# 1904 ICM - Heidelberg

## 1904 International Congress of Mathematicians - Heidelberg, Germany

The International Congress of Mathematicians was held in Heidelberg, Germany from 8 August to 13 August 1904.There were 336 full members of the Congress and 60 associate members. We give below a version of: Before presenting the material, we give a short Preface.

Preface by EFR and JJOC.

The 1904 Congress was held in Heidelberg and the German Mathematical Society decided to link the Congress to the celebration of the centenary of the birth of Carl Jacobi. Leo Königsberger was asked to give the first lecture on Jacobi's biography and this was printed and given as a gift to all the participants at the Congress. We give an English version of this biography at THIS LINK.

Königsberger also wrote a scientific biography of Jacobi which was available for the participants to purchase at ${{1}\over{3}}$ of the full price. Another interesting feature of the Congress was a lecture by Julius König in which he 'proved' that Cantor's Continuum Hypothesis was false. Cantor himself attended this lecture and said at the end how grateful he was to have lived to see this answered, even if it did show his conjecture was false. The 'proof' was, however, wrong and some time later Ernst Zermelo found the error in it.

1.       History of the Congress.

At the Second International Congress of Mathematicians in Paris in 1900, the German Mathematical Society took on the task of convening the next Congress in 1904. Already at the business meeting of the German Mathematical Society in Hamburg in the autumn of 1901, Heinrich Weber (Strasbourg) was elected the chairman of the Third International Congress of Mathematicians and in a preliminary meeting in Leipzig on 27 March 1902 a first basis for the organisation of the Congress was put in place. At that time there was already a clear mood for Heidelberg, and once the city council of Heidelberg had agreed to welcome the Congress hospitably, it was finally decided in the business meeting on 25 September 1902 in Karlsbad to invite the Congress to Heidelberg in early August 1904. The rapporteur was elected secretary of the Congress and a committee for the preparation of the III International Congress of Mathematicians, which, after some subsequent co-opting, consisted of the following members:

A Ackermann (Teubner, publishing bookseller in Leipzig). A von Brill (professor at the University of Tübingen). M Cantor (professor at Heidelberg University). M Disteli (professor at the University of Strasbourg). W von Dyck (professor at the Technical University of Munich). A Gutzmer (professor at the University of Jena). G Hauck (professor at the Technical University of Berlin). D Hilbert (professor at the University of Göttingen). F Klein (professor at the University of Göttingen). A Kneser (professor at the Bergakademie Berlin). L Königsberger (Professor at Heidelberg University). A Krazer (professor at the Technical University of Karlsruhe). J Lüroth (professor at the University of Freiburg). R Mehmke (professor at the Technical University of Stuttgart). F Meyer (professor at the University of Königsberg). Max Noether (professor at the University of Erlangen). C Runge (professor at the Technical University of Hanover). Hermann Schubert (professor at the Johanneum Hamburg). F Schur (professor at the Technical University of Karlsruhe). H A Schwarz (professor at the University of Berlin). P Stäckel (professor at the University of Kiel). J P Treutlein (director of the Real- und Reform-Gymnasium Karlsruhe). Heinrich Weber (professor at the University of Strasbourg).

This committee met for the first time on 20 April 1903 in Heidelberg for a preliminary discussion. The decisions made at that time remained decisive for the later organisation of the Congress and may therefore be communicated here.

Since the hundredth anniversary of the birth of the great German mathematician C G J Jacobi falls in 1904, the idea of a Jacobi celebration was considered, and after Leo Königsberger (Heidelberg) agreed to accept delivering a talk and presenting Jacobi's comprehensive scientific biography to the Congress, it was decided to combine a Jacobi celebration with the Congress, which culminated in a memorial speech for Jacobi to be given in the first general meeting by Königsberger.

With regard to the scientific lectures, it was decided that four major lectures should take place in two further general meetings, in such a way that one lecture was given in each of German, English, French and Italian. The chairperson was responsible for inviting the speakers.

All other lectures should take place in section meetings, for which two days were allocated. Six sections were formed and from among the members of the committee were selected those introducing them, who would arrange section lectures and to lead the composition of the sections at the Congress.
Section I: Arithmetic and Algebra.

Introducers: Adolf Kneser (Berlin) and Jacob Lüroth (Freiburg).

Section II: Analysis.

Introducers: David Hilbert (Göttingen) and Hans Amandus Schwarz (Berlin).

III. Section: Geometry.

Introductory: Alexander von Brill (Tübingen), Wilhelm Meyer (Königsberg) and Friedrich Schur (Karlsruhe).

IV Section: Applied Mathematics.

Introducers: Hauch (Berlin), Felix Klein (Göttingen) and Carl Runge (Hannover).

V. Section: History of Mathematics.

Introducers: Moritz Cantor (Heidelberg) and Paul Stäckel (Kiel).

VI. Section: Pedagogy.

Introducers: Hermann Schubert (Hamburg) and Peter Treutlein (Karlsruhe).

After the wish had already been expressed in Karlsbad to combine an exhibition with the Congress, it was now decided that an exhibition of mathematical models and apparatus as well as of mathematical literature would be held at the Congress, but that both exhibitions would focus on the more important phenomena of the past ten years, and only the former may include older, historically interesting original models. Introductory and explanatory lectures and demonstrations should be combined with the exhibitions. For the model exhibition, a commission consisting of Martin Disteli (Strasbourg), Walther von Dyck (Munich) and Rudolf Mehmke (Stuttgart) was elected; August Gutzmer (Jena) and the rapporteur were assigned to the literature exhibition.

