Marcel-Paul "Marco" Schützenberger (24 October 1920 – 29 July 1996) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and Doctor of Medicine. He worked in the fields of

formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symb ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

, and

information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

.Herbert Wilf, Dominique Foata, ''et al.'',
In Memoriam: Marcel-Paul Schützenberger, 1920-1996
," ''Electronic Journal of Combinatorics'', served from University of Pennsylvania Dept. of Mathematics Server, article dated 12 October 1996, retrieved from WWW on 4 November 2006. In addition to his formal results in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, he was "deeply involved in struggle against the

votaries Religious vows are the public vows made by the members of religious communities pertaining to their conduct, practices, and views. In the Buddhism tradition, in particular within the Mahayana and Vajrayana tradition, many different kinds of re ...

of eo-arwinism",Foata, Dominique, "In Memoriam," ''op. cit.'' a stance which has resulted in some mixed reactions from his peers and from critics of his stance on

evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

. Several notable theorems and objects in mathematics as well as

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

bear his name (for example Schutzenberger group or the

Chomsky–Schützenberger hierarchy In formal language theory, computer science and linguistics, the Chomsky hierarchy (also referred to as the Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by ...

Paul Schützenberger Paul Schützenberger (23 December 1829 – 26 June 1897) was a French chemist. He was born in Strasbourg, where his father Georges Frédéric Schützenberger (1779–1859) was professor of law, and his uncle Charles Schützenberger (1809–1881) ...

was his great-grandfather. In the late 1940s, he was briefly married to the psychologist Anne Ancelin Schützenberger.

Contributions to medicine and biology

Schützenberger's first doctorate, in medicine, was awarded in 1948 from the ''Faculté de Médecine de Paris''.Schützenberger, Marcel-Paul,
Contribution à l'étude statistique du sexe à la naissance
', Doctoral thesis, ''Faculté de Médecine de Paris'', 2 July 1948. His doctoral thesis, on the statistical study of biological sex at birth, was distinguished by the Baron Larrey Prize from the

French Academy of Medicine French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ...

.Besson, Jaques, "
La quête de M. P. Schützenberger en Médecine et Biologie
'," dated March 2001, retrieved on 5 November 2006. Biologist Jaques Besson, a co-author with Schützenberger on a biological topic, while noting that Schützenberger is perhaps most remembered for work in pure mathematical fields, credits him for likely being responsible for the introduction of statistical sequential analysis in French hospital practice.Schützenberger, Marcel-Parul, "
Une application de l'analyse séquentielle
'," ''Semaine des Hôpitaux de Paris'', Vol. 25 No. 60, pp. 2562–2564, 14 August 1949.

Contributions to mathematics, computer science, and linguistics

Schützenberger's second doctorate was awarded in 1953 from Université Paris III. This work, developed from earlier results is counted amongst the early influential French academic work in information theory. His later impact in both

linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...

and combinatorics is reflected by two theorems in formal linguistics (the

Chomsky–Schützenberger enumeration theorem In formal language theory, the Chomsky–Schützenberger enumeration theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about the number of words of a given length generated by an unambiguous context-free grammar. The ...

Chomsky, Noam & Schützenberger, Marcel-Paul
The Algebraic Theory of Context-Free Languages
, in ''Computer Programming and Formal Systems'', P. Braffort and D. Hirschberg (eds.), North Holland, pp. 118-161, 1963. and the

Chomsky–Schützenberger representation theorem In formal language theory, the Chomsky–Schützenberger representation theorem is a theorem derived by Noam Chomsky and Marcel-Paul Schützenberger about representing a given context-free language in terms of two simpler languages. These two si ...

), and one in combinatorics (the Schützenberger theorem). With

Alain Lascoux Alain Lascoux (17 October 1944 – 20 October 2013) was a French mathematician at the University of Marne la Vallée and Nankai University. His research was primarily in algebraic combinatorics, particularly Hecke algebras and Young tableaux. L ...

, Schützenberger is credited with the foundation of the notion of the

plactic monoid In mathematics, the plactic monoid is the monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified with semistandard Young tableaux. It was discovered by (who called it the tableau algebra ...

,Lascoux, Alain & Schützenberger, Marcel-Paul, "
Le monoïde plaxique
'," in ''Noncommutative structures in algebra and geometric combinatorics (Naples, 1978)'', volume 109 of ''Quad. Ricerca Sci.'', pp. 129–156, CNR, Rome, Italy, 1981. reflected in the name of the combinatorial structure called by some the Lascoux–Schützenberger tree. In

automata theory Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματο� ...

, Schützenberger is credited with first defining (what later became known as)

weighted automata In theoretical computer science and formal language theory, a weighted automaton or weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers. Finite-state ...

, the first studied model of automata which compute a quantitative output. The mathematician Dominique Perrin credited Schützenberger with "deeply nfluencingthe theory of semigroups" and "deep results on rational functions and transducers", amongst other contributions to mathematics.

