From Chapel Hill to Lotharingia

The note written by Herb Wilf [1] in memory of Marcel-Paul Schützenberger summarizes the superb intellectual and human qualities of the great master, mentor, friend that many of us have recently lost. He was indeed a versatile mind, keeping abreast of the scientific developments of his time. As Moshe Flato wrote in his contribution to ``Mots" [2, p. 70] he was ``one of the most pluridisciplinary scholars I had ever known." His discourse was full of unexpected images and paradoxes; he never had a banal view on any subject, but always developed a well-structured and original reasoning in which plenty of new ideas flourished naturally. He undeniably was a great master of the Word. A conversation with him was an enrichment in which all kinds of subjects would be discussed: Mathematics, Physics, Biology, Philosophy, Political Science, ... , or simply l'air du temps.

It is a shock to realize that my own conversation with him that started some thirty-six years ago is now interrupted. I met him for the first time in Chapel Hill, North Carolina, back in 1960. He was not yet forty. The late Professor Raj-Chandra Bose, who had just constructed, jointly with Dijen Ray-Chaudhury, the celebrated infinite family of error-correcting codes that carry their names, had invited him to spend a year in Chapel Hill. Marco had known the great period of the M.I.T. in the late fifties, when the pioneering work of Claude Shannon initiated Information Theory and he himself with Noam Chomsky made the theory of context-free languages accessible to linguists.

There was indeed at that time a demand for structured information codes that would be easy to conceive, analyze and implement. One answer was the concept of block code of finite length. It has kept active several generations of mathematicians and electrical engineers ever since. Marco did not work in that area proper, but rather laid down the foundations of what we call the variable-length codes in the context of formal languages. Bose thought that his vision of the problems related to Coding Theory in general would be of great help to his school in Chapel Hill. Marco gave several seminars there on the theory of formal languages, in his personal way, unorthodox, colorful, witty. In fact, the best of his teaching was given after class, around a cup of coffee, within a small group. Fortunately, he was never asked to address a big Freshman Calculus class!

In 1961-62 he joined the Harvard Medical School and returned to the Faculté des Sciences in Poitiers (in France the University, as such, was created in 1968 by aggregating several independent Faculties). He got a permanent position in Paris in 1964, first as a research director at the C.N.R.S., then as a professor at the Faculté des Sciences that later split into the so-called Université Paris VI and Université Paris VII.

I was very privileged to meet him again in Paris after my military service in 1963. My Doctorat d'Etat was really completed thanks to him and thanks to his outstanding guidance. A visit to his place could last the whole afternoon and the whole evening, as it was still the case last January when I saw him for the last time.

In the late sixties and early seventies he built a solid reputation in Paris as the world figure in the theory of Formal Languages and Theoretical Computer Science. Among his doctoral students at that time one finds Maurice Nivat, Jean-François Perrot, Maurice Gross, Jean Berstel, Robert Cori, Gérard-Xavier Viennot, André Lentin, Michel Fliess, Dominique Perrin. The list is not complete, for he had many other disciples in France and overseas.

We can wonder why he did not write himself the reference book on Formal Languages. The work was done instead by Samuel Eilenberg [3] who says in the preface of his first volume: ``The reader will find that the name of M. P. Schützenberger is often mentioned as author (or coauthor with me) of many of the new results or proofs that appear in this volume; most have not been previously published. However, his contributions went much beyond that; virtually every phase of the development presented here was endlessly discussed with him."

In the seventies he was elected corresponding member of the French Academy of Sciences. It was clear that this recognition on the part of the Establishment pleased him, although he kept joking that the main advantage of the appointment was the privilege of making speeches without being interrupted on the first occasion!

In 1988 he was promoted full member of the Academy. I remember asking him how he felt to belong to that respectable Assembly. The reply was: ``Well, now Jean-Pierre Serre shakes hands with me!"

One of his deep convictions was that most identities in Classical Analysis were simply accidents and could be derived by ad hoc geometric methods. Our monograph on the Eulerian polynomials [4] was written in that spirit. It is true that a good bunch of formulas in Special Functions can now be proved combinatorially, that is, sequences of finite structures have been found in which the underlying identity simply reflects the action of a transformation in the geometry of those structures.

