1908 ICM - Rome

1908 International Congress of Mathematicians - Rome, Italy

The International Congress of Mathematicians was held in Rome, Italy from 6 April to 11 April 1908. There were 535 full members, 165 family members, a total of 700. We give below a version of:
  1. Preparations for the Congress
  2. Regulations of the Congress
  3. Social Programme of the Congress
Before presenting the material, we give a short Preface.
Preface by EFR and JJOC.

Perhaps the greatest change in the 1908 Congress from the previous three was the much greater emphasis on applied mathematics. Another innovation at this Congress was the award of an international mathematical prize, the Guccia Medal. This had been announced in 1904 and was awarded at this Congress to Francesco Severi. It has never been awarded at any subsequent Congress. This Congress marks the first attempt to establish an International Mathematical Union but the following 1912 Congress reported failure to achieve this. Also at this Congress, an International Commission on the Teaching of Mathematics was set up and required to report at the next Congress. This would be highly successful.

1. Preparation for the Congress.

In the closing session of the Third International Congress of Mathematicians (Heidelberg, 13 August 1904) Professor Volterra proposed, on behalf of the Italian Members of the Mathematics Section of the R Accademia dei Lincei, and in agreement with the Presidency of the Circolo Matematico di Palermo, that the Fourth Congress should meet in Rome in the spring of 1908.

Following the favourable reception made by the General Assembly to this proposal, since June 1906 the Italian Members of the Mathematics Section of the R Accademia dei Lincei met several times to make some agreements concerning the organisation of the Congress. The following points were established:

1) The Congress is placed under the auspices of an international committee composed:

a) of the President and Italian Members and foreign members of the Mathematics and Mechanics sections of the R Accademia dei Lincei;

b) of the President and members of the Board of Directors of the Circolo Matematico di Palermo.

The Lecturers, referred to below, were then added to the said Committee.

2) The organisation of the Congress is entrusted to a Committee consisting of the Professors of Mathematics and Physics of the R University of Rome. The Chair of this Committee was assumed by Professor Pietro Blaserna, President of the R Accademia dei Lincei; Secretary was Professor Guido Castelnuovo, Treasurer Professor Vincenso Reina.

3) A large part in the Congress should be devoted to questions of general character, entrusting the discussion to illustrious scientists, preferably foreigners, invited to speak about the state of the main branches of pure mathematics and applied mathematics at the end of the 19th century. Professors Darboux, Forsyth, Hilbert, Klein, Lorentz, Mittag-Leffler, Newcomb, Picard and Poincaré accepted the invitation. Unfortunately, Professor Klein and Hilbert then had to give up the task, the first because of the many commitments he had offered to undertake, the second for health reasons. The theme, which Klein had proposed to address, was taken up and carried out by Professor von Dyck; while it was not possible to replace Hilbert at the time when the news he was unable to lecture reached us. Professor Veronese was called to represent Italy in this series of General Conferences; Professor Volterra was entrusted with the task of delivering a speech at the inaugural session of the Congress.

4) The Congress was divided into four Sections, the introducers named here would lead them:

Section I. Arithmetic, Algebra, Analysis. Introducers: Cesare Arzelà, Alfredo Capelli, Ernesto Pascal, Salvatore Pincherle.

Section II. Geometry. Introducers: Henry White, Corrado Segre.

Section III. Mechanics, mathematical physics, geodesy, various applications of mathematics. Introducers: Tullio Levi-Civita, Luigi Luiggi, Paolo Pizzetti, Guido Toja.

Section IV. Philosophical, historical and educational issues. Introducers: Federigo Enriques, Gino Loria, Giovanni Vailati.

Among the Applications of Section III it was decided to explicitly include Actuarial Mathematics.

To provide for the organisational costs, His Excellency the Minister of Education granted the sum of 10,000 Lire, which was entered into the Budget of the financial year 1907-1908. Various public and private bodies also wanted to increase the available funds with their contributions, thereby proving the ever-increasing interest that Mathematics, through its many applications, also arouses enthusiasm outside of pure science.

[We omit the list of contributors with the amounts given.]