According to the decisions made at the time, the secretary must publish a report on the negotiations concerning the Congress. This report was intended to describe the history of the Congress and its course, but especially all the lectures given at the Congress in the language in which they were given; it should be published as soon as possible and sent to all members of the Congress free of charge. Königsberger's memorial speech will be printed in a special format and will be handed over to all participants before the end of the Congress.

With regard to the festivities taking place at the Congress, the city of Heidelberg offered from the outset to arrange castle lighting at the city's expense and to provide the participants with boat trips for viewing the lighting. Furthermore, His Royal Highness had informed the Grand Duke of Baden that he was ready to offer a reception for the congress participants in the castle garden at Schwetzingen. The Congress itself envisaged a banquet, which every member should be entitled to attend. Finally the German Mathematical Society had considered organising evening entertainment.

At that time the government of Baden had already announced a grant of 3000 marks to secure the Congress financially, and the company B G Teubner had also made a contribution of 2000 marks to the Congress for any use.

It was decided to raise a contribution of 20 marks from each participant at the Congress upon delivery of a main card; the right to become a participant should not be subject to any special conditions. Such a main card entitles the holder to attend all meetings and social events of the Congress, to visit the exhibition, to receive the commemorative publication and the programme of the Congress, and also entitles the holder to Königsberger's biography of Jacobi published by B G Teubner at a significantly reduced price (at about ${{1}\over{3}}$ of the retail price). Each Congress participant also has access cards for the price of 10 marks for their relatives to participate in the general meetings and all social events of the Congress.

To cover the additional costs of the Congress, a committee was set up, to cover in particular the printing of the commemorative publication and the programme as well as the exhibition associated with the Congress, and to request a grant of a total of 10,000 marks from the Reich Government and the Prussian Ministry of Culture, emphasising the moment of national representation on the one hand and the Jacobi celebration on the other.

The committee members, Moritz Cantor and Leo Königsberger, met with the city councillors Ellmer, Fuchs, Krall and Krieger in Heidelberg for a local committee, and a women's committee for the reception and entertainment of the women was also considered.

The following months were devoted to preparing for the Congress based on these decisions.

In June 1903, the first invitation to participate in the Congress was sent to 2000 mathematicians from all countries. The principle was followed that these personal invitations should be sent to members of the major mathematical societies whose members should be first to be invited: the German Mathematical Society, the Société mathématique de France, the London Mathematical Society, the Dutch Mathematical Society of Amsterdam, the Mathematical Circle of Palermo, the Moscow Mathematical Society, the Kazan Mathematical Society, and the American Mathematical Society. For other countries like Hungary, Sweden, Norway, Spain, Portugal etc. lists of addresses were given by mathematicians there. In addition to these personal invitations, more than 25,000 copies of the invitation were distributed in the most important mathematical journals. The B G Teubner company also published a short invitation circular in all of its mathematical journals free of charge. Finally, notes were sent to the Allgemeine Zeitung in Munich and the Kölnische Zeitung.

Postcards were included with the personal invitations for the purpose of a non-binding message as to whether the addressee would probably attend the Congress or not. By the end of September 1903, commitments had been received on 357 main and 134 secondary cards, which later increased to 380 and 140.

At the invitation of the chairmen, Wilhelm Wirtinger (Vienna), Alfred George Greenhill (London), Gaston Darboux (Paris) and Corrado Segre (Turin), agreed to deliver lectures to the general meetings; to our great regret, Darboux later had to withdraw his promise as a result of other commitments. Paul Painleve (Paris) was kind enough to take over the lecture in his place.

On 27 June 1903 the Prussian Minister of Medical, School and Intellectual Matters approved a grant of 10,000 marks to cover costs of teaching and medical matters of the Congress from the finances of the Reich and of Prussia, and the Federal Council decided 5000 marks from this would be used to increase the budget, and furthermore a grant of 5,000 marks was awarded from the Supreme Disposition Fund of His Majesty the Kaiser and King, in particular to enable the production of Königsberger's commemorative publication dedicated to Jacobi's memory.

On 5 February 1904, His Royal Highness the Grand Duke of Baden had informed the secretary of the Congress that he would like to consider an invitation to participate in the Third International Congress of Mathematicians. On 7 May he received the chairman and the secretary in an audience to personally accept the invitation to the Congress, but at the same time announced that, considering that the Congress fell at the time when his doctor advised him to stay in St Moritz, it was necessary for him to be represented by His Royal Highness the Great Archduke heir Friedrich von Baden. His Royal Highness the Hereditary Grand Duke not only promised his appearance in person on 18 June at the first general meeting and at the banquets, but also agreed that he would accept the honour of Honorary President of the Congress.

On 6 March 1904, a second meeting of the committee took place in Heidelberg, in which the programme of the Congress was discussed in detail and fixed.

In May 1904, the definitive invitation to the Congress was disseminated in the same way as the previous, preliminary one. The personal invitations were now accompanied by a postcard, by means of which the addressee could have their apartment in an inn or private house arranged through the apartment committee, which had now met. Special invitations were sent to the Chancellor, to the Prussian Ministry of Culture, to the Baden ministries of foreign affairs and teaching, to the University and to the Faculty of Natural Sciences and Mathematics in Heidelberg, to the University of Freiburg, to the Technical University of Karlsruhe, to the city of Heidelberg and specifically for the Jacobi celebration to the Academy of Sciences in Berlin, to the Universities of Berlin and Königsberg, and to a number of Jacobi's relatives.

2.       Social Programme of the Congress.

Monday 8 August.