The first great paper that initiated the combinatorial theory of symmetric functions and the algebra of tableaux goes back to 1963 (``Quelques remarques sur une construction de Schensted" [5]), the second one being entitled ``La correspondance de Robinson" [6] that was published in the proceedings of The Strasbourg Table Ronde in 1976. In 1978 he started a fruitful collaboration with Alain Lascoux that lasted until the week of his death. In the list of Marco's publications up to 1988 that appeared in [2] there are already as many as fifteen joint papers. Some of those articles are rather rough reading. Perhaps. However their contribution is significant: the integrality of the Foulkes polynomials, the study of Schubert polynomials, the tableau algebras derived from the jeu de taquin, ...

In 1990 Alain Lascoux and Dominique Perrin prepared an original Festschrift dedicated to Marco, the ``Mots" volume. We can read in the preface: ``This volume is a homage to Marcel-Paul Schützenberger offered by his friends and disciples. Although the actual contributors form a restricted subset of the total set of his friends, students, disciples and admirers, the diversity in their contributions shows that they belong to a great variety of species. The outcome is this multi-faceted book that includes mathematical reasonings as well as historical analysis." Our duty is now to make the book accessible to a larger public, perhaps by means of Electronic Publishing.

As Herb mentioned in his note, Marco was deeply involved in his struggle against the votaries of Darwinism. His other bête noire was Artificial Intelligence. When he was asked to contribute to the volume ``Le Savant et la Foi" [7] in which ``nineteen scientists were invited to express why they were Christian and how they made their scholarly work compatible with their faith" Marco sent a paper entitled ``Intelligence artificielle, néo-darwinisme et principe anthropique." The paper is not a theological essay, but a convincing analysis of the failures of to-day's cosmological theories, neo-Darwinism, with or without the help of Artificial Intelligence!

Was Marco a believer? We had many discussions about religion in the past, but they are too personal to be reported in this note. In any case his family was of the Lutheran persuasion. At the end of his life he had reached a state of serenity. From his hospital bed he told me last June: ``Mon pauvre Dominique, je suis tout déglingué." (``I am an utter wreck!"). Alain Lascoux stayed with him to the very last; he will present the tenor of their ultimate joint work during our next Séminaire Lotharingien in Bellagio.

The name of Schützenberger is well-known in Alsace. One of his ancestors was the great chemist Paul Schützenberger who discovered the cellulose acetates. Like many of the pro-French Alsatian families, his great-grandfather left Strasbourg just after the Franco-Prussian War in 1871.

He is survived by his daughter Hélène who has been a great comfort to him when he became seriously ill. His wife Hariati died in 1993, and his son Mahar was killed in a car accident back in 1980 at the age of twenty-three. One the photos shows Marco with four-year-old Mahar on the ferry to Cape Hatteras.

One never dies as long as their memory lives with us.

[1] Herb Wilf, Marcel Paul Schützenberger 1920-1996

(http://ejc.math.gatech.edu:8080/Journal/Volume_3/Html/v3i1f1.html)

[2] M. Lothaire. Mots (Mélanges offerts à M.-P. Schützenberger), Hermès, Paris, 1990.

[3] Samuel Eilenberg. Automata, Languages, and Machines, vol. 1. Academic Press, New York, 1974.

[4] Dominique Foata et Marcel-Paul Schützenberger. Théorie des polynomes Eulériens, Lecture Notes in Math. 138, Springer-Verlag, Berlin, 1970.

[5] M.-P. Schützenberger. Quelques remarques sur une construction de Schensted, Math. Scandinavica, vol. 12, 1963, p. 117-128.

[6] M.-P. Schützenberger. La correspondance de Robinson, Lecture Notes in Math., no. 579, Springer-Verlag, Berlin, 1977, p. 59-113.

[7] Jean Delumeau, ed. Le savant et la Foi, Flammarion, Paris, 1989.

Dominique Foata

Strasbourg, September 20, 1996.