But another more conspicuous offer, although not translatable into precise figures, we must mention here, with expression of our warm gratitude to the Circolo Matematico di Palermo and the Director of the Rendiconti, Professor Giovanni Battista Guccia. Professor Guccia, whose contributions towards our science are universally known, had wanted to give new proof of his enthusiasm for geometric research by founding a prize of 3000 Lire, to be awarded during the Congress for a memoir on the theory of skew algebraic curves. Not satisfied with this personal offer, which increased interest in the Congress, Professor Guccia submitted, on 31 August 1907, to the Circolo Matematico di Palermo an agreement, already accepted by the Organising Committee, by virtue of which the said Circolo Matematico di Palermo assumed the task of producing all publications concerning the Congress, including the Volume of the Proceedings, in exchange for a very minimal contribution, which the Committee would have paid to it, with any possible profit to remain for the benefit of the Circolo and any eventual loss to be the exclusive responsibility of Professor Guccia.

On the basis of this agreement, the Circolo Matematico di Palermo printed with the usual width, and circulated in large copies the Invitation Circulars to the Congress, and also published the extracts of some of the lectures that would be delivered there; the Circolo was preparing to make the second and more conspicuous part of its commitments, relative to the publication of the Proceedings, when an unfortunate strike, which disorganised the Mathematical Typography of Palermo, forced Professor Guccia to ask, as a representative of the Circle at the Congress and Director of Rendiconti, that the Circle be released from the commitments not yet executed, giving up any compensation for expenses already incurred.

Having recognised the seriousness of the reasons given, the President of the Congress had to adhere to this request, while expressing his regret that the publication of the Proceedings could not be entrusted to a Society, such as the Circolo di Palermo, which would have given certainty of a prompt and perfect work.

No less valuable than the aforementioned financial contributions was the moral support which was extensively given by all the Authorities. We must express our gratitude in particular to His Majesty the King, who would grant High Patronage to the Congress and wanted to honour the inaugural Session by His presence; to the Minister of Education, the Hon Rava, who on various occasions wanted to express his interest in this scientific meeting; to the Mayor of Rome, to the Mayor of Tivoli, to the Rector of the R. University of Rome, who welcomed the illustrious guests, to His Excellency the Austrian Ambassador to the Quirinal, who with exquisite solicitude procured for members of the Congress permission to visit the Villa d'Esté. We must finally thank all those people, whose names would be too long to list here, who in a thousand ways have facilitated our task. All contributed, to varying degrees, to make the stay of Rome pleasant for the members of the Congress, and to promote the achievement of one of the main purposes that these international Congresses: to forge bonds of sympathy and friendship between men from the most distant countries, distinguished by languages and habits, albeit joined by a single ideal, the progress of science and humanity.

2.       Regulations of the Congress.

ART. 1. The first plenary session will be chaired by the President of the Organising Committee. In it we will proceed to the establishment of the definitive officials, which will include:

An actual President,

Some Vice-Presidents,

A Secretary General,

Some additional Secretaries.

ART. 2. The subsequent plenary sessions will be chaired by the actual President or by one of the Vice-Presidents.

ART. 3. The first meeting of each Section will be chaired by one of the Introducers appointed by the Organising Committee. In this session the Section will appoint a Secretary and one or more additional Secretaries. The Secretaries will remain in office for the entire duration of the Congress.

At the end of each session the members present will elect the President of the next session.

ART. 4. The Organising Committee will establish the order of lectures in each Section; however, this may be modified by a vote of the respective Sections.

ART. 5. The reading of a communication cannot last more than twenty minutes. During the discussion the speakers will not be able to speak for more than ten minutes, nor will they be able to take the floor more than once on the same subject, without the President's special permission.

ART. 6. Speakers are asked to send a brief summary of the topics discussed to the Secretary of the Section, as soon as the talk is completed. Once the talk is completed, the Secretary will draw up and present to the Secretary General an extract of the minutes for publication in the Bulletin of the following day.

The complete report, containing the summary of the talks given and the discussions that took place, must be drawn up by the Section Secretary during the day.

ART. 7. The Conferences and Communications read at the Congress will be collected in the Volumes of the Proceedings .......

The Authors are asked to deliver the text of their talks to the Secretary General of the Congress no later than 12 April 1908. For talks in foreign languages (French, German, English) the use of the typewriter is required (except for the formulas). If there are figures, the relevant "clichés" [stereotype used in moveable type printing] must be provided by the authors.

3.       Social Programme of the Congress.

Sunday 5 April.

