A nine-member International Advisory Committee, appointed by the International Mathematical Union, and chaired by Mr Adrian ALBERT, has constituted 33 specialised commissions; the compositions of this Committee, of these Commissions and the recommendations made by them to the Organising Committee are confidential.

The French National Committee of Mathematicians has constituted the Organising Committee whose members are: F Bruhat, H Cabannes, J Cerf, G Choquet, J Dieudonné, J-P Kahane, P Lelong, J Leray, President, A Lichnerowicz, J-L Lions, J Neveu, L Schwartz, J-P Serre.

This Organising Committee has set up a Local Committee whose members are: J Dieudonné, President, P Krée, E Ménager and a Finance Committee, whose members are: P Belgodère, R Chéradame, J Dieudonné, R Fortet, P Lelong, President, Y Martin, E Ménager, L Motchane, M d'Olier.

The Congress was assisted by a support committee for the dissemination of the work of the Congress, composed as follows: President: Mr Georges Desbrière, Vice-President of Péchiney, President of the Association for the Development of the Teaching and Research at the Faculty of Science of the University of Paris (A.D.E.R.P.).

Mr Étienne Wolff, Administrator of the Collège de France, was kind enough to host the Secretariat of the Organising Committee.

This Secretariat was provided by Mrs M Goyvaerts.

The publication of the Congress Proceedings was assumed by M Berger, J Dieudonné, J Leray, J-L Lions, P Malliavin, J-P Serre.

Saturday 5 September: Ball offered by the organising Committee (drinks not included) at the "Palais de la Méditerranée", starting at 9 p.m.

Sunday 6 September: Day Excursion offered by the organising Committee (lunch not included).

Monday 7 September: From 7 p.m. to 8.45 p.m., Documentary Movies at "Cinéma L'Escurial", avenue Georges-Clemenceau, offered by the organising Committee.
At 9 p.m., Ballet evening at the Opéra, rue Saint-François-de-Paule.

Tuesday 8 September: At 9 p.m., Organ Concert by Pierre Cochereau at Saint-Paul's church, offered by the organizing Committee. The total number of seats is 500.
At 9 p.m., second Ballet evening at the Opéra.

Wednesday 9 September: At 9 p.m., A Capella Vocal Music Concert by "Maîtrise Gabriel Fauré" from Marseille, at the "Palais de la Méditerranée", offered by the organising Committee. The number of seats is limited.

Mr Olivier Guichard, Minister of National Education, declared the International Congress of Mathematicians in Nice, open on Tuesday, 1 September 1970, at 9:30.

He gave the floor to Mr Henri Cartan, President of the International Mathematical Union, who proposed to the members of Congress that they elect Mr Jean Leray, President of the Organising Committee, as President of the Congress; this election took place in addition to that of Mr Paul Montel who was elected as Honorary President.

Mr Paul Montel and Mr Jean Leray welcomed the members of Congress and thanked the people who had collaborated in the organisation of the Congress.

Mr Jacques Médecin, Deputy Mayor of Nice, welcomed the members of the Congress to the Palais des Expositions of the City of Nice.

It is due to Professor J-C Fields' initiative that a foundation was created which would allow, on the occasion of each International Congress of Mathematicians, the honouring of mathematical works of exceptional interest by awarding two gold medals. His proposal was accepted, after his death, by the International Congress of Mathematicians in Zurich in 1932. The necessary funds came from a surplus of income from the International Congress of Mathematicians of 1924, held in Toronto, Canada, under the chairmanship of Professor Fields. The first two Fields Medals were awarded in 1936 at the Oslo Congress; then, after a long interruption due to the war, two medals were awarded at each International Congress of Mathematicians: at Harvard in 1950, in Amsterdam in 1954, at Edinburgh in 1958, and in Stockholm in 1962. At the Moscow Congress, in 1966, four Fields Medals were awarded. Each medal is accompanied by a cheque for 1,500 Canadian dollars; the name of Fields is not on the medals.

Following a procedure now well established, the Executive Committee of the International Mathematical Union appointed, some time ago, an International Committee of eight members, in charge of choosing the laureates for the present Congress. This Fields Committee for 1970 consisted of Professors J L Doob, F Hirzebruch, L Hörmander, S Iyanaga, J-W Milnor, I R Shafarevich, P Turan, and myself as president. I highly appreciated the collaboration of each of my colleagues, and I am pleased to express my warm thanks. I am also grateful to the mathematicians who, privately consulted, prepared reports that greatly helped our Committee in its task.

