathematician gave an eloquent address in honour of his science, and although I did not understand much of what he actually said, his speech, to my ears, sounded like angelic music coming from heaven. I think it was not so much because of the English language, but rather because he spoke on a celestial subject.

You certainly have had the experience that, when politicians and other practical people talk about the merits of mathematical work, they point to the great services that these studies render to many technical inventions which, in fact, would have been unthinkable without mathematics. Indeed, I shall not blame you for having been of practical and even economic utility to the rest of mankind. But I prefer to lay stress upon another aspect of your studies. Though not, myself, belonging to the initiates, I venture to praise your science as leading in the expansion of the human mind.

Is it not one of the greatest and most alluring aims of all human effort to make ourselves spiritual masters of the whole world, to compress in the small brain of man all the laws and forces of life and matter? And is it not true that the visions and logics of mathematical thinking are opening up even larger vistas of ever new realms of perception and comprehension? Are you not instinctively enjoying the strength of your mental powers when you discover and conquer new fields of life for human thought?

I congratulate you upon your work, and I want to assure you that in the Norwegian people you will find strong sympathy for your ideals.

Some decenniums ago it happened that there was in this country a member of parliament - a simple farmer - with no more education than the poor elementary school of his day could give, but yet intimately devoted to mathematical studies. When his colleagues of the opposite party did not want him to speak on a question, they induced a university professor of mathematics, who was also a member of parliament, to put some mathematical problem or other before him. This farmer member thereupon became so absorbed in solving the problem that he actually forgot everything going on around him - even his dearest political issues !

I would not affirm that all members of parliament in this country are similarly equally interested in mathematics, but this simple farmer may give you a glimpse of the spiritual yearnings of our people, and he affords me the right to wish you welcome here in the name of the whole Norwegian nation. I trust that you may find here a true home for your studies and your discussions.

Professor R Fueter, President of the 1932 Zurich Congress, proposed Carl Stormer be elected President of the Congress, a proposal which the assembly approved by acclamation. Carl Stormer thanked the audience for the honour shown to him and took the chair.

According to the proposal of the President, the following Vice-Presidents were elected H Bohr, T Carleman, M Fujiwara, G Julia, S Lefschetz, E Lindelöf, K Menger, G Pólya, E Schmidt, J A Schouten, W Sierpinski, and E T Whittaker.

As secretary general we elect - according to the proposal of the President - Professor Edgar B Schieldrop.

That done, Professor É Cartan took the floor and said:
In its closing session of 12 September 1932, the International Congress of Mathematicians of Zurich decided to accept the legacy of the late Professor Fields allowing two young mathematicians who would have distinguished themselves by particularly remarkable works to be awarded two gold medals at each international congress. At the same time he had appointed a commission to designate the two laureates for the Oslo Congress, and composed of George D Birkhoff, Constantin Carathéodory, Élie Cartan, Francesco Severi, and Teiji Takagi. This commission was chaired by Francesco Severi; but the latter, prevented from coming to the Oslo Congress, asked me to replace him in the presidency. The committee has agreed to designate as the first two holders of the Fields medals, Lars Ahlfors from the University of Helsinki, and Jesse Douglas from the Massachusetts Institute of Technology, Cambridge. Constantin Carathéodory was kind enough to take on reporting on the work of the two laureates; he will read you his report.

Professor C Carathéodory read his report, published in full among the general lectures of the Congress.

After Constantin Carathéodory had read his report, Élie Cartan thanked the President of the Oslo Congress, Carl Stormer, for having kindly let him have the honour of presenting the first two Fields medals to the two winners. He regretted that Jesse Douglas was tired and could not come to receive himself the medal intended for him. He presented two medals to Lars Ahlfors and to Norbert Wiener replacing Jesse Douglas.

The President requested the Congress to authorise him to send a congratulatory telegram to His Excellency Crown Prince Olav, Honorary President of the Congress, a proposal approved by the Congress with enthusiasm. The Secretary General announced that Aleksandr Gelfond and Aleksandr Khinchin, registered on the Congress programme as speakers, regretted having to apologise for their absence.