After the Congress participants who had arrived by then had gathered in the Café Imperial in the afternoon at the request of the daily newspaper, the official part of the Congress began at 20:00 in the evening with the reception of the Congress participants in the town hall. The hall quickly filled with guests from all over the world. At 22.30 Moritz Cantor (Heidelberg) as chairman of the local committee greeted those present and warmly welcomed them to Heidelberg. No further speeches were made; the evening was only intended to give the Congress participants the opportunity to get to know each other, to make new acquaintances.

Tuesday 9 August.

At around 10.45 His Royal Highness, the Hereditary Grand Duke, who had just arrived in Heidelberg and had been received by the heads of the state and city authorities at the train station, drove with his companion to the Heidelberg Museum building, which was being used for university purposes, where he was received by the Chairman and the Secretary of the Congress and led up to the great hall in which the first general meeting was to take place. The Congress participants had already gathered there in full and made a lively ovation to the incoming Grand Duke. After the latter had introduced the members of the committee, Heinrich Weber (Strasbourg) opened the Congress with the following speech:
His Royal Highness the Hereditary Grand Duke Friedrich von Baden has gracefully accepted the Honorary President of the III International Congress of Mathematicians and has commissioned me to open the Congress. So I extend a warm welcome to all of you who have accepted our invitation.

For the third time, mathematicians from all countries have come together to work together, and the question arises: What brought us together? What have we achieved and what do we hope to achieve?

It is no different in mathematics than in all other areas of culture. It has been recognised that there is more to be gained by common work of like-minded people than when everyone goes their own way. It has been recognised that science also has the task of staying in touch with life, that the individual does not stand for himself, but that his work is due to the whole. Even if every significant advance in the scientific field is the act of a single enlightened mind, the great stream should not diverge into little rivulets.

That is why science needs, in addition to the ever more in-depth individual research, a summarising activity in which it becomes aware of its position and task in the whole organism of our cultural life. Such times of collection are also the times of the richest scientific life, where each activity stimulates and promotes the other. Such were the days of Newton and Leibniz. And so it was at the turn of the 18th and 19th centuries, when the great intellectual movement emanated from France, that alongside the richest scientific production, the classic textbooks that we still admire came into being. Only in the times ahead will we be able to judge whether we are in such a period again and what fruit of science grows from it. But we do our duty when everyone does their best, and when we work together in ungrudging cooperation.

Allow me to take a glimpse of the fate of our science over the years that have passed since our first Congress. Many of the people we looked up to as masters at that time are no longer among the living. For some of us, one or the other of them is more than a teacher, he was his friend and father. I am urged to dedicate a few words of grateful memory to them at this point.

We first lament our Karl Weierstrass, who left us in 1897, grieved by numerous students and friends. For a long time, he gave direction to research in functional theory. He constantly pointed out the points where the basics of mathematics did not seem secure enough, and worked with felicity and ingenuity on the fixing of these foundations. The influence of his powerful and amiable personality has left us with indelible marks which we knew he had left behind, and its effectiveness extends far beyond the borders of his fatherland. Nowadays, it is not only Germany but non-German countries that see Weierstrass further develop functional theory.

I next commemorate with sadness a man who is unforgettable to anyone who has been lucky enough to come into contact with him, Charles Hermite, who was called from earthly life in 1901. The short time I have does not allow me to touch his scientific magnitude even briefly. But I can commemorate the warm, humble man without falsehood, who had selfless recognition for every scientific endeavour, from whatever side, who generously communicated to each the richness of his spirit and encouraged every aspiring talent through stimulation and encouragement. The hours I spent here with him eighteen years ago are unforgettable, since he brought the congratulations of the Paris Academy of Sciences to Heidelberg University for its large anniversary celebrations.

England suffered a severe loss in 1897 when the 83 year old James Sylvester died. Even though he did not master and cultivate the entire broad field of mathematics as universally as his younger, greater compatriot and familiar colleague Arthur Cayley, who had preceded him two years earlier in death, his original ideas and unusual methods, his brilliant approach, who anticipated results of everlasting value and paved the way to them in algebra and number theory. The third in the league of the great 19th century English algebraists, George Salmon, the master in the application of algebra to geometry, has also recently passed away (in 1904).

I also commemorate the late Sophus Lie, who, spiritually related to his great compatriot Abel, opened new paths in modern group theory, who worked the best part of his life here in Germany, but who, already ill, then fell in love with the North and returned home to Norway, where he found an early grave (in 1899).

Francesco Brioschi, who was the focal point of our first Congress as a revered senior member, soon departed this life (in 1897). What modern algebra owes to him, how he further developed the new ideas emanating from Gauss, Abel, Galois and made them accessible to the public is fresh in the memory of contemporaries. However, his work as a statesman is also not forgotten in his homeland, the merits he has earned in the newly created Kingdom of Italy for lifting the level of teaching and in other areas of state administration.

And when we put the preparations for this our third Congress into practice, we had hoped to welcome Luigi Cremona here and maybe hear him speak, the co-founder of the newer geometry, the great mathematician and brave patriot, to whom today's Italy owes so much. A few months ago, death also put an end to this life full of action.

Let me also say a few words to the memory of Erwin Bruno Christoffel, who in 1900 suffered a lonely life under severe physical suffering. Anyone who knew the handsome and interesting man retains the image of an unusual and important personality. He left deep traces in science in everywhere he worked as a teacher, in Zurich, in Berlin and in Strasbourg. He has been one of the most outstanding members of the German University of Strasbourg from its foundation for more than 20 years until the complaints of old age forced him to give up teaching.