Offices, honors, and recognitions

;Professorships and other teaching * Professor in the Faculty of Sciences at the

University of Poitiers The University of Poitiers (UP; french: Université de Poitiers) is a public university located in Poitiers, France. It is a member of the Coimbra Group. It is multidisciplinary and contributes to making Poitiers the city with the highest studen ...

(1957–1963) * Lecturer in the Faculty of Medicine at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

(1961–1962) * Director of Research at the

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ...

(1963–1964) * Professor at the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

(1964–1970) * Professor in the Faculty of Sciences at the

University of Paris VII A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

(1970-until his death in 1996) ;National honors * In 1988, after having been a ''Correspondant'' since 1979, Schützenberger was made a full ''Membre'' of

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

. ; Posthumous recognitions After his death, two journals in theoretical mathematics dedicated issues to Schützenberger's memory. He was commemorated in this manner by ''

Theoretical Computer Science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...

'' in 1998"Special issue: papers dedicated to the memory of Marcel-Paul Schützenberger", ''Theoretical Computer Science'', Nivat, M. & Perrin, Dominique (eds.), Vol. 204, Issues 1-2, September 1998. and again by the ''

International Journal of Algebra and Computation The ''International Journal of Algebra and Computation'' is published by World Scientific, and contains articles on general mathematics, as well as: * Combinatorial group theory and semigroup theory * Universal algebra * Algorithmic and computatio ...

'' in 1999."Special Issue: Dedicated to the Memory of Marcel-Paul Schützenberger," ''International Journal of Algebra and Computation'', Vol. 9, Nos. 3-4, June & August 1999. Issue at URL: https://www.worldscientific.com/toc/ijac/09/03n04 The mathematician

David Berlinski David Berlinski (born 1942) is an American author who has written books about mathematics and the history of science as well as fiction. An opponent of evolution, he is a senior fellow of the Discovery Institute's Center for Science and Culture ...

provided this dedication in his 2000 book ''The Advent of The Algorithm: The Idea that Rules the World'': À la mémoire de mon ami . . M. P. Schützenberger, 1921-1996.

Trivia

* The character "Dr. Schütz" in

Boris Vian Boris Vian (; 10 March 1920 – 23 June 1959) was a French polymath: writer, poet, musician, singer, translator, critic, actor, inventor and engineer who is primarily remembered for his novels. Those published under the pseudonym Vernon Sulliva ...

's 1948 novel, ''Et on tuera tous les affreux'', is said to have been inspired by Schützenberger.See: http://www.astroline.ro/P_Marcel-Paul_Schutzenberger__145.html * Together with many of his students, Schützenberger is one of the contributors of the pseudonymous collective

M. Lothaire M. Lothaire is the pseudonym of a group of mathematicians, many of whom were students of Marcel-Paul Schützenberger. The name is used as the author of several of their joint books about combinatorics on words. The group is named for Lothair I.. ...

Works

For the complete list of his papers, see
Papers
* ''De la diversité de certains cancers''. Pierre Florent Denoix, Paris (1954)/''About the diversity of some cancers'' * ''Théorie géométrique des polynômes eulériens'', with

Dominique Foata Dominique Foata (born October 12, 1934) is a mathematician who works in enumerative combinatorics. With Pierre Cartier and Marcel-Paul Schützenberger he pioneered the modern approach to classical combinatorics, that lead, in part, to the current ...

, Berlin, Heidelberg, New York, Springer (1970)/''Geometric theory of

Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

polynomials'' * ''Triangle de pensées'', with

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vande ...

and

André Lichnerowicz André Lichnerowicz (January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a noted France, French Differential geometry and topology, differential geometer and Mathematical physics, mathematical physicist of Poland, Polish desc ...

, Paris, O. Jacob ; Saint-Gély du Fesc : Espace 34 (2000)/''Triangle of thoughts'' * ''Les failles du darwinisme'', La Recherche, n°283 (January 1996)/''The miracles of darwinism'' * ''Œuvres complètes'', edited by

Jean Berstel Jean Berstel (born 1941) is a French mathematician and theoretical computer scientist known for his contributions to combinatorics on words and formal language theory. He is a currently a professor emeritus at the University of Marne-la-Vallée. ...

and

Dominique Perrin Dominique Pierre Perrin (b. 1946) is a French mathematician and Theoretical computer science, theoretical computer scientist known for his contributions to coding theory and to combinatorics on words. He is a professor of the University of Marne-la ...

, Institut Gaspard-Monge, Université Paris-Est (2009)/''Complete Works'' The Complete Works of Marcel-Paul Schützenberger
Complete Works

References and notes

External links

Publications of Marcel-Paul Schützenberger
(A list of 266 works authored or co-authored by Schützenberger from 1943 to 2000.) * * * {{DEFAULTSORT:Schutzenberger, Marcel-Paul 1920 births 1996 deaths 20th-century French mathematicians French people of German descent 20th-century French physicians Combinatorialists French statisticians French information theorists French National Centre for Scientific Research scientists Members of the French Academy of Sciences University of Poitiers alumni University of Poitiers faculty Scientists from Paris University of Paris alumni