At 21.30, by the kind invitation of the Rector of the University of Rome, Professor Alberto Tonelli, almost all the members of the Congress who had already arrived in Rome, together with numerous ladies, gathered for a friendly meeting in the Aula Magna of the University.

Professor Tonelli, with brief words, offered the guests a warm and cordial greeting.

The meeting extended very animatedly until 23.30.

Monday 6 April.

At 10.00 in the Sala degli Orazi and Curiazi of the Campidoglio and in presence of His Majesty and Supreme Leader King Vittorio Emanuele III, the Fourth International Congress of Mathematicians was solemnly inaugurated.

His Majesty and Supreme Leader the King was received on his arrival by His Excellency the Minister of Public Instruction, by the Mayor of Rome, Mr Ernesto Nathan, by Senator Professor Pietro Blaserna, President, and by other Members of the Organizing Committee of the Congress.

After His Majesty and Supreme Leader the King and those present had sat down, the Mayor greeted the many attendees:
For those who minutely investigate, as for those who seek the history of civilisation in large strokes and in summary, the recent excavations of the Roman Forum, due to the brilliant intuition of Giacomo Boni, offer a singular interest. The memories of the pre-Roman Italic people, populating the seven hills, are the first stratification of civil geology in the burial grounds and cinerary urns; close to them the evidences of Romulus overlap, tracing the Urbe; farther away the vestiges of the Republic are scattered, until the dominating colossal equestrian statue of Domitian dominates. Horse, knight, collapse and ruin in the midst of the ruin of a world empire supported by the force of arms, by the force of arms broken apart, destroyed. And the eagle with powerful wings, sharp claws, a hooked beak, symbol of that strength, is replaced by the cross, symbol of faith. Then it is the dome of St Peter that dominates the city and the world, and the new era of civilisation, with its centre in Rome a second time the word of humanity, radiating beyond, it expands it and develops it among the peoples. And faith affirms itself, conquers, reigns, until old passions refine it, new insights break the unity, and the colossal dome of Michelangelo, like the colossal pedestal of the equestrian monument, remains to attest to a great power that was.

Because in the anxious rush to search for the truth a new factor advanced, overlapped; the flashes of faith weakened, the eyes of men turned to a new star that rose in the firmament, whose serene light indicated new paths, which the intermittent luminosities of the dominant faith had taken from our gaze: and the conscience of a people, from the enlightened science, through the breach in the Porta Pia and on the ruins of two ancient civilisations, it pointed to a third mission among the people of the eternal city. In the name of that science, of that new, intense, constant light, gentlemen, you are here gathered from various parts of the world; you among the most worthy lovers of human knowledge, since you represent in your studies, in your research, in your irrefutable inferences, the granite base on which stands that majestic building of modern wisdom that has transformed men and things, subjugating nature to social needs and creating new bonds and relationships in human coexistence.

And yet to me, humble lover of economic disciplines - how much my illustrious colleague Professor Tonelli was more suitable - is grateful to give you, masters of exact sciences, the welcome: with reverence in my name, with applause in the name of the city that I have the honour of representing.

Not only because of the sublime sum of knowledge you represent as a whole, in which I am grateful to note that the third Italy is not a negligible quantity, but also for the broader idea from your overshadowed meeting.

In past times, when the scattered members of the homeland were still assembled into unity, scientific meetings took place in this or that city, and the elect gathered there, while at the same time they took as a visible argument that branch of knowledge that most properly belonged to them, seized the occasion of the happy meeting between men of various regions, to cement, affirm, weave that unity that above the various acts of advocacy was at the top of their thoughts.

They left with a heart reassured by that fraternal communion, with the clearest thought around the common work incumbent on them: the many scientific disciplines which contribute to preparing, constituting, strengthening the native organism: it was a great, a beautiful, a noble idea that dominated the various branches of science to unite them all in the formation of a national conscience. Today, here in Rome, the capital of Italy, the highest goals await your work and sanction. They are no longer the scientists of one country, gathered in a community of aspirations limited by borders; it is the scientists of the whole world who, in the representation of various peoples, of various intellects, of various cognitions, come together, unite in the name of science for the formation of, no longer a national conscience, but an international conscience. Your works turn to the search for a single truth, although it can be expressed in many languages; and this admirable clearing house for exchanging scientific values is one of the most powerful weapons for breaking down frontiers, destroying animosities, calming hatreds, rekindling affections among peoples. It is a prelude to that universal brotherhood that science knows and senses, but politics today ignores and suspects.