Finally - especially in Heidelberg - I can't ignore the memory of one man, Lazarus Fuchs, who died in 1902. He happily greeted the news that mathematicians should gather here on the ground that had become his second home. But he himself was no longer allowed to experience it. In his work on the theory of differential equations, he has set an imperishable monument.

The list of those who have been taken from scientific work in recent years is far from being exhausted. I cannot mention all of them and I ask that if I do not speak of the others, I do not consider it a sign of inferior appreciation.

I have to confess that when I began to recall the history of science in recent years at the forthcoming Congress, at first I had the impression that I was only standing at the graves of the past; death held such a rich harvest.

But I see a different picture when I look at the work and success of our science today. Fresh life is everywhere here. Nowhere is there a standstill. The thoughts and suggestions of the past period are pursued in all areas. New questions are asked, new research areas are opened up. Nobody can escape this impression of constant progress if they look back on a large piece of the history of science with their own memories.

Questions that were in the foreground of interest in our teenage years are receding, partly because they are considered to be definitely answered, partly because research has turned to new questions.

A time not long behind us mastered the formal side of mathematics, shaped its methods into a nicely rounded whole, which we are still enjoying, even if the current generation no longer places decisive weight on it.

The radical reorganisation of physics has had a great influence on the further development of our science, which has led to a powerful upturn in our day, partly due to the discovery of new facts, but partly also due to a changed view of the nature of force and matter. Securing the implications of these new ideas is a task of mathematics, which the old tools were not always up to.

It is probably more of a vision of the future if I point to a development in analysis, the approaches of which can be recognised here and there - especially among English researchers - which, without the mathematical definition of the terms, meets the needs of physics by using the blurred boundaries and gradual transitions inherent in our perception of the outside world. The requirements that modern technology places on our science work in the same sense.

The fact is that this sets in motion a lot of new thoughts that struggle for clarification, and further development gives our science a fresh, lively life.

On the other hand, the abstract branches of science, which - according to a drastic expression by Dirichlet - have not yet been stained with any application - are seriously studied, in which the purity of the mathematical idea is an end in itself. Indeed, it is by nature impossible that questions such as the squaring of the circle or the trisection of the angle ever acquire any practical meaning. Nevertheless, as far as historical tradition goes, such questions have kept scientific thinking busy and intense, and they have been of the greatest importance for the development of the mathematical mind.

Throughout the entire history of science there is a continuous connection, which in the 19th century was characterised by the brilliant names of Gauss, Lagrange and Abel. Our time has also solved some old problems in this area and opened the prospect of new ones. So the squaring of the circle is a thing of the past for us today, and algebra and number theory have come together to form a whole in which the harmony and regularity of the number system shines out more and more beautifully.

Hardly has there been a time when the philosophical part of our science, the question of the ultimate reason for our mathematical conviction, has taken on such a general interest as it does now. These age-old questions have been brought back into flux through the investigations of Gauss, Riemann, Helmholtz, and have been attacked in our day from a new angle. And if this shakes the naive belief in the unconditional nature of our science, it has been shown, on the other hand, that we have a goal to aim to continue to develop science, to search downward for the roots and ultimate reasons which we may approach, but we will never quite reach.

Pedagogical questions ultimately play a major role nowadays. The diverse life of our time has also given young people new tasks. The material has expanded and the question arises how to unite it to be able to teach young people the sum of the knowledge and skills necessary for life without sacrificing the harmonious training of the mind to full humanity. And at the level of university teaching, it is also a question of combining the gymnastics of the mind, which is gained through the strict discipline of mathematical thinking, with the demands of specialist courses without overloading students.

It will be the task of our Congress to give an account of the entire life of our science and of its current state. We have endeavoured to provide characteristic samples for each branch of our science in the sections and in the general assemblies, and we have found a willing courtesy for which I am already grateful.

But we still have a reverential task to do. Two years ago we celebrated the hundredth anniversary of Niels Henrik Abel's birth with heart-warming hospitality from his home country Norway. His rival and comrade-in-arms Jacobi was born two years later than Abel. So the year of our Congress marks the hundredth birthday of this great mathematician. The main celebration of his memory is today, the opening day of our Congress.

I hereby declare the Third International Congress of Mathematicians open.

Upon completion of this speech, His Royal Highness, the Hereditary Grand Duke, expressed warm greetings to Congress from him and his High Father, which Heinrich Weber replied to with a few words of thanks. Ministerial Director Freiherr von Marschall on behalf of the government of Baden, Vice-Rector Professor Braune on behalf of Heidelberg University and the two other universities in Baden, and Mayor Dr Wilckens on behalf of the city of Heidelberg. After the secretary had read out a welcoming telegram from the Prussian Minister of Culture and the chairman thanked him for the greetings that had taken place, Leo Königsberger (Heidelberg) took the floor to make his speech on the life of Carl Gustav Jacob Jacobi.
For a version of this speech, see THIS LINK.

After this speech, Hans Amandus Schwarz (Berlin) rose to deliver the following address:
I have been given the honour, on behalf of the Royal Prussian Academy of Sciences, as well as on behalf of the Rector and Senate of the Royal Friedrich Wilhelms University of Berlin, and also on behalf of the representative of the Royal Albertus University in Königsberg here in Prussia, to thank the German Mathematical Society for inviting them to take part in the Jacobi Celebration Associated with the Third International Congress of Mathematicians.

With undivided joyful approval, the above-mentioned bodies, to which Jacobi was closely associated during his brilliant effective academic career, have become aware of the decisions of the German Mathematical Society to organise a special ceremony in honour of Jacobi.