Expressing the hope that the following days - with the benefit of a rich and fruitful scientific collaboration - would give the opportunity to strengthen and multiply the purely human relationships which bind all mathematicians around the world, the President declared the opening session closed.

5.       Closing Session Protocol.

The Closing Session was held in the University Aula on Saturday, 18 July at 17.00.

At the request of the President of the Congress, the Secretary General, Edgar B Schieldrop, took the chair during the first part of the meeting.

5.1. Telegrams.

The Secretary General read telegrams from Her Majesty the Queen and His Royal Highness the Crown Princess, to whom the Congress had sent flowers. Congress authorised by acclamation that the organisers of the Congress should send letters of thanks to His Majesty the King and Her Majesty the Queen as well as to His Royal Highness the Crown Prince and Her Royal Highness the Crown Princess for the great kindness they had shown in the regard to the Congress.

The secretary then read a telegram from Professor Friedrich Engel from Giessen, in thanks for the congratulatory telegram sent by the plenary session on Wednesday, 15 July, when the Sophus Lie bust was unveiled.

The Congress warmly applauded the idea of sending telegrams to David Hilbert, Emile Picard and Vito Volterra.

5.2. The International Mathematical Union.

The Secretary General of the Congress gave the floor to Gaston Julia, who reported on the activity of the Commission entrusted by the Congress of Zurich to study the question of an international organisation of mathematicians.

An Executive Committee, chaired by Francesco Severi, was chosen from this commission in Zurich, and further comprising Gaston Julia, Hermann Weyl, Wilhelm Blaschke and Constantin Carathéodory.

The Committee, responsible for preparing the work of the Commission, met in Rome in March 1934, then in Paris in February 1935. The work of the Committee, including the minutes, transmitted to all the members of the Commission, requested the opinions of all these members, have shown increasing difficulties in the establishment of an international organisation of mathematicians. Following its second meeting, the committee adjourned until the eve of the Oslo Congress, in the hope that a plenary meeting of the competent committee, scheduled by the Zurich Congress, would help to find a solution. The Commission met twice in Oslo, on July 13 and 15. In the absence of Francesco Severi, the chairmanship was assumed by Gaston Julia, to whom Francesco Severi had transferred his powers.

During an in-depth discussion, it appeared that the circumstances were even less favourable than in February 1935 for the organisation of an International Mathematical Union, no formula having been able to achieve the agreement within the Commission.

The Commission therefore thought that it was appropriate to expose this failure outright at the closing session of Congress. It instructed Gaston Julia and Constantin Carathéodory to write a text, unanimously approved, intended to be read at this closing session. It also decided to give the minutes of the Executive Committee and Commission meetings to a representative of each nation present at the Congress.

Gaston Julia read the text adopted by the Commission:
The Commission appointed by the Congress of Zurich deeply regretted the absence of its president, Francesco Severi. It could not, for various reasons, reach a unanimous agreement on the question of an International Mathematical Union. It hoped that in the future the question posed could receive a solution.
With the deposit of this text at the Congress office, the Commission appointed by the Zurich Congress considers its mission to be completed.

Then speaking on his own behalf, Gaston Julia expressed his persistent hope that an international organisation of mathematicians would be established in the future, which he considered very useful to Mathematics and Mathematicians.

The resolution was adopted unanimously.

5.3. International Commission for Mathematical Education.

The floor was given to Henri Fehr, who said:

On behalf of Section VIII of the Congress, I have the honour to submit for your approval a resolution to renew the mandate of the International Commission for Mathematical Education for a further period of four years.

The Commission was established in Rome in 1908, following a resolution of the Fourth International Congress of Mathematicians; it was confirmed in 1912 in Cambridge, in 1928 in Bologna and in 1932 in Zurich. Chaired successively by Felix Klein, D E Smith and J Hadamard, it has published numerous studies of great interest on the teaching of mathematics in the main countries. At a time when international cooperation still faces obstacles in other fields, we are pleased to be able to point out here that the work of the Commission has been able to continue in an excellent spirit of understanding and collaboration.