In the name of that idea of peace and civilisation, in this historic hall, in the presence of the Highest Representation of the Nation, among you, distinguished men, a singular example of science and conscience, Rome gives with its heart a good-luck greeting to all of you from the Italic regions and from Foreign regions.
After the Mayor, the President of the Congress Organising Committee, Professor Blaserna took the floor:
Sir!

On behalf of the Organising Committee of this Congress and on behalf of the R Accademia dei Lincei, who took over its management, I thank His Majesty the King for having accepted the High Patronage and for having wanted to honour this first meeting with your august presence.

His Majesty the King wanted to prove, once again, how much the sciences and the arts of our country are dear to him, and how his heart beats in unison with that of the nation in all its noble and highest manifestations.

Ladies and gentlemen!

Anyone who cultivates a science, easily realises that two lovers of the same subject, even if distant and belonging to different nations, are closer to each other, than two other scholars of different sciences even if they live in the same city.

This concept has created in the past centuries those admirable correspondences between foreign scientists, in which the results of their investigations were communicated to each other. Opportunities were rare: international scientific papers did not exist, and it was private correspondences that served to fill the serious gap.

Today, the same concept has created International Congresses of a single science, Congresses which had, and which have, a beneficial influence. And also Mathematics has felt this influence. The first International Congress of Mathematicians took place in Zurich, then with a regular period of four in four years, in Paris, and in Heidelberg. To this last, in 1904, the R Accademia dei Lincei, which I have the honour of presiding over, made with the help of its very distinguished partner, Professor Volterra, and in agreement with the Circolo Matematico di Palermo, the proposal that the next International Congress of Mathematicians meet in Rome, and this proposal was warmly welcomed.

The Academy became an Organising Committee, with its Mathematics and Mechanics sections, to which it added the distinguished Rector of the University and some distinguished professors, as well as the President of the Circolo Matematico di Palermo, which under the powerful initiative of the Professor Giovanni Battista Guccia has acquired national and even international status.

The idea immediately had many supporters: the Honourable Minister of Public Instruction wanted to take the lead in the movement, and his colleagues from the Ministry of Agriculture Industry and Commerce, from the Treasury and from the Ministry of Public Development, proposed in their turn, that the Congress was not only of pure mathematics, but also of applied mathematics. This is how this Congress was born.

Today we will retire to the Academy building for quiet and peaceful work; but I owe a warm thanks to the distinguished mayor of this city for the noble initiative he took, with wanting to greet the great gathering on this classic hill, which reflects so much greatness and so many hopes of our homeland.
The Honourable Rava, Minister of Public Instruction, gave a speech which we reproduce here in summary:
In the name of the Government I extend to all who are gathered here, distinguished scholars of mathematical sciences from all civil nations, the auspicious greeting of Italy.

A feeling of high scientific and civil ideals has made you suspend your assiduous individual researches, to bring the contribution of your wisdom to a collective task, which aims at the general assumptions and the special progress of your disciplines. Your conference will achieve the appropriate reward in the beautiful harmony of the results, which you will be able to achieve with your combined energies.

These temporary reviews of common work respond to the deepest demands of modern knowledge. The more urgent and pressing the necessity of the division of scientific work appears, so it seems to be always inadequate that any more fervent intellectual activity aimed at achieving even a part and, one might almost say, a fragment of truth; on the other hand, our spirit yearns for the unitary conquest of knowledge, and only in the unity of truth does it recognise and feel the supreme effort of human intellect.

This requirement - before any other group of sciences - has been felt by mathematicians, as well as in achieving and maintaining their order with respect to other disciplines, as in animating them and guiding - with a perennial light of tireless research - their internal progress.

