# Henri Fehr

### Biography

**Henri Fehr**was the son of Heinrich Fehr and Lina Scheller. Fehr attended secondary school in Geneva. His university studies were carried out at several different universities. He began by taking courses at the University of Geneva, continued at the Federal Institute of Technology in Zurich before going to the Sorbonne in Paris, where he obtained the degree of 'licence ès sciences mathématiques' in 1892. He began to undertake research and published his first paper

*Remarque sur le théorème de M Moutard*Ⓣ in 1894. His second paper

*Sur l'emploi de la multiplication extérieure en algèbre*Ⓣ was published in the following year. In this work he extended methods of exterior multiplication developed by Emmanuel Carvallo to methods of resolution and elimination for systems of linear equations. The importance of these methods for the theory of invariants is also explained with reference to the work of Grassmann and Schlegel.

From 1895 to 1900, Fehr taught at the École Professionnelle and at the College of Geneva and, at the same time, he gave a course at the University as a docent. Remarkably, at this very early stage in his career, he founded the Mathematical Library [5]:-

Henri Fehr, at the very beginning of his career in 1897, founded the Mathematical Library, which he administered until his last years with particular care, taking advantage of all the opportunities to enrich it despite very limited funds, carefully avoiding all that could have diminished it.During these five years, in addition to the heavy teaching duties, he prepared his doctoral dissertation. He submitted his thesis

*Application de la méthode vectorielle de Grassmann à la géométrie infinitésimale*Ⓣ to the University of Geneva and he successfully defended it in 1899. This thesis was published as a book in Paris, also in 1899, and reviewed by Edwin Wilson who writes [12]:-

As a thesis, the work contains nothing original either in vector analysis or in geometry. All the results and methods were known well enough before. ... The presentation of the elements of differential geometry given by M Fehr is hardly to be excelled. The usual important and fundamental results are obtained in much less space and time than is customary, and yet with perhaps a gain instead of a loss in clearness. ...For a list of contents in the form of chapter and section headings of the thesis as well as a longer extract from Edwin Wilson's review, see THIS LINK.

Jacques Hadamard was impressed with Fehr's thesis and wrote in Volume 19 of the

*Revue générale des Sciences pures el appliquées*:-

What is certain is that M Fehr has produced a small treatise on infinitesimal geometry in which the exposition is of rare elegance and simplicity.In addition to his thesis, Fehr published a further three articles in 1899, namely:

*Sur l'enseignement des éléments de trigonométrie*Ⓣ;

*La préparation mathématique de l'actuaire*Ⓣ; and

*Sur la courbure moyenne quadratique*Ⓣ. Yet another of his achievements in 1899 was his founding, with Charles-Ange Laisant, of a new journal

*L'enseignement mathématique*which had the subtitle

*Revue internationale, paraissant toutes les deux mois*. The first volume of the journal appeared in 1899 with Fehr as editor and, remarkably, he continued to edit the journal for over 50 years until his death in 1954. Fehr and Laisant wrote in the first issue:-

At a time when science has made so much progress, some simplifications may be desirable, the programmes of the different branches of teaching require more or less complete reforms. Linked to this there is a fundamental issue whose importance should not be overlooked: namely that of the education of teachers. All these changes ought not to be carried out in an abrupt way, nor without serious preliminary reflections. But is not the first requirement for proceeding in such a study in a judicious and fruitful way, to be aware of what happens in other countries, to know the way mathematics teaching is organised in each of them, what teaching programmes are in force, the methods by which the studies are approved, etc.? ... Despite the strong rapport that has been established today among scientists of the same field, despite the international congresses of mathematicians, so brilliantly inaugurated in Zurich in 1897 and accepted as a principle for the future, the world of education proper has not up to now been able to join this great movement of scientific solidarity as fully as would have been desirable ... . It has been our wish, through the publication of our Journal, to overcome the obstacles to reciprocal communications and to create a kind of continuous mutual correspondence between men who have devoted their lives to this noble mission: the mathematical education of young people. In view of this aim, our first concern has been to give this periodical a clearly and openly international character.A list of the members of the first Committee for the journal shows that support it received from leading mathematicians worldwide: Paul Emile Appell, Nicolai Vasilievich Bugaev, Moritz Benedikt Cantor, Luigi Cremona, Emanuel Czuber, Zoel García de Galdeano y Yanguas, Alfred George Greenhill, Felix Klein, Valerian Nikolaevich Ligin, Paul Mansion, Gösta Magnus Mittag-Leffler, Gabriel Oltramare, Julius Peter Christian Petersen, Émile Charles Picard, Henri Jules Poincaré, Pieter Hendrik Schoute, Kyparissos Stephanos, Francisco Gomes Teixeira, Alexandr Vasil'evich Vasil'ev, Alexander Ziwet.

In 1904, in the sixth volume of the journal, Fehr and Laisant wrote:-

The word "Enseignement" has for us the widest possible meaning. It means the teaching of pupils, as well as the teaching of teachers - and, indeed, you can hardly have the one without the other.The journal rapidly became successful and in 1905, when it was only six years old, it was awarded a gold medal at the International Exhibition in Brussels.