On the agenda of the Oslo meeting was the presentation by national delegations of reports on current trends in mathematics education. After examining these reports, Section VIII unanimously decided to submit the following resolution to the Congress for approval:

The Congress requests the International Commission on the Teaching of Mathematics to continue its work, prosecuting such investigations as shall be determined by the Central Committee.

The resolution was adopted unanimously.

5.4. Topology conference.

Solomon Lefschetz gave the following communication:
At the Topology Conference which took place in Moscow in September 1935, there was constituted a committee to organise a Topology Conference in 1939. The members of the Committee present at Oslo [Freudenthal, Heegaard, Lefschetz, Sierpinski, also Nielsen by invitation] met and considered a very cordial invitation extended by Professor Sierpinski in his own name, that of his colleagues and his government, to meet in Warsaw in 1939. This was unanimously accepted with thanks and it was agreed that the Conference would meet in Warsaw at that time if circumstances made it at all possible.

5.5. Fields Medal.

According to a proposal made by the Executive Committee of the Congress in collaboration with Henri Cartan, Constantin Carathéodory and George D Birkhoff, members of the previous commission, the new Fields Medal Commission had the following members: G H Hardy, president, and Pavel Alexandroff, Erich Hecke, Gaston Julia, Tullio Levi-Civita; substitutes Solomon Lefschetz and Rolf Nevanlinna.

Unfortunately G H Hardy, in a letter of 7 August 1936, informed the Secretary General that he could not accept this task, while the others promised their assistance. Solomon Lefschetz will therefore take the place of G H Hardy.

The commission must nominate two candidates for the award of the Fields Medal at the Congress.

5.6. Place of the next Congress.

Carl Stormer took the chair and gave the floor to Luther Pfahler Eisenhart who, speaking on behalf of the American Mathematical Society, invited Congress to come to the United States in 1940, the choice of city being left to the choice of the American Mathematical Society:

The American Mathematical Society hereby extends to the International Congress of Mathematicians now in session in Oslo an invitation to hold the next congress in the United States of America, the place of meeting to be determined later by the Society. This invitation is presented by the official delegates of the Society in accordance with action taken by the Council of the Society, viz. :

G D Birkhoff, H F Blichfeldt, S Lefschetz, M Morse, V Snyder, O Veblen, N Wiener, L P Eisenhart, chairman.

This invitation was accepted by acclamation, and the President warmly thanked The American Mathematical Society and the American mathematicians for their kind initiative.

Then Jan A Schouten spoke:
On behalf of all foreign guests, he expressed the feelings that prevailed in everyone at the last moments of the congress, the sadness at the hour of departure, the joy of working together so intensely, especially in this period of our time, because once again it was demonstrated what was well organised international cooperation is able to achieve, finally the gratitude of all congress participants for the hospitality shown to them in such abundance.

First and foremost, he thanked the State of Norway for its generous hospitality, mentioning in particular the great honour and joy that all members of the Congress had received from the lively interest shown by the Norwegian Princely House in the Congress.

He then thanked the City of Oslo Authority for everything it had done to promote the Congress.

He expressed special thanks to the gentlemen of the Executive Committee for the exemplary organisation of the Congress, as well as to the ladies of the Women's Committee, who knew how to ensure in such an excellent way that the stay in Oslo will also be unforgettable for the ladies.

In conclusion, he pointed out that science is only truly science if it is international and asked his Norwegian colleagues to accept the assurance that everyone who has been here and who will now go their own ways will never forget what the small country of Norway achieved by organising this international conference of mathematicians for the promotion of international science.

The President thanked Jan Schouten and declared the Congress closed as follows:
On behalf of the Organising Committee and all the Norwegian mathematicians, I have the difficult and pleasant task of trying to express how we were moved by the praise of our dear colleague on the success of our Congress.

But this success, dear colleagues, is only a small part, due to us. It was the collaboration of all the delegates who ensured the lecture programme was of the highest value.

Our joint work is finished. The large number of lectures that have been given is a clear witness to the mathematical discoveries that have been made in recent years by mathematicians from all countries.