Mathematics is such a science that only recognising the place that it belongs to is accompanied by a broad enlargement of the mental horizon. Plato, who built the most seductive harmony of ideals that has ever flourished in the mind and heart of man, glorifies mathematics as a divine music of proportions; the Romans, who cement the most granitic juridical structure of the civil order, consecrate in their laws the learning and the exercise of mathematical art of public interest and decorum; Dante, who is a mathematician in the conception of the immortal poem, compares himself in the search for sublime truths to the geometer
that everything is affixed
to measure the circle, and does not find again
thinking, that principle on which he claims;
Leonardo, who in the heart of the Renaissance scrutinises the unknowns of nature and life with an acute eye and sagacity that still seems miraculous, declares 'to make the sciences so much more true, the more they learn about mathematical methods'; Galileo that
to the Angel that so much wing has extended there
first cleared the ways of the firmament,
considers all nature as a book whose characters are written with geometric symbols, and the geometry 'master of the honest acquisition of the useful, the delectable, the beautiful, the good'; Newton, Descartes who create analytic geometry, infinitesimal calculus; Emanuel Kant - from whose crumbling criticism of dogmatic ghosts the whole modern philosophy resurfaces - all affirm the principle that a science of nature is science only in so far as it is mathematics.

But in these names - which mark significant points in the trajectory of human thought - it is nothing but a reflection and a projection of what was the internal development of the mathematical sciences by those who devoted their lives to its purpose. Since the mathematical sciences present such an uninterrupted and disciplined growth from century to century, that no other scientific group could beat them in comparison. Even the apparent pauses are nothing but a dynamic concentration of future achievements.

Leonardo had written: where one shouts it is not true science, because the truth has only one term, which being published, the quarrel is forever destroyed, and if it arises again, it is a lying and confused science and certainty not reborn.

It is worth remembering, to understand the evolution of science, the ready fertilisation of the first sprouts of mathematics, such as abstract sciences, in the historical plate of Greek intellectuality. It is not without profound meaning that a people, who gave the world an art that seemed the ideal type of perfection, also had - and even in decadence - a flourishing period of mathematical research.

It is worth remembering the Italy of the urban republics and the Renaissance, with the names of Fibonacci, Tartaglia, del Ferro, Ferrari and so many others, who prepared for the revival of science by preserving the historical ripening of new spiritual and social needs. After Fibonacci, two streams appeared, one was seen in the studies of pure theory, and the other grounded in the studies applied to commerce, in which Italy was finding its renewed fortunes. And thus the double-entry bookkeeping with Luca Pacioli and his flourishing school of commercial arithmetic arose.

Gentlemen.

Making the hope that the fervour of your work will give to each of you, when the Congress completed, the comfort of multiple energies - and they are already so great - to spend in service of the scientific mission that so highly honours you, let me express to you the vow, as Minister of Instruction, that from your discussions will come mature, even precious, seeds of opportune suggestions to those who care about the improvement of the modern school which we owe, as a fruit of our tenacious and high resolutions, to the young generations.

Italy by tradition never stopped honouring your studies. Now there is no cultured person who does not know - I will say it with noble words of Luigi Cremona - that "even if a secular experience does not tell to us that the most abstract mathematical theories come at a time more or less close to not evenly suspected applications; even when the history of so many illustrious men who never gave up cultivating pure science were the most effective promoters of the present civilisation; this science is worthy of you loving it; its beauties are so many and so sublime, that it cannot fail to exert a high educational influence on the generous and intact souls giving the serene and inimitable poetry of truth."

These beautiful words that Luigi Cremona pronounced in the University of Bologna ten years before Rome was in history - as it was already in the heart of every Italian - Capital of Italy, still today express such a noble expression of faith, that they play well in Italian Rome in the presence of the King, the noble lover of modern studies and ideals, and in the presence of the scientists of the civilised world gathered here for the progress of their high doctrines."
Professor Volterra then delivered his lecture: Mathematics in Italy in the second half of the nineteenth century.

You can see this lecture at THIS LINK.

At 15.00 the first plenary session took place, with many speakers. The President of the Organising Committee, having opened the session, invites the Assembly to appoint the President of the Congress. The President of the Organising Committee, Professor Blaserna, is elected by acclamation.

He thanked the Assembly and proposed that the Presidency, together with him, be constituted as follows:

Vice-Presidents: Cerruti, D'Ovidio, Forsyth, Gordan, Jordan, Lorentz, Mertens, Mittag-Leffler, Newcomb, Vassilief, Zeuthen.

Secretary-General: Castelnuovo.

Vice-Secretaries: Fano, Reina.

Additional secretaries: Barnes, Borel, Hadamard, Holgate, Krazer, Phragmén, Schlesinger.

These proposals are all accepted by the Assembly.

The General Secretary informs that the Royal Academy of Sciences, Letters and Fine Arts of Belgium sends its best wishes and dedications to the Congress.

