E334 -- Recherches generales sur la mortalite et la multiplication du genre humain

(General investigations on the mortality and the multiplication of the human race)

Summary:

Euler deals with questions of mortality and life expectancy. In particular, he addresses six questions (The questions here are taken from the translation by Richard Pulskamp):

A certain number of men, of whom all are the same age, being given, to find how many of them are probably yet alive after a certain number of years.
To find the probability that a man of a certain age be still alive after a certain number of years.
One demands that probability that a man of a certain age will die in the course of a given year.
To find the term in which a man of a given age is able to hope to survive, of the kind that it is equally probable that he die before this term as after.
To determine the life annuity that it is just to pay to a man of any age all the years, until his death, for a sum which will have been advanced first.
When the interested parties are some infants newly born and when the payment of the life annuities must begin only when they will have attained a certain age, to determine the amount of these life annuities.

Publication:

Originally published in Memoires de l'academie des sciences de Berlin 16, 1767, pp. 144-164
Opera Omnia: Series 1, Volume 7, pp. 79 - 100

Documents Available:

Original publication: E334
E334 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
Richard Pulskamp has put together a fantastic page on Euler's Probability & Statistics, including a lot of interesting background and historical work. The page includes an English translation of E334.
Another English translation has been done by Todd Doucet.
Euler published four other works on life insurance and annuities, listed below:
1. E335, Sur les rentes viageres
2. E403, Des Herrn Leonard Eulers nothig berechnung zur Einrichtung Einer
3. E473, D'un Etablisement publie pour payer des pensions a des veuves fonde sur les principles les plus solides de la probabilité
4. E599, Solutio quaestiones ad calculam probabilitatis pertinentis quantiam disconceges persolvere debeant ut suis haeradibus post utriusque mortem certa argenti summa persolvatur
The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E334 include:
- Samuelson PA., “Resolving a historical confusion in population analysis.” Human Biology, 48 (3), pp. 559-580 (1976).
- Stearns SC., “Life-history tactics - review of ideas.” Quarterly Review of Biology, 51 (1), pp. 3-47 (1976).

Return to the Euler Archive