Mathematical sciences are increasingly becoming one of the most fundamental bases of human civilisation, and gives us the feeling that our work is not useless.

Ladies and Gentlemen, I wish you successful years of good work until we all meet at the next congress. With these words I declare that the International Congress of Mathematicians in Oslo is closed.

6.       Speeches.

Dinner was offered by the City of Oslo at the "Bristol" hotel, at 20.00 on Wednesday, 15 July. Four speeches were delivered on this occasion (6.1, 6.2, 6.3 and 6.4 below). An excursion on the Fiord of Oslo on the "Stavangerfjord" took place on Thursday, 16 July when the fifth speech (6.5 below) was delivered.

6.1. Congratulatory speech by S Gann, Director of Squares and Markets representative of the Municipality of Oslo.
Ladies and gentlemen.

On behalf of the City of Oslo, I have the great honour to welcome everyone to the Norwegian capital, welcome to Norway.

When a layperson like me is faced with such eminent scholars, it is probably easy to express the conventional wishes that are addressed on such an occasion, but it is more difficult for this layman to pay tribute to the science that you represent here, ladies and gentlemen.

For us dilettantes, mathematics is like a crystallisation of what is pure, of what is clear in the human brain; we quite easily believe that mathematics in itself constitutes the translation into a technique of thought, but I do not think I am wrong in saying that the greatest progress that has been made in mathematics, is the result of an imaginative impulse, of the incomprehensible genius of intuition, of these living, intensive thoughts which are in the realm of inspiration.

My personal impression based on my experience of life leads me to believe that all our thoughts bear the imprint of our mind and our feelings. It is in a physiological nervous vibration that we find the source of all our thoughts, from the simplest to the most brilliant. It is precisely because the most superior mathematics that exists, is born from inspiration, imagination, intuition that are ultimately anchored in the domain of feelings, and that is why also, it is not only scientists and laymen who meet at this table, above all they are human beings. The language of science is international and so is the language of feelings; science and feeling destroy all prejudices, break down all the borders of languages and races and oblige us to recognise what is most noble in life, greatness in feeling, genius in thought.

When in the name of the City of Oslo I ask the Congress to accept my tributes and express my best wishes for the progress of the science which animates it and to which humanity owes so much, it is with hope that free science and free thought have the understanding of city and that both spread their benefits everywhere and for all.

6.2. Speech by E Schmidt, Professor at the University of Berlin.
Ladies and gentlemen!

On behalf of the German-speaking participants of the Congress, I have the honour to thank the organising committee of the Congress, headed by our honoured President Professor Stormer, and the city of Oslo, who welcomed us so kindly and whose hospitality allows us tonight to speak out for the scientifically and humanly rich days that we can spend here and whose rich impressions we will take home as a permanent profit.

Norway with its gorges and bays, its rocks and legends, with its great poets, with whom the power of imagination seems to rival the force of native nature, is a country of longing for every German. We German mathematicians, however, still feel a special bond in the awareness that two of the greats of our science, Sophus Lie, whose bust was unveiled today, and Niels Henrik Abel were Norwegians who were linked in close relationship with German intellectual life. Lie worked for many years at the University of Leipzig, and Abel was in promising negotiations about accepting a call to the Berlin University when suffered an untimely death.

When I left Berlin, everything resounded and echoed there from the joyful preparations for the Olympic Festival. Everything was being prepared to receive the converging people with dignity and to celebrate the spectacle of their peaceful competition.

Well - is that which brings us together here not also an Olympic in spirit! a friendly competition of all people in the field of science, and in particular mathematics, which is many thousands of years old, but for their self-confidence as pure science, i.e. as knowledge for the sake of knowledge, only awoke in the classical country of Olympia, in Greece.

Here everyone is happy about each other's progress. Because in the light and pure atmosphere of the spirit it is easier for man to understand that the wealth and the ascent of one people is not a disadvantage, but only a great happiness for all other people.

What particularly enchants us about the Nordic summer that surrounds us here is the bright, clear, sharply contrasting colours and the long days when evening glow and dawn shake hands.

