Died: 20 June 1963 in Paris, France

**Raphaël Salem** was born in Saloniki, (now in Greece) to Jewish parents of Spanish origin. His father, Emmanuel Salem, was a well known lawyer who dealt with international problems while his mother was Fortunée Salem. Raphaël was brought up in a truly international atmosphere for he lived in the Ottoman Empire, in a Jewish family who followed the Spanish traditions of their ancestors but spoke Italian and French at home. From this mixture of influences it is perhaps surprising that he attended an Italian school in Saloniki.

When Salem was 15 years old, his family moved to France and set up home in Paris. Salem attended the Lycée Condorcet for two years and then entered the Law Faculty of the University of Paris. It is not entirely clear how much the choice of law was that of Salem or that of his father. Certainly Salem's father wished his son to follow in his footsteps, and another factor here is that Salem always had a great respect for his father. It may well have been, therefore, that he did not take this course of study unwillingly, but at the same time it was clear that his interests were not in law but rather they were in mathematics and engineering.

Of course there were few better places in the world to study mathematics than Paris, and Salem was soon taking mathematics courses with Hadamard. The tension between his interests and his official course of study became greater as the course progressed. He received his law degree, graduating as Licencié et lauréat in 1919. He even began working for a doctorate in law but quickly decided that he had to change direction to science, which he had been studying for years in parallel to his work in law.

He received his Licencié ès sciences from the Sorbonne, also in 1919, then worked for a degree in engineering. He received the degree of Ingénieur des Arts et Manufactures from the École Centrale in 1921. Now, having made the change away from law to science and engineering one might have expected Salem to seek a profession using these qualifications, but in fact he went into banking. This again may well have been as a result as pressure from his family or he may just have been happy to make money in banking while he regarded mathematics as a hobby to enjoy. Whenever he had free time in the evenings he worked on Fourier series, a topic which interested him throughout his life.

He worked for the Banque de Paris et des Pays-Bas from 1921. In 1923 he married Adriana and they had a daughter and two sons. Zygmund writes in [3]:-

In spite of his absorbing career Salem's interest in mathematics, which he acquired in his early studies, grew stronger and with time developed into an interest in mathematical research. He was spending on it most of his spare time, working mainly in the evenings. He became attracted to Fourier series, and the interest in the subject remained undiminished throughout his life. ... Although he read some of the current literature on Fourier series, he apparently worked all alone...

He did have some connections with Paris mathematicians, however, particularly with Denjoy who may have influenced him towards Fourier series. His career in the bank progressed well and in 1938 he became one of the managers of the Banque de Paris et des Pays-Bas. It was around this time, with a deteriorating political situation, that Salem finally made the decision to change career and become a mathematician. Denjoy was certainly a factor in this decision, for he well realised Salem's potential as a mathematician and tried to persuade him to take a doctorate in mathematics. Another factor was the arrival of Marcinkiewicz in Paris in the spring of 1939. Salem collaborated with this brilliant young Polish mathematician and of the mathematics papers he wrote while working for the bank, the one he wrote with Marcinkiewicz was his only joint work.

World War II broke out in September 1939. Salem was called up for military work and attached to the Deuxième Bureau of the General Staff of the French Army. He had already taken Denjoy's advice and submitted his published papers, with some minor improvements, for a doctorate, and this was awarded in 1940. As part of his military duties, Salem was sent to England to assist the Head of the Franco-British Coordination Committee but he was demobilised in June 1940. By this time his family had managed to escape from France and they were in Canada. Salem left England in the autumn of 1940 and emigrated to the United States where he settled in Cambridge, Massachusetts. He went to Cambridge, Massachusetts via Canada where he spent a short time and met up with his family. In 1941, he was appointed as a lecturer in mathematics at the Massachusetts Institute of Technology.

It was very fortunate for Salem that he had obtained his doctorate in mathematics in the previous year from the University of Paris. It is hard to see how he would have been appointed without this mathematics qualification for he had no experience as a lecturer. This did not seem a problem, however, for [3]:-

.. he was a born teacher and he enjoyed teaching though initially it was an effort for him to teach in English. He had a style of his own which combined verve and naturalness, precision and elegance. The way he could explain essential things without going into calculation were always admired by people attending his lectures and appreciating the difficulties inherent in mathematical presentations.

He was in the right place to carry on with his interest in Fourier series, and he collaborated on this topic with Norbert Wiener and Zygmund (with whom he wrote joint papers). Zygmund, reviewing [2], puts Salem's contributions to Fourier series into perspective:-

For the last few decades two problems were central in the field: convergence almost everywhere of Fourier series and the nature of the sets of uniqueness for trigonometric series. With recent results ... the first problem is essentially solved. But the second problem still challenges, in spite of progress here. Much of this progress is due to[Salem]and people influenced by his ideas, and acquaintance with his work seems to be a prerequisite for those who would like to contribute to the solution of the problem. Another direction in which[Salem]did a lot was applications of the calculus of probability to Fourier series and, curiously enough, this has connection with problems of uniqueness. Moreover, it seem that, far from being incidental, as it might have appeared some30or so years ago, the calculus of probability is becoming a standard method of attacking problems of trigonometric series. Going through the papers of[Salem]one sees this growing role of the calculus of probability. Incidentally, the reader will greatly appreciate the elegance and lucidity of[Salem's]style.

We should also note that Salem introduced the idea of a random measure into harmonic analysis. This began an area of research which is still very active today.

Returning to details of Salem's life we should emphasise how difficult the war years were for him. His father died in Paris in 1940 while his mother, his sister, his sister's husband, and his sister's son, were all arrested and deported by the Nazis to a concentration camp where they died. Salem's older son however, survived the war. He enlisted in the free French Forces and took part in Allied landings in the South of France in 1944.

Salem was rapidly promoted at MIT where he became an assistant professor in 1945, and an associate professor in 1946. However, happy as he was in the United States, once the war had ended and his country was again free, Salem longed to return to France. It is worth noting how, despite his multi-national upbringing, he was a Frenchman with a true love of France. For some years he split his time between Paris and Cambridge, Massachusetts, spending one semester in each. In 1950 he was appointed Professor at MIT and also Professor at the University of Caen in France. He continued to split his time between the two countries until 1958 when he was appointed as Professor at the Sorbonne. He lived in Paris from that time on until his death.

After Salem died his wife established an international prize for outstanding contributions to Fourier series [1]:-

The list of those who have received the prize, first awarded in1968, is impressive and testifies to the explosive activity in this area of mathematics.

As to Salem's personality we quote from [3]:-

[

Salem's]intellectual brilliance ... attracted people, the more so that it was accompanied by personal charm and natural friendliness. He had a great sense of humour, a vivid way of speaking and was always interested in conversation. But he also had a warm personality and was sensitive to human hardships ... he extended[hospitality]easily and it was gladly accepted by his many friends...

Finally we should mention his interests outside mathematics. He loved music and played the violin, preferring to play in quartets. He was also interested in the arts, particularly French and Italian literature, while his sporting interests were skiing and horse riding.

**Article by:** *J J O'Connor* and *E F Robertson*

**September 2001**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Salem.html]