If, under ordinary circumstances, the three bodies, in whose name I have the honour to speak, would undoubtedly have had the next right to hold a celebration in honour of Jacobi, but at the point in time at which the decision was taken of holding the Third International Congress of Mathematicians on German soil in Heidelberg, the situation has become completely different. None of the three bodies mentioned would have been able to give the Jacobi celebration the incomparably beautiful setting that Heidelberg offers; because there is only one Heidelberg among all the lovely and most beautiful spots, which our German fatherland has!

It would certainly also have been difficult to find a man outside Heidelberg who was equally suited and inclined to research the life and scientific achievements of the great mathematician with the same loving devotion and to present them with the art and perfection that the previous speaker has done.

I will fulfil the mandate given to me if, on behalf of the three bodies mentioned, your Royal Highness, the German Mathematical Society and all of the participants in the Third International Congress of Mathematicians, I express their thanks for the honour that you have given to Jacobi's memory through today's celebration.

I have another assignment to fulfil.

The Prussian Academy of Sciences is honouring Jacobi by publishing his scientific works; but it has fulfilled another duty of respect towards the great scholar.

A few years ago, a member of the Academy received the announcement from the then very old wife of the deceased that she was no longer able to care for Jacobi's grave. This was the reason for the Academy to immediately initiate the necessary negotiations and to successfully carry them out, in order to use the academy's funds to acquire Jacobi's grave at the Trinity Church in Berlin, where the burial site is located (at Blucherplatz in front of Hallisches Tore), so it will remain as a cemetery at all.

The academy took over the further care of Jacobi's tomb and erected a cross on it and took care of a suitable, simple but dignified fence around the same. As a result of the decision of the physics-mathematical class of the Academy, I am commissioned to present a photographic image of the Jacobi burial site in its present state to the participants of the Congress.

I have also been asked to hand the picture over to secretary Koenigsberger, the biographer of Jacobi, after the Congress participants have looked at it, with the request that it be taken by him and given a place in his house.

This ended the programme of the first general session; His Royal Highness the Hereditary Grand Duke stayed in the hall for a long time in order to be able to meet a large number of the foreign members of the Congress.

In the afternoon at 16.00 the sections were formed, the activities of which are reported separately below.

The banquet began at 19.00 in the town hall, at which His Royal Highness the Hereditary Grand Duke appeared. The chairman, Heinrich Weber (Strasbourg), opened the meal with a toast to the Kaiser and the Grand Duke and a greeting to the Hereditary Grand Duke, to which the latter replied with a toast to the heads of state of all countries represented at the Congress. The following telegrams of homage were then sent to the Kaiser and the Grand Duke:
To His Majesty the Kaiser, Berlin.
The International Congress of Mathematicians, gathered for the first time on German soil, sends the most respectful homage to the powerful ruler of the German Reich, the tireless guardian of peace.
On behalf of: Professor H Weber, Professor Krazer.

We pay homage and gratitude to the revered prince and lord of the beautiful country, whose hospitality we enjoy, the warm protector of art and science.
The Third International Congress of Mathematicians gathered in Heidelberg.
On behalf of: Professor H Weber, Professor Krazer.
Felix Klein (Göttingen) then expressed the thanks of the German Mathematical Society to all authorities that had contributed to the establishment of the Congress, in particular to the government of Baden, on behalf of which Ministerial Director Freiherr von Marschall replied with a cheer to mathematical science. The secretary then greeted the foreign colleagues on behalf of the German mathematicians; Karl Geiser (Zürich) thanked him by emptying his glass to the friendship of nations through science. A toast from Max Noether (Erlangen) to the city of Heidelberg was replied to by Mayor Walz. Finally, Lothar Heffter (Bonn) rose with a toast to mathematical ladies that was met with lively applause. At around 22.00 His Royal Highness the Hereditary Grand Duke left the banquet, the participants of which then gathered together in smaller groups.

Wednesday 10 August.

Section sessions filled the morning. For the afternoon, His Royal Highness the Grand Duke had invited the Congress to a reception in the castle garden in Schwetzingen, where two special trains took the guests at 16.20 and 16.30. Shortly before the Congress participants, on behalf of His High Father, His Royal Highness the Hereditary Grand Duke had arrived in Schwetzingen. He waited for the guests in the palace garden and socialised with all those present until around 19:00. Tea was served in the garden during the reception. Later the Congress participants gathered in front of the buffet set up in the orangery. At 20.00, after Heinrich Weber (Strasbourg) had given His Royal Highness the Hereditary Grand Duke a cheer, the guests returned to the train station to return to Heidelberg with the special trains departing at 20.10 and 20.25.

Thursday 11 August.

At the beginning of the second general meeting in the university auditorium at 10.00, the secretary first read the following telegrams, the replies from the Kaiser and the Grand Duke, which had arrived the day before:
To the Congress of Mathematicians, Heidelberg.
From Swinemünde.
His Majesty the Kaiser and King offer to the members of Third International Congress of Mathematicians, who has gathered on German soil for the first time, His Imperial Salute and says thank you for the telegram of homage. His Majesty wishes the work of the Congress the best of success. In the highest order
von Tschirsky, Royal Envoy.

To Professors H Weber and Krazer, Heidelberg. From St Moritz-Bad.
I would like to ask both of you to extend my warmest thanks to the members of the highly valued mathematicians' congress for the very friendly greeting that is dedicated to me and for the expression of your feelings. I am very pleased that the venerable Ruprecht Karl University of Heidelberg has been granted the privilege of having such a rare congress in its midst and offering it true hospitality. I sincerely wish you all to keep a friendly memory of your stay in my country.
August Gutzmer (Jena) then presented the History of the German Mathematical Society, which he had written on behalf of the board, in the following words:
More than in other sciences in general, mathematics requires its disciples to immerse themselves in loneliness in order to be able to discover the laws of measure and number far from the mechanisms of real life.

