## Symposium dedicated to the memory of Henri Fehr

A symposium dedicated to the memory of Henri Fehr was held on 1-2 July 1955 in Geneva under the patronage of the Geneva Cantonal and University Authorities, and of the Executive Committee of the International Commission on Mathematical Instruction. In the opening session of this Symposium, Georges Tiercy and Heinrich Behnke praised Fehr. We give below extracts from these speeches (see

*L'Enseignement Mathématique*(2)**1**(1955), 10-20).**Speech by Georges Tiercy.**

The qualities of Henri Fehr as a mathematics teacher at the Gymnasium and a professor at the University have already been noted. He had an extremely adroit manner, instinctively adapted to each of his pupils, to show them the path to follow; individuals who are well endowed by nature in the field of mathematics have been able to work very hard and with joy; the less gifted were encouraged, none felt crushed; and finally all, we believe, have enjoyed the same spirit and shared a certain pleasure.

This is a very warm eulogy that I bring to the good pedagogue that was Henri Fehr; and I imagine that, in this enclosure, several members of the former flocks of pupils and students of Fehr now think again with emotion of this good teacher of mathematics, who had found the secret to encourage, direct and to enthuse his disciples.

It seems to me to be particularly interesting to note the following point: it was not by brilliant speeches that Henri Fehr trained his pupils; it was not his style; he spoke little; but he had the skill to suggest to his students what they should do, how to arrange their work and direct their efforts. Experience has proved that this method by example is more fruitful than that of beautiful speeches. On the other hand, what was to be said or written was always expressed in the best terms without confusion. Much of the advice that is being given today on mathematics education and comments on the role of mathematics was already part of Henri Fehr's working recipes from the beginning of his activity; and his students have benefited greatly from these indications.

Henri Fehr insisted, and this was a novelty at the time, on a distinction to be made between the teaching of mathematics for pure theorists and that addressed to technicians and practitioners, astronomers, physicists, engineers, biologists, sociologists, psychologists; the goal to be attained is not the same, he said; it is up to the professor to perceive the arrangements to be made; pure mathematics lovers cannot be content with rigorous definitions and demonstrations of theorems; they are called to show imagination and invention if they wish to solve the thorny questions they encounter; on the other hand, engineers and practitioners of all kinds, using formulas or theorems, do not have to worry about making a demonstration again at the time of the application; but they will have to know exactly what assumptions these formulas are based on. For this application work, they do not have to demonstrate a mathematical invention; their spirit of invention is of another kind.

It goes without saying that it is possible to produce an excellent practitioner while at the same time a purely logic mathematician; but we must not wait for exceptions.

In short, it is necessary to discern the essential; Henri Fehr discerned it very well.

Moreover, it may be added here that in fact there is no separation between pure science and applied science; the second brings out the problems that the former is responsible for studying; and it is there that mathematicians generally come into play with the well-known danger of running the risk of losing sight of reality, which then forces one to return to the facts.

These are the things we talk about today, which were extraordinary novelties at the beginning of Henri Fehr's career.

So there will be interest for the mathematics teacher, and this is the summary of Henri Fehr's ideas on this subject, to work and to work a little differently, depending on whether he is dealing with a pure logician or an application technician. This is a good sense which may be the responsibility of the teacher, both a social and a scientific responsibility.

One may wonder if all mathematics teachers today think enough about it.

One inevitably comes to refer to the very teaching of mathematics from the pedagogical point of view.

And here we fall again, into an area where our late master innovated. Henri Fehr rendered a considerable service to the cause that was dear to him by creating in 1899, with C-A Laisant, L'Enseignement mathématique, a periodical which was mentioned above.

Henri Fehr has from the beginning of his career considered coordinating international points of view with regard to the teaching itself. And it is certain that, again, he was an innovator. The name of the journal indicates what were the essential concerns of its founder; his personal interest was from the beginning and remained focused on the problems of the technique of teaching, on pedagogy applied to mathematics at all levels. Henri Fehr has always sought to improve programmes on the one hand, and on the other hand to find the best way to present the principles involved and to deduce the consequences.

It has been said, in what precedes, what was the success of L'Enseignement mathématique as soon as it appeared.

Henry Fehr's journal is still alive, although it has suffered from the periods of the last war and the post-war period; its continuation will probably be ensured in 1955 thanks to the understanding of the cantonal authorities and under the high patronage of the "International Commission on Mathematical Instruction", set up by the International Congress of Mathematicians of 1954 in Amsterdam, the Commission itself which made us the honour of coming to Geneva.

Needless to say, we are all happy about it. The work of coordinating the teaching of the exact sciences in the different countries, undertaken by Henri Fehr, will be continued; and it will be a blessing.