He also announced that the Torricelli Honorary Committee, in greeting the members of the Congress, hoped to have them in Faenza, at the time of the commemoration of the great scientist.

Finally he presented the books sent to the Congress by the publishers Longmans & Co and Teubner.

Professor Segre, also on behalf of his colleagues Max Noether and Henri Poincaré, read the Competition Report for the Guccia Medal. Three memoirs were presented for this competition; but the jury, while paying tribute to them, believed that none of them could be awarded the prize, and instead having examined the works which, without being presented to the competition, were nevertheless published on the subject of the competition itself and in the period during which this competition remained open, they unanimously reached the conclusion to award the prize to Professor Francesco Severi for his works on Geometry on algebraic surfaces.

Professor Corrado Segre then presented the Guccia Medal to Professor Francesco Severi.

Professor Mittag-Leffler then gave his lecture: Sur la représentation arithmétique des fonctions analytiques générales d'une variable complexe.

The lecture by Professor Andrew Forsyth followed: On the present condition of partial differential Equations of the second order, as regards formal integration.

The President, in closing the meeting, proposed that Professors Newcomb and Jordan should be chosen as Chairmen of the next plenary session. The Assembly accepted the proposal.

Tuesday 7 April.

At 9.00 the individual Sections met.

At 15.30 the Chairman, Professor Newcomb, opened the plenary session and gave the floor to Professor Darboux to deliver his talk: Les méthodes et les problèmes de la géométrie infinitésimale.

After the talk, Professor Newcomb gave the role of Chairman to Professor Jordan; Professor Walther von Dyck delivered his talk: Über die mathematische Encyklopädie. Professor Gordan was appointed Chairman for the next plenary session.

Wednesday 8 April.

At 9.00 the individual Sections met.

At 16.00 the plenary session, chaired by Professor Gordan, took place. The following talks were given:

Simon Newcomb, La théorie du mouvement de la lune; son histoire et son état actuel.

Hendrik Antoom Lorentz, Le partage de l'énergie entre la matière pondérable et l'éther.

Professor Mittag-Leffler was appointed as Chairman for the next plenary session.

At 10 o'clock a Reception took place in the Capitoline Museum, offered to members of Congress by the Municipality of the City of Rome.

The scientists who came to Rome and the women who accompanied them attended in great numbers.

The Mayor, Mr Ernesto Nathan, the Deputy Mayor Professor Alberto Tonelli, and the other Municipal Councillors did the honours of the house with refined courtesy.

Refreshments were served to the invited guests.

The lively meeting only broke up after midnight.

Thursday 9 April.

At 9.00 the individual Sections met.

In the afternoon the members of the Congress visited the Palatine, at the invitation of His Excellency the Minister of Public Instruction.

The members of Congress hastened to join the crowd; and, subdivided into various groups, accompanied by Professor Vaglieri and other expert guides who provided them with the appropriate illustrations in different languages, they visited those centuries-old ruins with satisfaction and interest.

The visit was attended by His Excellency Rava, with his wife and young daughters; and almost all the members of our committee were also present.

After the visit, the guests did not fail to pay due honour to the exquisite buffet.

At 9 o'clock the recently inaugurated Corea Amphitheatre welcomed the members of the Congress for the announced Concerto conducted by Luigi Mancinelli. The members of the Congress occupied several balconies and almost all the seats in the stalls.

During the evening, some of the most illustrious foreign scientists attending the Congress were cordially entertained, on the Town Hall stage, by His Excellency Rava and by the Mayor of Rome, Mr Ernesto Nathan

Friday 10 April.

At 9.00. the individual Sections met.

At 15.30 the Chairman Professor Mittag-Leffler opened the plenary session. The Minister of State was assisted by His Excellency the Minister of Instruction and His Excellency Luzzatti.

Professor Poincaré being indisposed, his announced lecture on the theme: L'avenir des mathématiques, was read instead, on his behalf, by Professor Darboux.

After which the Chairman thanked Professor Darboux, and asked him to inform his colleague Poincaré of the gratitude of the Assembly and of the good wishes for his forthcoming recovery.

The meeting is suspended for ten minutes.

Resuming the session, the Chairman announced a telegram of congratulations to the Congress sent by the Société Mathématique de France.

Then another interesting lecture was given: Émile Picard, La mathématique dans ses rapports avec la physique.