But in addition to the questions that the individual tries to answer, which may have become only problems in his head, there are also tasks of various kinds in mathematics that can only be accomplished through the cooperation of mathematicians.

In order to characterise the wide range of these tasks to some extent, we only need to remember the important question of the appropriate design of lessons, the question of an appropriate formulation of examination regulations, the consideration of the applications of mathematics to the problems of life, astronomy, geodesy and physics and - certainly not least - of technology. It should also be pointed out the special importance to, for example, individual researchers who own papers and encyclopaedias that can only be made by a community of experts.

As certain as it is, and it will remain, that the great advances in mathematics will be brought about by the discoveries of individual researchers, it can be safely asserted that there are always questions that require cooperation and that there are times when settling these questions is as important as discovering one theorem or another.

We seem to be living in such a time now. Everywhere, in England, in France, in America, in Germany, important questions of this kind have been dealt with or are waiting to be solved soon.

In Germany, the German Mathematical Society has followed the designated circle of questions with uninterrupted attention and helped to solve and clarify them. There appeared to be a need to give an account of the Society's activities. This was done in a small paper that I wrote on behalf of the board. I do not want to fail to express my gratitude to all the gentlemen who supported me with messages and remarks, and also to thank the accommodating B G Teubner publishing house in Leipzig.

The undemanding booklet is dedicated to the participants of the current Congress, and I am particularly honoured to have this "History of the German Mathematical Society" here in Heidelberg, where 15 years ago, at the suggestion of Georg Cantor, the plan for its founding was announced to the outside world that, in light of an illustrious international assembly, I would like to hand over herewith to you, Mr President.

After Gutzmer had finished, Felix Klein (Göttingen), on behalf of the Academic Commission (on behalf of its chairman Walther von Dyck (Munich)), handed over the now completed first volume of the Encyklopädie der mathematischen Wissenschaften. In addition to a general introductory report by the chairman and a special foreword by the editor Wilhelm Meyer (Königsberg), the final issue of the volume contains in particular an extensive alphabetical index of authors and subject matter worked out by the latter. The lecturer thanked all employees (whose dedication primarily allowed the volume to come into being), thanked furthermore Wilhelm Meyer, whose initiative the encyclopaedia's plan initially came from and who now has the satisfaction of being able to present a completed volume, finally also thanked the publisher's bookstore, which has put its great performance in the service of the company, so to speak, without restriction. On the further volumes II-VI for example work continued uniformly, so that one can look forward to their completion in the foreseeable future. But at the same time, there are already prospects for further company continuation. Jules Molk (Nancy) will immediately publish the first issue of a French edition, which will be published with the help of the best French authors and can thus appear as the second improved edition of the previous edition. One can hope that a new German edition will follow later, in which all the many materials of corrections and completions that will have been collected by then will be incorporated. The editors of the German edition are already asking mathematicians at home and abroad to send them their material of this kind.

Jules Molk (Nancy) then gave the following address, presenting the first volume of the French edition of the encyclopaedia he had published:
I have the honour to present to you the first volume of the French edition of the Encyclopédie des sciences mathématiques. This French edition is an addition to the German edition of the same Encyclopaedia. It is not a simple translation: it is a presentation, made by French-speaking mathematicians, of the articles contained in the German edition; these articles are supplemented, updated; the mode of presentation is also entirely in line with French traditions. However, the general character of the first edition is preserved: the French edition is published under the auspices of the same Academies; a delegate from these Academies monitors their publication; on the other hand, the considerable role played, in the realisation of the very conception of the Encyclopaedia, by the editors of the different volumes of the German edition is highlighted by the mention of the name of these editors on the title page of each of the volumes of the French edition.

The names of the editors of our edition, B G Teubner in Leipzig and Gauthier-Villars in Paris are universally known and everyone knows what mathematical science owes them. Their common currency is and will be: Viribus unitis.

To facilitate the reader's research, the title of each article is reproduced, in whole or in part, from two pages to two pages; this title is framed by the name of the author of the German article and by that of the author of the French presentation. These two authors thus form a complex where the second unit, the French unit, completes the first unit, the German unit. It would certainly be desirable for other units to join these two units to give the Encyclopaedia even more universal character than mathematics itself; this addition is possible without anything being changed in the guiding idea printed in the Encyclopaedia by the editors of the first edition: our French edition will provide a first tangible proof.

François Viète, our master, wrote at the head of one of his main works:
I make mine as much as God allows
Let everyone do their own and science will grow.
By giving us their support in the field that they have deepened the most, each of you, Gentlemen, can contribute to ensuring that the Encyclopaedia responds better and better to the needs of contemporary mathematicians and engineers. And by that very fact "science will increase".

Then followed the lectures by Paul Painlevé (Paris): Le problème modern de l'intégration des équations différentielles, and by Alfred Greenhill (London): The mathematical theory of the top (considered historically).

The exhibition of mathematical literature and mathematical models and apparatus was opened in the museum hall following speeches by August Gutzmer (Jena) and Martin Disteli (Strasbourg) in the afternoon at 16.00. These speeches were followed by a short lecture by Carl Runge (Hannover) on the Leibniz computing machine, followed by demonstrations the Zeiss epidioscope and a lecture with silhouettes by Hermann Wiener (Darmstadt).