What we all do our life work for is also a day - a day of the spirit. May it be so bright and clear, so long, so victorious in overcoming the shadows of the night, as we all experience here in Oslo in nature and in the light-seeking sense of the population, with a grateful and happy heart.

The hospitality that we share here can best be characterised in all respects, from the spiritual to the material, by an old German saying:
Never lack the feeling -
And never feel the lack!
With this motto I say thankfully:
To our great hostess the city of Oslo - cheers!

6.3. Speech by L P Eisenhart, Professor at Princeton University.
Chairman, Ladies and Gentlemen:

An unusual honour has been conferred upon me in requesting me to say a few words at this dinner for the English speaking countries represented at this Congress. These countries have made great contributions to mathematics, but after all we do not think of mathematics as developed along national lines. When one observes that at this Congress there are representatives of at least thirty nations, and all of them are interested in the history and development of the same science, one realises that mathematics is international. As such, it does not recognise national boundaries; these have to do with political and economic considerations. Perhaps it is because maps deal with national contours and mathematicians are international in their way of thinking that mathematicians have never been able to solve the four-colour map problem.

The layman thinks that mathematics deals with facts and that thus there can possibly be no differences of opinion among mathematicians. We know that this is not the case. However, there are several fundamental propositions to which I think all those present will agree. The first of these is that, because of the very fine contributions which Norwegians have made to mathematics, it is very appropriate that a Mathematical Congress should be held at Oslo. Another proposition is that we have been most cordially and graciously entertained during our sojourn in Oslo. We appreciate greatly all the opportunities for the meetings and for informal intercourse which have been provided by the University of Oslo and the entertainments which the members of its staff have arranged for us. This applies equally well to those members of our families who have accompanied us to the Congress and who do not even pretend to understand the lectures. We appreciate the cordial reception extended to us by the King and Queen, and the generous contributions which have been made toward the success of this meeting by the representatives of business in this community. Throughout our stay here we have been conscious of the courtesies which have been extended to us by the Municipality of Oslo, which tonight acts as our host at this dinner. I have the honor to propose a toast to the Municipality of Oslo.

6.4. Speech by G Julia, Professor at the Sorbonne.
Ladies and gentlemen.

The Congress Organising Committee wanted a French voice to be heard at this evening's meeting. Whoever is speaking to you right now is very moved that he has been asked to make this voice heard.

He hopes that his heart in the circumstances, will suggest words to him so that he might express the feelings of all his compatriots. The beautiful country that welcomes us today with open arms is firstly, for a Frenchman, a country of snow and mountains, a country of sailors, the country of the Vikings, Nansen and Amundsen, where these legendary tales of heroic exploits took shape, which moves the child and the man, which also excites him. He is aware, this Frenchman, that he is the cousin of the Nordic, and that his beautiful Normandy was once the land where the Normans, the men from here, approached.

Browsing through your literature, the French also learns what virtues your poets exalt. These are virtues which he strives for, and which our own poets have exalted. Our Lugné Poe let him know and appreciate Bjornson and Ibsen. Let me tell you in particular what flame of enthusiasm the magnificent "Brand" of Ibsen kindled in the soul of a young man I knew well. Let me also tell you that his "Agnes" has generous and painful sisters in the theatre of our Racine.

If the Frenchman I speak of is a mathematician, the relationship becomes even closer. He knows that your Abel and our Galois are two brilliant and painful brothers, whose history, very simple, sad and as little known as it is, is well worth a legend. He knows, and we reminded him this morning, that your Sophus Lie, heir and successor of these two illustrious adolescents, wanted to unite them in a common expression of admiration, by dedicating to them his work on Transformation Groups at the École Normale Supérieure in Paris.

There are in this room a number of French mathematicians from this École Normale; I am sure they are happy to hear me express the admiration we feel for your two mathematical glories: for Abel and for Sophus Lie.

He finally knows, this Frenchman we are talking about, that this country is a homeland of art, and, to speak only of music, there is no one among us who does not dream or is not lifted up by the works of your Grieg.