Saturday 11 April.

At 9.00 the individual Sections met again.

At 15.45 the Chairman Professor Blaserna opens the closing plenary session of the Congress.

He informed the session that Senator Professor Giuseppe Veronese, due to a slight indisposition, cannot hold the announced lecture on Non-Archimedean Geometry La geometria non-archimedea, which, nevertheless, will be included in the Proceedings of the Congress.

He then read a paper by Professor Georg Cantor, directed to Professor Guccia, and containing greetings and good wishes for the Congress. The Assembly, sad that Professor Cantor could not come to Rome, returned the cordial greeting.

The Assembly, with lively applause, adopts the Agenda voted that morning by Section IV of the Congress:

The Congress, having recognised the importance of a thorough examination of the programmes and methods of teaching mathematics in the secondary schools of various nations, confers to Professors Klein, Greenhill and Fehr the task of establishing an International Committee to study the matter and report to the next Congress.

Professor Jacques Hadamard presented, briefly illustrating it, the following proposal:
Section III (Mechanics), after an exchange of views, in which the importance of a unification of vectorial notations was recognised, proposes to Congress the appointment of an International Commission to study this question.

The president of this section for the meeting of 11 April proposes to the Congress to ask its Organising Committee to be good enough to constitute this Commission and submits to it the list of the names put forward, in this regard, in the meeting of 11 April.
This proposal was also approved with lively applause.

Professor Alberto Conti presented the following proposal:

"The Congress requires the establishment of an International Mathematicians Association to be put on the agenda of the next Congress."

The proposal is approved.

Professor Maurice d'Ocagne made the following proposal:
It follows from the exchange of views which took place in Section III-B that it would be highly desirable to bring about an increasingly close understanding between those who are engaged in perfecting mathematical methods and those who need apply them to a practical object.

To this end, the Section expresses the wish that mathematics applied to Engineering Science will be the subject of a special Section at the next Congress.

In addition, Section III-B proposes the constitution of an International Commission responsible for preparing the work of this new Section. The composition of this International Commission will be determined by the bureau of the Fourth Congress.
This proposal was also accepted by unanimous votes.

Section IV in its meeting of 9th April resolved to present the following Agenda item to the Congress:
The Fourth International Congress of Mathematicians in Rome considers as a matter of utmost importance for the pure and applied mathematical sciences the publication of all the works of Euler.
The Congress gratefully acknowledged the initiative taken in this regard by the Society of Swiss Naturalists, and vowed that the great work be performed by the Society itself with the collaboration of mathematicians from other nations.

The Congress asked the International Association of Academies, and especially the Academies of Berlin and St Petersburg, of which Euler was a famous member, to promise help with the enterprise.

The President declared that, if that agenda is approved, he will bring the matter to the meeting of the International Association of Academies, which will be held next year in Rome.

Darboux observed that the matter had already been discussed in other Congresses, and also in the recent meeting of the Association of Academies in Vienna. The request will therefore probably find an already favourable ground.

After that the agenda was approved by a unanimous vote.

With regard to the publication of the "Proceedings of the Congress", the President recalled that it had been arranged to be done by the Circolo Matematico di Palermo and under the direction of the Director of the Rendiconti, Professor Guccia. Unfortunately, following a strike by the typographic workers of Palermo, which led for an indefinite time to the disorganisation of the typography used for the publications of the same Circolo, Professor Guccia, as Delegate of the Circolo to the Congress, wrote to him explaining that the Circolo finds it impossible to provide for the publication of the Proceedings. The President added that the said publication will take place in any way by the Organising Committee of the Congress. And therefore, after the closing of the Congress, all manuscripts to be inserted in the Proceedings must be sent to the Secretary General of the Congress.

Being now required to designate the place and time of the Fifth International Congress of Mathematicians, the President gave the floor to Professor A R Forsyth, who, recalling the desire already expressed in Heidelberg by Professor Greenhill, and favourably welcomed by that Assembly, that this Congress if it be held in England, he formally proposed that it be held in Cambridge in 1912; and this on behalf of the Cambridge Philosophical Society, which will take care of the preparation of the Congress. This is also desired by the London Mathematical Society and by many English, Scottish and Irish mathematicians. It concludes with the following words:
The Cambridge Philosophical Society invites the International Congress of Mathematics to hold their fifth meeting in 1912 in Cambridge.
This invitation was supported by the London Mathematical Society.