At 19.30 a special train was ready for the trip to Schlierbach, from where the ferry transported the participants to Ziegelhausen. At 20.00 the signal for departure sounded and the congress participants sailed down the river in the boats provided by the city of Heidelberg to view the castle lighting and the fireworks that followed. The boats moored at the town hall at around 22:30. The congress participants left the boats giving a cheer for the city of Heidelberg and remained animated and moved by the unique spectacle they had seen for a few hours while in casual conversation.

Harry Walter Tyler, who worked at the Massachusetts Institute of Technology, described the trip down the Neckar in an article in the Bulletin of the American Mathematical Society:
After an invasion of the Gartenwirthschaft in number for whom the landlord unfortunately could not duplicate the miracle of the loaves and fishes, decorated stone-boats were taken in the evening for the romantic descent of the Neckar. Below the arches of the Carlsbrücke, each pier poured a fountain of fire into the river, while high above the town the castle burst into dazzling light with red fires, burning steadily for some fifteen minutes. In the midst of a beautiful display of fireworks from a boat on the river, the pythagorean diagram stood out brilliantly against the sky, an appropriate symbol of the nature of the meeting. The whole effect was finely spectacular.
Friday 12 August.

The morning, like Wednesday, was devoted to section meetings. In the afternoon from 16.30 lectures and demonstrations took place in the exhibition hall.

Demonstration of apparatus from the Carl Zeiss's optical workshop in Jena; II. Demonstration lecture by Hermann Wiener (Darmstadt) on the development of geometric shapes; III Lecture and demonstration by Martin Schilling (Göttingen).

The evening entertainment organised by the German Mathematical Society in honour of the members of the Congress began in the castle restaurant in the evening at 19.30. The evening's program consisted of three parts: a musical part, in which the city orchestra alternated with male choirs from the Heidelberg Singers Association performing a series of pieces of music. The second part of the programme was a firework display below the Scheffel terrace, initiated by lighting the east facade of the castle. At 22.00 the third part was followed by a general Kommers (Drinking evening) chaired by Hermann Schubert (Hamburg), which kept the congress participants together until after midnight.

Saturday 13 August.

After a brief meeting of the committee in the morning at 9:00, the business meeting of the Congress began at 9.30, the minutes of which are printed below. This was immediately followed by the third general session with the lectures by Corrado Segre (Turin): La geometria d'oggidì e i suoi legami coll'analisi, and by Wilhelm Wirtinger (Vienna): Riemann's lectures on the hypergeometric series and their meaning. The secretary then read the following telegram from His Royal Highness the Hereditary Grand Duke, received during the meeting, for a homage sent to him during the previous evening:
Professor Schubert, Heidelberg.

I would like to express my most sincere thanks to the participants in the Third International Congress of Mathematicians, who were so friendly during the evening entertainment organised by the German Mathematical Society yesterday. It will always be a worthwhile memory to me of the gentlemen who personally greeted me and that I was able to participate at the beginning of the congress, which I hope has the most enjoyable and satisfying conclusion.

Friedrich, Hereditary Grand Duke of Baden.
Heinrich Weber then closed the Congress with the following address:
We are nearing the end of the Congress and it is my pleasant duty to thank everyone who has contributed to the success of the Congress. First of all, everyone who came here to take part in the Congress, who in part did not shy away from travelling very long distances in order to join us here for scientific work; they want to return to their home satisfied and with beautiful impressions and memories. In particular, I have to commemorate all of those who have given us material support to enable us to offer you what you have found here.

Since it was established that the Third International Congress of Mathematicians was to take place in Germany, the board of our Society dealt with the question of organisation. The first question that arose was in which city of the wide German Empire we should receive you, and then the consideration that it would be easier in a smaller city to bring our colleagues closer than in a big city was the decisive factor that we invited you not to the capital of the Reich, but to Heidelberg, which offers such extraordinarily favourable conditions for a scientific congress.

Then we were concerned with the question that in earthly matters is so attached to the bold flight of thoughts and hopes as a lead weight: where do we get the means to receive our guests worthily and to offer them all the scientific and literary gifts that we had in mind. But here, too, we didn't get stuck in need for long. When informed that the Congress should gather in Heidelberg, the Baden state government immediately promised a contribution of 3,000 marks for free use, which the State Parliament approved in grateful liberality. We were then granted by His Majesty the Kaiser and King of Prussia from his disposition fund, with special regard to the Jacobi celebration and the related publication of the Jacobi biography, 5000 marks, and the same amount was added by the Reich government. Furthermore, we received a grant of 2000 marks from the Teubner company, the always helpful friend of our science.

With such a wealth of resources, we dared to start preparing without too much frugality and I would like to express my sincere thanks to everyone who has contributed so generously to securing the financial basis of the Congress. Of course, the financial situation cannot yet be completely overlooked at this point, but we can certainly count on the fact that the deal will be more favourable. We will file an exact invoice for the board of the German Mathematical Society as soon as possible.

In addition, warm hospitality has helped to make the Congress such a beautiful party. First of all, I would like to thank His Royal Highness the Grand Duke of Baden, who expressed his warm interest in our cause in such an uplifting manner, and His most eloquent son, the Hereditary Grand Duke Friedrich, who received us in the Grand Duke's name and as Honorary President has taken over our opening meeting. We were all enchanted by the lovely kindness of the noble prince.

I would also like to thank the City of Heidelberg, which, by sending representatives to the preparatory work of the committee, has been interested in our meeting from the start and has now given us such a warm welcome.

I then thank His Magnificence the Vice-Rector of the University, who granted us shelter in the University's rooms and who honoured us with his presence at the meetings. In the beautiful new hall of the university, the very instructive exhibition of mathematical literature, models and apparatus, the success of which we owe to the sacrificing cooperation of the exhibitors and our committee, has found a worthy place.

