In this talk we will don't speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange's reception at the nineteenth Century. "Who read Lagrange at this Times?", "Why and How?", "What does it mean being a mathematician or doing mathematics at this Century" are some of the questions of our conference. We will give some elements of answers and the case Lagrange will be a pretext in order to explain what are doing historians of mathematics: searching archives and – thanks to a methodology – trying to understand, read and write the Past.
Lagrange - mathematical press - complete works - bibliographic index of mathematical sciences (1894-1912) - Liouville - Boussinesq - Terquem[-]

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.[-]

The most important works of the young Lagrange were two very learned memoirs on sound and its propagation. In a tour de force of mathematical analysis, he solved the relevant partial differential equations in a novel manner and he applied the solutions to a number of acoustic problems. Although Euler and d'Alembert may have been the only contemporaries who fully appreciated these memoirs, their contents anticipated much more of Fourier analysis than is usually believed. On the physical side, Lagrange properly explained the functioning of string and air-column instruments, although he did not accept harmonic analysis as we now understand it.
Lagrange - acoustics - propagation of sound - harmonic analysis - Fourier analysis - vibrating strings - organ pipes[-]

One fairly standard version of the Riemann Hypothesis (RH) is that a specific probability density on the real line has a moment generating function (Laplace transform) that as an analytic function on the complex plane has all its zeros pure imaginary. We'll review a series of results that span the period from the 1920's to 2018 concerning a perturbed version of the RH. In that perturbed version, due to Polya, the log of the probability density is modified by a kind of mass term (in quantum field theory language). This gives rise to an implicitly defined real constant known as the de Bruijn-Newman Constant, Lambda. The conjecture and now theorem (Newman 1976, Rodgers and Tau 2018) that Lambda is greater than or equal to zero is complementary to the RH which is equivalent to Lambda less than or equal to zero; The conjecture/theorem is a version of the dictum that the RH, if true, is only barely so. We'll also briefly discuss some connections with quantum field theory and the Lee-Yang circle theorem.[-]

In his 1947 essay, Tjalling Koopmans criticized the development of an empirical science that had no theoretical basis, what he referred to as measurement without theory. The controversy over the status of relations based on mere statistical inference has not ceased since then. Instead of looking for the contemporary consequences, however, I will inquire into its early beginnings. As early as the 1900s, Walras, Pareto and Juglar exchanged views on the status of theory and its relation to economic data. These private exchanges acquired the status of scientific controversy in the aftermath of the First World War, with the dissemination of Pareto's work. It is precisely this moment that I will try to grasp, when engineers began to read and write pure economic treatises, questioning the relation between theory and empirical problems, the nature of their project and the expectations that the subsequent development of economics has tried to fulfill.

Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.[-]

In order to explore the advances made on the economic issue of business cycles, I will present the work of the American economist Henry Ludwell Moore, who published four works on the question between the years 1911 and 1923. Within this framework, I will introduce several issues, such as the duality of empirical and theoretical approaches, the causal and semiological interpretations of the correlation, the notion of the ceteris paribus law in economics, the notion of non-probabilistic statistical mathematics, the development of the notion of the dynamic model at the end of the 1920s, the diverse analysis techniques of chronological series and their artefacts. I will also make reference to the contributions of other actors in this field.

Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.[-]