This proposal is strongly supported by the President and is approved by the Assembly in a unanimous vote and with lively applause.

After this, Professor Forsyth added:
I desire to thank this Congress for the honour they have done to Cambridge by accepting the invitation of the Cambridge Philosophical Society. The meeting will be held in the month of August 1912: doubtless you will be willing to allow the Executive Committee, which will be formed, to fix the exact date in that month. Meanwhile, let me assure you that we shall do everything in our power to promote the scientific interests of the Congress.
Professor Mittag-Leffler made the following statement:
As a Swedish mathematician and editor of the Acta Mathematica, I have the honour of inviting the International Congress of Mathematicians to meet in Stockholm in 1916.

My august Sovereign, King Gustave, has graciously entrusted me with the task of expressing to Congress that he would be ready to take it under His patronage in the event that Congress decides to meet in Stockholm, and that he would welcome it with pleasure to his beautiful capital.

We Swedish mathematicians would consider ourselves happy as much as honoured, if the Congress wanted to accept our invitation, and we will do everything we can to make the stay of members in our country as pleasant and as informative as possible.
The President declared that a resolution on this will only be taken by the next (Fifth) Congress; but that this proposal will be inserted in the text of the Proceedings of the current Congress, and strongly recommended in the future Congress.

Jacques Hadamard submitted a personal request to the Congress:
Convinced of the usefulness of the rapprochement between Mathematics and Physics, also convinced that this rapprochement is not yet as intimate as it would be desirable, he issued the request that in future it may possibly to convene together the International Congresses of Mathematics and Physics. However, he does not want to influence the decisions already taken.
The Assembly associated itself with this request.

Andrew Forsyth declares that in Cambridge the request will be implemented as far as possible.

The President, declaring the Congress closed, offered everyone a warm greeting. He thanked the participants that with their valuable contributions and their numbers they gave such importance to the Congress, and it is certain that this scientific meeting will leave a profound mark on science, and will contribute to strengthening solidarity and fruitful harmony among the lovers of it.

Professor Darboux was certain that he interpreted the sentiments of all the members of Congress, by giving the warmest thanks to all the authorities and to the people who have contributed to making the Congress, about to close on that day, so important. He begs the President to thank first of all His Majesty the King for the noble proof of his interest in science that he wanted to give by speaking at the Opening Session. His gratitude was then addressed to His Excellency, the Minister of Public Instruction, to the Mayor of Rome and to the Rector of the University for the festive welcome they wanted to give to the members of Congress. Thanks in advance to the Mayor of Tivoli for the kind hospitality that he proposes to exercise on the following day. He finally thanked the distinguished President, the Secretary General, and the other members of the Congress Board for how the Congress was organized and directed; as well as all its employees and the employees of the Secretariat Office for their constant courtesy and promptness.

With these words, welcomed by unanimous applause, the sitting was closed at 16.45.

Sunday 12 April.

This last day was dedicated to the excursion to Tivoli, in which about 600 people participated including members of Congress and guests. Two special trains of the Rome-Tivoli railway line transported those on the expedition to the Villa Adriana station, where numerous carriages were ready to take them into the imperial Villa. After visiting those grandiose ruins, refreshments were offered by the Tivoli Town Council, represented by the Mayor Benedetti and the Councillors. The journey resumed by train to Tivoli, there a banquet took place in the Restaurant des Cascades, after which several toasts were delivered in various languages, all greeted with warm applause.

After the banquet, the Congressmen split up to visit Villa Gregoriana with its picturesque waterfalls, and the magnificent Villa d'Este, of which the Archduke Ferdinand of Austria had graciously granted free entry.

With several special trains the return to Rome took place.

Finally, we give C L E Moore's description of the trip, taken from the Bulletin of the American Mathematical Society:
The first stop was at Hadrian's Villa. Carriages were ready to take those who did not care to walk from the station to the villa. On entering the ruins, we found refreshments, provided by the municipality of Tivoli, ready and waiting to be served. After spending about two hours here, we proceeded to Tivoli, where a banquet awaited us. The banquets closed with toasts in Italian, French, German and Latin. The afternoon was spent in visiting the cascades and the Villa d'Este. The returning trains arrived an Rome about 20.00. This was the unofficial but real close of the Congress.