**Jean Delsarte** was a French mathematician known for his work in mathematical analysis.

- Jean had been a brilliant pupil at primary school in Fourmies where he studied during 1913-14 at the Collège St-Pierre, and later he did outstandingly well in his secondary education at the Lycée Corneille in Rouen.
- In 1922 Delsarte entered the École Normale Supérieure in Paris.
- In particular he met with mathematics student André Weil and the physicist Yves Rocard who were both in the same year as Delsarte.
- After one year they were joined by Henri Cartan, Jean Coulomb who studied mathematical physics, Paul Dubreil, René de Possel and the future philosopher of mathematics Jean Cavaillès.
- Several entering the École Normale in 1924 also joined the group of Delsarte's friends; these included Marcel Brelot, Jean Dieudonné and Charles Ehresmann.
- In the following year Claude Chevalley and Jean Leray entered the mathematics classes adding to the group of friends and future colleagues who combined their talents in a remarkable collaboration as Bourbaki in 1935.
- It was a collaboration in which Delsarte took a leading role and, looking at reports of their meetings, one is struck with the humour, the passion, and the self-belief that these young men of the École Normale displayed.
- Delsarte graduated from the École Normale in 1925.
- Delsarte was to remain on the staff at Nancy for the rest of his career but his first promotion was to Maître de Conférences in October 1928.
- In 1932 Delsarte's outstanding research was recognised with an invitation to address the International Congress of Mathematicians in Zürich.
- Not only did Delsarte teach some outstanding mathematics courses at Nancy but he taught a public course on astronomy from 1929, continuing to give this when at Nancy for the rest of his career.
- It was during his regular visits to Paris during 1934-35 that Delsarte became heavily involved in the Bourbaki project to write a new analysis textbook which expanded into the remarkable Éléments de Mathématique Ⓣ(Elements of mathematics).
- Delsarte cooperated with André Weil and Henri Cartan, both by this time lecturers in Strasbourg, in organising a joint seminar programme between Nancy and Strasbourg.
- He was able to bring many of his outstanding colleagues to Nancy; Paul Dubreil taught there between 1933 and 1937, Jean Leray was apointed part-time lecturer in applied mathematics in 1936 becoming a lecturer in 1937, and then professor of applied mathematics in 1938.
- Jean Dieudonné was appointed as a lecturer in Nancy, also in 1938.
- There was another aspect of Delsarte's work during the 1930s which is quite unusual for a young mathematician, for he involved himself in several major administrative roles.
- Already trained as an artillery officer during his time at the École Normale Supérieure, Delsarte was put in charge of a unit in September 1939 which he commanded until August 1940.
- Delsarte now went to the Faculty of Sciences at Grenoble to replace Jean Favard, the professor of mathematics, who had been captured by the Germans and was being held as a prisoner of war in Germany.
- The safest course for Delsarte would have been to remain in the comparative safety of Grenoble as long as possible, but he did not choose the easy option, returning instead in September 1941 to Nancy which was in a dangerous closed area.
- While the war slowly ran its painful course, Delsarte continued to undertake duties for French mathematics both in Nancy and in Paris at the Centre National de la Recherche Scientifique where he served on a pure mathematics commission, and also as an examiner for entry to various Écoles.
- He repeated this after the war ended bringing Laurent Schwartz (1945-1952), Roger Godement (1946-1955), Jean-Pierre Serre (1954), and Jacques-Louis Lions (1954-1964).
- Delsarte's involvement with Bourbaki, and the continual appearance of members of Bourbaki at the Institute, led to widespread belief that the Élie Cartan Institute was the Bourbaki group.
- Let us look at some of Delsarte's mathematical contributions.
- Delsarte worked in analysis extending work on series expansions due to Whittaker and Watson.
- One of the most surprising of Delsarte's results was a generalisation of a result due to Gauss.
- Delsarte showed that fff is harmonic under the weaker condition that f(x)f (x)f(x) is the mean value on two spheres centre xxx, radius aaa and bbb, provided a/ba/ba/b does not take one of a particular finite set of values.
- Other important work by Delsarte was on transmutation operators.
- Although Delsarte remained permanently on the staff at Nancy all his life, he did lecture in many different universities from 1947 onwards, particularly ones in India, North America and South America.
- Delsarte had originally intended to spend four years in Japan but cut short his visit, partly due to health problems, in particular his eyesight was rapidly deteriorating.
- Despite his health problems, Delsarte taught the mechanics course in 1967-68.
- Delsarte had, of course, always advocated educational reforms, but he did not support the extreme methods adopted by some students.
- Near the end of September 1968 Delsarte suffered a heart attack.
- Delsarte received many honours and we have already mentioned some above.

Born 19 October 1903, Fourmies (Nord), France. Died 28 November 1968, Nancy, France.

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Astronomy, Bourbaki

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive