Abstract : Benoît Mandelbrot and Marcel-Paul Schützenberger first met at the Institut Poincaré in Paris in the 1950s, when both were working on topics in the then novel field of information theory. Their paths crossed again at the other end of the Atlantic on the East Coast where they were drawn into discussions on formal models of language. This was an important topic in the U.S. because these models could be useful for automatic translation, and for automatic coding of information and of programs for digital computers. In the late 1950s, a vivid debate raged whether probabilistic models or rather grammatical or rule-based models were appropriate for describing (natural) language, with notably Noam Chomsky and his students attacking the probabilistic approach. As Mandelbrot arrived in the U.S., the probabilistic model of language he had developed in his PhD became part of the discussion. Also Schützenberger got involved in the debate with his early work on coding theory. Eventually, Chomsky's arguments against probabilistic models would prevail. As a result, Mandelbrot's research went into a slightly different direction that would bring him to fractal geometry, whereas Schützenberger, via his frequent visits to the U.S., became one of the architects of the mathematics behind formal languages and coding theory.

Keywords : mathematical models for language; Mandelbrot; Schützenberger; Chomsky; coding theory