Fehr was appointed as an ordinary professor of Algebra and Higher Geometry at the University of Geneva on 24 July 1900, a position he held until 1945. The chair had become vacant due to Gabriel Oltramare (1816-1906) retiring after fifty-two years as a teacher. Fehr wrote the obituary [4] for Gabriel Oltramare. We note that Oltramare was one of the organisers of the first International Congress of Mathematicians held in Zurich in 1897 which Fehr also attended.

In fact Fehr had the remarkable record of attending every International Congress of Mathematicians from this first in 1897 until the 1950 Congress. He gave the invited talk

*L'enquête de "l'Enseignement Mathématique" sur la méthode de travail des mathématiciens*Ⓣ at the 1904 Heidelberg Congress, and was chairman of one of the sessions. In 1908, at the Rome Congress, he gave the talk

*Les mathématiques dans l'enseignement secondaire en Suisse*Ⓣ. This Congress was important for Fehr's career as Guillermo Curbera explains in [1]:-

An idea conceived by David Eugene Smith from New York was then discussed and presented to the general assembly of the congress, where it was approved with lively applause: "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." Thus, the origins of the Commission Internationale de L'Enseignement Mathématique, also known by its English name International Commission on Mathematical Instruction (briefly, ICMI), lay in the attention paid to educational issues at the Rome congress. The commission was linked from its beginning to the journal 'L'Enseignement Mathématique', founded in 1899, which since then has been its official journal.Fehr presented the printed report on the work of the International Commission on the Teaching of Mathematics to the 1912 Congress held in Cambridge, England, as well as presenting the reports of Denmark, Greece, Russia, Finland and Switzerland. Curbera writes [1]:-

The congress expressed its appreciation for the impressive work done by the International Commission on the Teaching of Mathematics, led by its oddly entitled Central Committee (formed by F Klein, A Greenhill, and H Fehr) with the aid of D E Smith. They reported that "every country in nearly every part of the world has contributed in its own department to the Reports for Cambridge - so that there were about 150 different volumes with about 300 articles brought to the Congress."He was Vice-President of the 1924 Congress held in Toronto, and gave the talk

*L'Université et la préparation des professeurs de mathématiques*Ⓣ. For the 1932 Congress held in Zurich he was a member of the Organising Committee. He was President of Section XIII for the 1936 Congress in Oslo.

As well as editing

*L'Enseignement mathématique*Fehr contributed many articles to it. Fluvia Furinghetti writes [3]:-

The main contribution of Fehr as author of articles in the journal was in the field of mathematics instruction. He singled out some central points, such as: (i) innovations in the mathematical programmes and their links with the development of science and technology, as an echo of what was happening in many countries; (ii) the relationship between pure and applied mathematics and its influence on the mathematics teaching; (iii) the education of mathematics teachers; and (iv) new trends in mathematics teaching.As an example, here are the titles of five papers that he published in

*L'Enseignement mathématique*in 1904:

*Un hyperbolographe à liquide*Ⓣ;

*Les études mathématiques à l"École normale de l"Université Columbia de New York*Ⓣ;

*Rapport et décret concernant la nouvelle organisation de l"École Normale supérieure de Paris*Ⓣ;

*Le 3e congrès international des mathématiciens; les expositions de bibliographie et de modèles et instruments*Ⓣ; and

*George Salmon*. These were all written in French except George Salmon's obituary which was written in German.

In 1907 Fehr married Mathilda Elisabetha Merkling.

The outbreak of World War I in 1914 created severe problems for Fehr in his international efforts supporting the teaching of mathematics. He wrote in 1914 in

*L'Enseignement mathématique*:-

The European war carries with it an appreciable impact on international institutions. In the fighting countries and in the neighbouring neutral countries all those whom the nation considers to be able-bodied are in uniform. Thus it becomes practically impossible to continue with activities requiring the support of numerous collaborators. Peaceful activities like ours have to take second place. Furthermore, being in pursuit of a freely chosen common ideal, they demand a willingness for unity, which ought not to be asked of scientists in a period as troubled as the one in which we are living now.Heinrich Behnke spoke about Fehr's contributions to the teaching of mathematics at the symposium dedicated to the memory of Henri Fehr which was held on 1-2 July 1955 in Geneva. For extracts from his talk, see THIS LINK.

Georges Tiercy spoke at the same symposium about Fehr's approach to teaching. For extracts from his talk, see THIS LINK.