All the essential details that I have just mentioned are enough, I think, for everyone to understand why Henri Fehr will remain in history one of the mathematicians of French-speaking Switzerland who played a large role on the international scene.

I wish to reiterate, in closing, our gratitude to the "International Commission on Mathematical Instruction" for having wished to hold in our city its inaugural meeting of the Executive Council as well as this symposium dedicated to the memory of Henri Fehr; I thank again the "Council of the International Mathematical Union", whose President Heinz Hopf has come to sit among us; finally, I once again express our gratitude to the cantonal and university authorities who have turned to our international interests and concerns.

**Speech by Heinrich Behnke.**

It is the characteristic of mathematical research to obtain not only new results, but also to consider the results already achieved in a constantly renewed aspect. It is therefore able to benefit the already known theories of the effectiveness of new concepts. Up to this point perhaps, and to a certain degree only, we observe an analogy of mathematics with other sciences. However, the constant efforts made to condense mathematics by summarizing multiple and different results by means of ever new abstractions gives this ability and tendency a special power. The consequence is a constant creation of very varied and essentially new disciplines in their very foundations.

This tendency clearly appears to us if we take the example of Bourbaki, whose influence makes us understand the modern revision of our knowledge. This French work, although still unfinished, has an undeniable influence on our university courses. Some authors even, relying on Bourbaki's work, propose future modifications of mathematical education in secondary schools.

Such situations have always existed in mathematical research and teaching, and will never cease to exist. It is certainly painful for the learner, especially when he is not young, to be obliged to mingle with the students to learn what he must teach. Naturally a resistance manifests itself. Thus there is always some tension in the relationship between university education, which is strongly influenced by research, and secondary and primary education, which are necessarily conservative and follow the reforms with a delay of at least thirty years. The pupil and the student bear the consequences of this lack of intellectual contact between secondary and university professors. When mathematics presents itself in two aspects, that of research and that of education, it is essential to consider them in their entirety. However, the danger of focusing only on one or the other of these two aspects lurks for researchers and masters. Also the foundation of the International Commission for Mathematical Education on the occasion of the Fourth International Congress of Mathematicians of 1908 was an important event. The mathematicians then took the following resolution:

"The Congress, recognizing the importance of a thorough examination of the programs and of the methods of teaching mathematics at secondary schools of different nations, charges Professors Klein, Greenhill, and Fehr to constitute an International Commission to study these questions and to report to the next Congress. "

These three men set to work without delay. Henri Fehr was appointed secretary and served for forty-four years, until 1952. He took part as secretary in the work of the Commission during the productive first period before 1914. At that time, the survey was not limited to secondary schools preparing for university studies, but extended to all school mathematics teaching.

A voluminous literature was published on mathematics education in institutions of all kinds and in a large number of countries. In publications issued before or after the First World War, about two hundred and ninety articles were published by the Central Committee, now known as the Executive Committee. The Commission meets at the General Assembly on the occasion of the International Mathematical Congresses of Cambridge (Great Britain), 1912 ... It also organized international "colloquia" which were real congresses of mathematical education. They were held in Brussels in August 1910, in Milan in September 1911 and in Paris in April 1914.

As soon as the international relations, interrupted by the First World War, were renewed, the work of the Commission recommenced. Of all the former members of the Commission, only Henri Fehr remained. He was then the 'rector spiritus' of the resumed work. At the 1928 Bologna Congress, the 1932 Zurich Congress and the 1936 Oslo Congress, he drew up the reports and edited the conference reports. Thus, about forty more articles were published by Henri Fehr in the years following 1928. Of course, during these years, much more difficult for international life than those preceding 1914 or those in which we are now living, he could not pursue an activity as intense as that of Felix Klein, D E Smith and Sir George Greenhill. But in this difficult situation, the whole burden of the International Commission rested on Fehr alone. He maintained to this day the flame of enthusiasm for mathematical education and the awareness of the need to strengthen the relationship between research and teaching in the very interest of Western civilization. It is certainly a pleasure for the University of Geneva to have counted Henri Fehr for so long among its professors and to keep its magnificent archives.

The Commission will always remember the incomparable work of Henri Fehr. It honours the memory of its honorary president by holding the first meeting of this new period in Geneva, promising to be worthy of its founders, especially Henri Fehr and, being aware of the responsibility it has assumed, to continue the activity of its predecessors.

The Commission warmly thanks the University of Geneva for the interest shown and the assistance it has given to this event. It is also happy to be able to meet in the city where Piaget has given a new impetus to elementary mathematical teaching through his scientific research and the establishment of his Institute.