At the very least, my thanks go to all those who gave the congress its scientific content through lectures in the general and section meetings or through demonstrations in the exhibition, and finally to all those who did this in hidden and modest work in the various committees complicated gear train in progress.

But I offer all of you a hearty farewell. Keep a friendly memory of the Heidelberg Days!

See you in Rome!

In the afternoon there was official coffee for the ladies in the Stiftsmühle. Some of the men accepted Wolf's invitation to visit his astrophysical institute and later also left there and arrived at the Stiftsmühle. Baron von Bernus had kindly sent the Congress an invitation to visit Neuburg Abbey and to view its collections, which was taken up by many.

3.       Resolutions of the Congress.

The following are from the Minutes of the business meeting of III International Congress of Mathematicians held on Saturday, 13 August 9:30.

Making decisions on the resolutions proposed to the Congress.

There were four resolutions:
I. Resolution.

The undersigned ask for their consent:

Considering that the history of mathematics is now an undeniably important discipline, that its use from both a purely mathematical and a pedagogical point of view is becoming more and more important, and it is therefore essential to teach it appropriately in public instruction, and

taking into account the wishes of the 5th Section of the International Congress for Comparative History (Paris, July 1900) and the 8th Section of the International Congress of Historians (Rome, 1903), the III International Congress of Mathematicians in Heidelberg adopts the international wishes expressed by the Congress in Rome:

1)    That the history of exact science is taught at universities by setting up appropriate lectures for the four parts:

1. Mathematics and astronomy.

2. Physics and chemistry.

3. Natural sciences.

4. Medicine.

2)    That the elements of the history of the exact sciences be included in the programme of the individual subjects of the high schools.

P Tannery. A von Braunmühl. E Lampe. G Loria. M Simon. D E Smith. P Stackel. E Wolffing.

The resolution was adopted by the assembly by acclamation.

II. Resolution.

The Third International Congress of Mathematicians, considering that the complete edition of Euler's works is of great scientific importance, supports the proposal made to the Carnegie Institution by the Mathematical Committee established under the chairmanship of Mr E Moore and hopes for its prompt resolution.

Considering on the other hand that the success of this edition requires the assistance of several scientists from all countries whose meeting for the elaboration of the plan and the discussion of the other questions relating to it could be done during the next Congress, the Third International Congress of Mathematicians requests the Organising Committee of the next Congress to present to it a report on the state of the question as well as on the measures which the Congress could have taken to contribute on its part to the success of this important scientific endeavour.

F Morley. A Wassilief.

The assembly shares the conviction of the great importance of a complete edition of Euler's works, notices that steps have already been taken to implement the enterprise on the part of the academies in St Petersburg and Berlin, and expresses the hope that the next Congress can be informed about the progress of the matter.

III. Resolution.

The 5th section of the Third International Congress of Mathematicians in Heidelberg declares that it is desirable that a closer association of the historians of the mathematical sciences be established. Since the tasks of such a society are international, the society should become an international one and cooperation with similar and related national societies, journals, museums etc. should be sought.

It adds the wish that this resolution be placed on the agenda of the next Congress.

The resolution is adopted by the assembly by acclamation.

IV. Resolution.

The Congress warmly welcomes the efforts of mathematicians that the facilities essential for the modern operation of mathematical studies (enough chairs, libraries, drawing rooms, work rooms, model collections, projection facilities, etc.) may be found everywhere, and urges that governments and other relevant authorities provide them with the necessary support.

The resolution is adopted by the assembly by acclamation.

4.       Determination of the Fourth International Congress of Mathematicians.

Vito Volterra (Rome) delivered an invitation from the Accademia dei Lincei to hold the Fourth International Congress of Mathematicians in Rome in spring 1908, as follows:

The members of the mathematical section of the Accademia dei Lincei met last June and they have decided to propose that you hold the next International Congress of Mathematicians in Rome.

After the audience accepted the invitation with vigorous applause, Volterra continued:

Thank you for the honour you have done us in choosing Rome as the seat of the next Congress. I propose to convene the Congress in the spring of 1908, leaving it to the committee to specify the date.

At the same time I have the honour to inform the Congress that Giovanni Guccia has made available to the Circolo Matematico di Palermo the sum of 3000 francs. for an international prize which, under the name of the Guccia medal, will be awarded during the next congress to a dissertation making essential progress in the theory of algebraic space curves. The commission that will judge the competition is composed of Max Noether, Henri Poincaré and Corrado Segre.

Alfred Greenhill (London) then expressed the wish that the Fifth International Congress of Mathematicians be held in England, by the following:
I left London under the impression that England was to be honoured with the visit of the International Congress of Mathematicians on the next occasion after Germany; and I think this impression was shared by the other English present here.

But we find now that Italy is the fortunate country, and is to receive the Congress in 1908.

Disappointed in our expectation we must congratulate Italy and Rome on its good fortune, and we must content ourselves with the next best in our wish, and hope that England may be selected at this Assembly as the meeting place in 1911 or 12.

I beg then to place before this General Meeting the formal proposition that the International Congress of Mathematicians, next after Italy, shall be held in England.

[This proposal was not accepted since the venue of an International Congress of Mathematicians could only be decided at the previous Congress.]

After a brief business notification by Felix Klein (Göttingen) to the meeting that the exhibition was still open to visitors on Sunday morning, Hans Amandus Schwarz (Berlin) took the floor to express the thanks of the Congress participants to the chairman and secretary of the Congress as well as the head of the exhibition, Disteli (Strasbourg), for their efforts.

The business meeting was then closed.