The Committee decided, with some hesitation, to conform to the tradition that only the names of mathematicians under the age of forty should be taken into consideration. The candidates proposed by the various members of the Committee initially composed a list of about twenty names. After a discussion during which, in accordance with the wishs of Professor Fields, we only took into account the scientific point of view, leaving aside any question of nationality, we have gradually arrived at a list of four names. It was a difficult choice; we are perfectly aware that other very brilliant mathematicians could also have been chosen for a Fields Medal; we also know that others, still younger, and whose names have not even been discussed this time, may have serious chances in four years. Be that as it may, we are convinced that those whom we have finally chosen are mathematicians of exceptional merit, and that each of them has contributed to giving a new face to an important branch of mathematics. These are, in alphabetical order:

Alan Baker,

Heisuke Hironaka,

Sergei Novikov,

John G Thompson.

Unfortunately, Sergei Novikov was unable to come to this Congress. I ask Messrs Baker, Hironaka and Thompson to come forward and receive their medal from the hands of the Minister of National Education, Mr Olivier Guichard.

- each morning, two consecutive general lectures, each of one hour, are delivered to all the members of Congress;

- each afternoon, a choice of specialised lectures, each of fifty minutes, each member of the Congress having the opportunity of listening to three;

  - each member of the Congress received, printed, the 265 individual communications; it is not possible to deliver these orally;

- groups of members of the Congress can obtain rooms for mathematical meetings which are not included in the official programme.

The work of the four new Fields Medalists is then reported in the articles printed in the Proceedings.

The Acts of the Congress will be printed as soon as possible, and distributed to every mathematician regularly registered at the Congress. The cost of the printing will be borne partly by the fees of the participants, partly by a subsidy from the French government, and partly by a subsidy granted by the "Committee for Support for Dissemination of Congress Proceedings" sponsored by associations of French companies and chaired by Mr G Desbrière, Vice-Chairman of Péchiney.

As you know, this Congress is the first one in which there are no 10 minutes talks, although printed communications have been accepted. The decision to allow only 50 minutes lectures given by invitation was taken unanimously by the international advisory Committee and the organising Committee. Of course the corresponding Committees for the 1974 Congress are not bound by this decision and may adopt a different policy. But the Organising Committee thinks that it might be useful to the organisers of the 1974 Congress to have the opinion of this Congress regarding the new organisation of the lectures. I will therefore ask those who are in favour of the continuation of the policy adopted in the 1970 Congress, namely to have only 1 hour and 50 minutes invited talks, plus written communications, but no 10 minutes talks, to raise their hands.

Against this continuation, and for a return to the previous tradition?

Abstentions?

As Past President of the International Mathematical Union, I have the pleasure of announcing that the Sixth General Assembly of the Union, held in Menton on August 28 and 29, 1970, elected for a period of four years, beginning January 1, 1971, the new Executive Committee as follows:

President:
Professor K Chandrasekharan

Vice-Presidents:
Dean Adrian A Albert,
Academician M Pontryagin,

Secretary:
Professor Otto Frostman

Members:
Professor M F Atiyah,
Professor Y Kawada,
Professor N H Kuiper,
Academician M Nicolescu,
Professor G Vesentini.

You, like me, would like to wish the new Executive Committee every success in the tasks ahead. The International Mathematical Union will strive, I am sure, to take all initiatives that can promote active and friendly cooperation between mathematicians around the world, or contribute to the development of mathematics in the less favoured countries.

I am delighted that this Congress has brought together in Nice many delegations from almost every country where mathematics is cultivated. The participation of some of them should have been more complete; I express the wish that it be so at the next Congress of 1974.

On behalf of the Committee which has been designated to study the venue of the 1974 Congress, I request President Leray to give the floor to Professor H A Heilbronn, who will speak on behalf of the Mathematical Society of Canada.

Mr H A Heilbronn, on behalf of the Mathematical Society of Canada and on behalf of the University of British Columbia, invited the International Congress of Mathematicians to meet in 1974 in Vancouver, Canada.

This offer was warmly accepted by the Congress, whose President thanked Mr H A Heilbronn and the University of British Columbia.