Duvillard: an important contributor to social mathematics

Emmanuel-Etienne Duvillard de Durand (1755-1832), a mathematician and the first French actuary, contributed significantly to social mathematics, particularly through his mathematical model of mortality. INED has published the transcription of a previously unknown manuscript that offers a brilliant synthesis of his work in this area.


Duvillard, a disciple of Condorcet and appreciated by Laplace, Lagrange and Legendre, was set on giving population statistics a probabilistic dimension. The manuscript recently published by INED, written in 1813, takes an approach to mortality in line with the work of the great mathematician Lambert. Duvillard also attempted to apply probability calculation principles to population science, thereby laying the theoretical foundations for precise evaluation of the limits within which the number of individuals making up a population may be estimated with some degree of probability. He set out to construct an equation that would accurately represent the dying out of a human generation. 


The simplest formula he could find to express the mortality process was:

  • z represents the number of survivors
  •  x is a given age
  •  i is a mortality measure (“ratio of the dead to the living” divided by the unit)
  • y expresses variation in the force of mortality at each age.

Giorgio Israel, a member of the International Academy of the History of Science and the executive committee of the International Commission on the History of Mathematics and director of the Centro Interdipartimentale di Ricerca in Metodologia delle Scienze, University of Rome-La Sapienza, and Luca Dell’Aglio, a historian of sciences and professor of mathematics at the University of Calabria, discovered these archives and patiently deciphered and transcribed the manuscript, thereby accomplishing a full-fledged labour of memory, with the firm intention of doing justice to an extraordinary figure and giving him the place of honour in the history of science that he so richly deserves.