On 4 September 1910, at an annual meeting of the Swiss Society of Natural Sciences, in collaboration with Rudolf Fueter and Marcel Grossmann, he founded the Swiss Mathematical Society. He was the second president of the Society from 1913 to 1915, Fueter being the first (1910-1912) and Grossmann the third (1916-1917). Urs Stammbach writes in [10]:-

Over time, the scientific demands of mathematics grew, and the lack of a Swiss publication for scientific mathematical work became painfully obvious. In the course of the 1920s, the plan arose for the Society to found its own journal. The project was prepared by H Fehr together with some former presidents of the Society. Because of Switzerland's multilingualism, it was clear from the start that neither a German nor a French title could be considered; for this reason, a Latin name was sought, with 'Commentarii Mathematici Helvetici' being selected from three different proposals.We followed Fehr's career as far as his appointment as ordinary professor of Algebra and Higher Geometry at the University of Geneva in 1900. Let us briefly note that he was Dean of the Faculty of Science from 1914 to 1922, and again from 1926 to 1928. He was vice-rector of the University of Geneva from 1928 to 1930, then as rector from 1930 to 1932. In 1945 he reached the age of 75 so had to retire. He was appointed as an honorary professor at this time. We see from these details that during World War I, he was the Dean and he was still in post during World War II. In World War I he was president of the Geneva Committee of the Swiss Academic Work for student prisoners of war. For this work Fehr was made Chevalier de la Légion d'honneur and awarded the French Médaillé de la Reconnaissance in recognition for the services he rendered to internees. In 1940, during World War II, he was rector of a Faculty of Science set up in the Berthoud camp where French and Polish internees were held. Lectures were organised for the prisoners.

The author of [5] writes:-

We saw him continuing almost until his last days to come to the University on every occasion and in particular to the Mathematical Library, missing neither a Dies Academicus, nor an opening session, or strolling in his peaceful neighbourhood of Florissant where he welcomed his friends so well. We had become accustomed to seeing him very alert and always finding on his face that expression of gentleness and deep kindness. The University has kept the memory of a dean, a vice-rector and a rector concerned with good administration and admirable management of university funds. It also remembers his personality, attentive to human problems and above all to the intellectual and moral development of his students, who have shown him on many occasions their gratitude for his understanding, kindness and delicacy. With regard to his colleagues, his dedication has been actively exercised on the Pension Fund Committee.As one would expect, given Fehr's passion for teaching, he played a leading role in the Swiss Association of Mathematics Teachers, which he chaired from 1905 to 1909. He also spent 20 years working for the Euler Commission, which was set up to organise the publication of Leonhard Euler's works.

Finally, let us quote from Fehr concerning the qualities he thought a teacher should have [5]:-

It is necessary that the teacher, giving his lesson, be extremely attentive to the visible reactions on the faces of the students; according to the nature of these reactions, he must be able to change completely, and at the same time keeping pace with his explanations; in other words, he must not be a prisoner of the prepared lesson.

### References (show)

- G P Curbera,
*Mathematicians of the World, Unite!: The International Congress of Mathematicians - A Human Endeavor*(A K Peters, 2009). - H Behnke, Symposium dédié à la mémoire de Herri Fehr, Allocution de H Behnke,
*L'Enseignement Mathématique*(2)**1**(1955), 14-20. - F Furinghetti, Mathematical Instruction in an International Perspective: the Contribution of the Journal L'Enseignement Mathématique,
*Monographie de L'Enseignement Mathématique***39**(2003), 19-46 - H Fehr, Obituary: Gabriel Oltramare (1816-1906),
*Actes de la Société Helvétique des Sciences Naturelles***89**(1906), LXXVIII-LXXXIII. - Henri Fehr 1870-1954. Sa vie et son oeuvre,
*L'Enseignement Mathématique*(2)**1**(1955), 4-10. - E Neuenschwander, Henri Fehr,
*Dictionaire Historique de la Suisse DHS*(28 November 2005). https://hls-dhs-dss.ch/fr/articles/043114/2005-11-28/ - G de Rham, Henri Fehr,
*Verhandlungen der schweizerischen naturforschenden Gesellschaft***135**(1955), 334-339. - J Ruffet, Henri Fehr,
*Elemente der Mathematik***10**(1955), 1-4 - G Schubring, Henri Fehr: Zürich 1870 - Geneva 1954,
*International Commission on Mathematical Instruction*(2019). https://www.icmihistory.unito.it/portrait/fehr.php - U Stammbach, Geschichte der Schweizerischen Mathematischen Gesellschaft,
*Swiss Mathematical Society*. https://math.ch/about-sms/HistorySMG.pdf - G Tiercy, Symposium dédié à la mémoire de Herri Fehr, Discours de G Tiercy,
*L'Enseignement Mathématique*(2)**1**(1955), 10-14. - E B Wilson, Review: Application de la méthode vectorielle de Grassmann à la géométrie infinitésimale, by Henri Fehr,
*Bull. Amer. Math. Soc.***7**(5) (1901), 231-233. - M Zack and E Landy, Henri Fehr (1870-1954), in
*M Zack and E Landy (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2014 Annual Meeting in St. Catharines, Ontario, Proceedings of the Canadian Society for History and Philosophy of Mathematics*(Birkhäuser, 2015), 179-185.

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Written by J J O'Connor and E F Robertson

Last Update January 2020

Last Update January 2020