**Family background.**

Michel Plancherel's father, Donat Plancherel, was born in 1863 in Bussy, a village in the

*district de la Broye*in the

*Kanton Fribourg*, close to Estavayer-le-Lac. Donat Plancherel was a teacher, first in Villaz-Saint-Pierre and later in Bussy. Michel Plancherel was born January 16, 1885, as the first of 8 children. However two of Michel's siblings died in early life. In 1892, the family moved to Fribourg (Freiburg), where Donat Plancherel worked as administrator of the printing plant

*St-Paul*and as an editor of

*La Liberté*, the local newspaper. Simultaneously, he was a professor at the

*Collège St-Michel*(1896-1912) and at the

*École secondaire de jeunes filles*. Michel's character was coined by his father's sense of order, conciliation, affability and directness. His father was appreciated for his hard work, his reports were known as models of clarity and concision.

**Education.**

After moving to Fribourg, Michel was sent to school and attended the *Collège St-Michel* in the section which prepared for ETH Zürich (called Eidgenössisches Polytechnikum at that time). However, Michel chose to study at the faculty of science at the University of Fribourg. There, between 1903 and 1907, he was a student of Mathias Lerch and the Dutchman Mathieu Frans Daniels. Under Lerch's supervision, Michel finished his excellent doctoral thesis *Sur les congruences (mod *2* ^{m}) relatives au nombre des classes des formes quadratiques binaires aux coefficients entier et à discriminant négatif* Ⓣ in 1907. He wrote the thesis in part during his mandatory service in the Swiss army. With a grant of the state of Fribourg, he continued his studies in Göttingen (1907-1909) and Paris (1909-1910). In Göttingen, he followed the courses of Felix Klein, David Hilbert and Edmund Landau, and got to know Herman Weyl, his future colleague at ETH Zürich. At Sorbonne and Collège de France, he met Émile Picard, Henri Lebesgue, Édouard Goursat and Jacques Hadamard.

**Career.**

In 1910, Michel Plancherel became Privatdozent at the University of Geneva, and in 1911 extraordinary professor in Fribourg being the successor of Lerch who went to Brno in 1906. Two years later, in 1913, he was promoted ordinary professor. In the sequel, still being deeply grateful for the grant Fribourg awarded him as a student, he declined offers of the Universities of Bern and Lausanne. Finally, in 1920 he accepted a professorship at ETH Zürich, where he was the successor of Adolf Hurwitz who had died the year before. Plancherel occupied his chair for higher mathematics during the next 35 years, until he retired in 1955. During that time, he declined calls from several universities. The confidence his colleagues put in Plancherel bestowed him the dignity of rector at ETH between 1931 and 1935.

**Teaching.**

At ETH Plancherel gave courses not only for mathematicians but also for students of electrical and mechanical engineering. His teaching was clear although not easy to grasp, since he lectured in a rapid French. In his exams, he was of military severity but always correct and fair. He applied the same high standards and discipline to his students that he used for himself. A list of his PhD students is available below.

**Commitment.**

Michel Plancherel was president of the Swiss Mathematical Society between 1918 and 1919, vice-president of the International Congress of Mathematicians 1932 in Zürich, and president and co-founder of the foundation for the advancement of the mathematical sciences in Switzerland and served in several other institutions (see the list below).

In the Swiss army, Michel Plancherel reached the rank of colonel. In 1939 he was appointed to the General Staff, and during the critical years of World War II, he was the officer responsible for the press and radio division.

After the flight of 550 Hungarian students in 1956 to Switzerland, the rectors of the Swiss universities commissioned Michel Plancherel to raise funds to help these students. Plancherel collected over 2 million Swiss Francs, an immense sum at that time. During the great depression in the 1930's Plancherel was the director of the service for voluntary work, and, after 1948, president of the Swiss *Winterhilfe*, an organization to help people during hard winters. It is reported that Plancherel was deeply enrooted in his Christianity: among other activities he presided the *Mission Catholique Française* in Zürich.

**Private life.**

Michel Plancherel was married to Cécile Tercier, born January 15, 1891 in Adrey, close to Gryère. They became acquainted with each other when she was a student at the nurse's training school in Fribourg. They married on September 8, 1915, and had 9 children together, five boys and four girls. Thirteen grandchildren were the joy of Plancherel's older days, after Cécile died November 24, 1952.

Michel Plancherel died on March 4, 1967: In full possession of his physical faculties and of unbroken intellectual freshness. He was on his way home from a meeting with experts of the federal maturity commission on March 1. As was his habit, he was walking from ETH to his home at Zürichberg, when he was hit by a car. He succumbed his severe injuries on March 4, without having regained consciousness. Michel Plancherel was buried on March 8, 1967, on the cemetery of Fluntern in Zürich.

**Scientific work.**

Michel Plancherel's main research fields were analysis, mathematical physics and algebra. In a series of articles he generalized results in the classical Fourier theory to more general spaces (Hilbert spaces) by investigating various orthonormal systems of functions, their summability and the representation of functions in such systems by Fourier series and Fourier integrals and more general integral transformations. In his work he achieved fundamental results, one of them is the famous Plancherel theorem in harmonic analysis and which is now known in many generalizations (Plancherel measures). He applied his results in the theory of hyperbolic and parabolic partial differential equations.

He also contributed to the solutions to variational problems via Ritz's method and to ergodic theory. In 1913 he gave a proof that mechanical systems cannot be ergodic (see Stephen G. Brush: Milestones in mathematical physics. Proof of the impossibility of ergodic systems: the 1913 papers of Rosenthal and Plancherel.* Transport Theory Statist. Phys*. **1** (1971), no. 4, 287-298). The papers by Rosenthal and Plancherel marked a watershed in the development of the foundations of statistical mechanics, for they brought to a close the classical age of Maxwell, Boltzmann and Ehrenfest and stimulated the development of ergodic theory as a new branch of mathematics.

In algebra Plancherel obtained results on quadratic forms and their applications, to the solvability of systems of equations with infinitely many variables and to the theory of commutative Hilbert algebras (theorem of Plancherel-Godement).

The scientific estate of Plancherel is administered by the library of ETH Zürich (Wissenschaftshistorische Sammlungen der ETH-Bibliothek).

**Article by:** *Norbert Hungerbühler* and *Martine Schmutz* University of Fribourg, Switzerland

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