To this evocation of the links which tie all French people to this beautiful country of energetic and voluntary men, beautiful and tenderly human women, illustrious scholars, poets and generous artists, allow me, adding a personal memory, express to you the emotion that I feel this evening to evoke the special gratitude that I owe to Norway.

Twenty years ago, an injured young officer who had just been operated on was brought back to his room one evening. He was already falling asleep when the blood, flowing in his mouth, woke him up: an artery had just reopened. He had time to warn before he lost consciousness.

When he regained consciousness, he recognised the reassuring figure of the nurse-in-service close to him. In the absence of the surgeon, who had left the hospital, and the doctor on duty elsewhere, with time pressing, she had, without hesitation, with a safe hand, buffered and stopped the bleeding, and finally revived this failing body. When the doctor came running, he recognised that everything had been done well - he praised her decision and her skill.

Fearing that the accident would happen again, and with a gesture as spontaneous as charitable, this generous girl decided that she would spend the whole night of the ordeal at the bedside of the wounded. For me, I will never forget this long night, where, unable to speak except with the greatest difficulty, broken by the haemorrhage, and unable to sleep, I felt reassured by the presence of this woman sitting near me, sewing noiselessly in the discreet circle of light from the lamp, listening at regular intervals to my breathing, taking my pulse and scrutinising my eyes which, with a glance, expressed my ardent gratitude.

Ladies and Gentlemen - this generous woman, this strong woman, was a girl from Norway. You will easily understand that I feel bound to this country by a debt of special gratitude.

Having accepted speaking in this chamber on behalf of my compatriots, I am doubly happy to be able here to pay tribute to the valour, the legendary energy of the men of Norway, the wisdom, the dedication of its women, the beauty of the whole country, and the warm welcome of the city of Oslo.

6.5. Speech in honour of foreign mathematicians by Edgar B Schieldrop, Secretary General of the Congress.
Your Royal Highnesses!

My dear colleagues!

A few days ago Carl Stormer expressed the feeling of joy and gratitude felt by the mathematicians of Norway to see you gathered in Oslo, to know you here for a whole week. Mr President, at that time, was the perfect interpreter of our feelings for all of us. Now, in a welcome speech, we are forced - you know this well - to form a priori judgments, to express hopes, to hazard expectations.

A speech of this kind may be inspired by sincere feelings, kind and flattering expressions for the audience - it must rather be filled with it - it is nonetheless true that the speaker must remain in the vague domain, since he has no experience yet, no final results on which he could base himself. Before him there is a future which, although close, has not yet revealed its secret. I, on the other hand, have the advantage, when addressing you today, of being on safer ground.

Three days have passed, and already belong to the past. We Norwegian mathematicians already know that these three days will be, thanks to you, something that we will talk about and talk about for years.

If we consider the domain of the civilised world, Norway is what we used to call "a point on the contour". And you know from professional experience how careful you have to be when approaching such a point. By the way, we admit it frankly, we showed little modesty, little sense of proportion by summoning you here. We are few in number and we live in a peripheral country. However, it is precisely by emphasising these two fatal truths that we hope, my dear colleagues, to deserve your indulgence and your forgiveness.

We need you so much! We need to speak to you, to have direct, personal relationships with you, to benefit from the immense amount of knowledge that you represent in your totality, finally to feel close to us, if only for a few days. It was the desire to establish relationships of this kind, to experience the charm of your presence, which gave us the idea of meeting you here, in the limited space of this boat, where the mathematical density must reach an extraordinary value, difficult to calculate numerically, but certainly a maximum in maritime history.

My dear colleagues. You see before you Norwegian colleagues, full of gratitude. We are grateful because you have come so that the pure claret of your knowledge can water our mathematical furrows, and we are proud since such an illustrious assembly has been able to meet on our soil, demonstrating the common efforts of all people, demonstrating this intellectual cooperation of which our troubled and worried world, our threatened civilisation, needs so much these days, an assembly whose work has a single goal, that of advancing human thought and serving humanity as a whole.