The 100 years between 1650 and 1750 saw remarkable progress across the broad spectrum of human endeavour and societal development. The Scientific Revolution was in full flow, with fundamental breakthroughs occurring in mathematics, physics, astronomy and other branches of science, as well as in the development of the scientific method itself. In Britain, the Royal Society, founded during Charles Il’s reign, had established itself as a significant arbiter of intellectual endeavour by the early eighteenth century. The Enlightenment and the age of reason brought important developments in philosophy and economics that would further influence and challenge society.
From the perspective of British finance, London emerged particularly strongly from this period. The City of London transformed itself from being a laggard of financial sophistication relative to practices in cities such as Amsterdam, Antwerp and Florence into a leading banking and insurance centre, with a respected Bank of England.
The developments in probability and life contingencies over the period can be viewed as intrinsic parts of these broader scientific, economic and industrial developments. Mathematical probability fully emerged as a branch of applied mathematics over this period, and its early development fully represented its holistic nature, involving contributions from disciplines as varied as jurisprudence and number theory. The use of statistical population data to model mortality and analyse its implications for the pricing of life contingencies developed contemporaneously. These early forms of statistical analysis pre-dated a rigorous theory of statistical inference, and did not directly rely on the theoretical developments in mathematical probability that were occurring at the same time. The two disciplines overlapped, but were generally each developed by a different cast of characters. Occasionally, however, titans such as de Moivre straddled both these disciplines and made substantial and lasting contributions to both.
Up until 1750, the developments in thinking in probability and life contingencies were pregnant with possibility, but were still awaiting application to real life. The tiny level of demand for short-term life assurance that existed during the first half of the eighteenth century limited the incentive to develop practical applications of the emerging actuarial science. The application of this new discipline would require a societal change in demand for mortality risk transfer, and a form of life contingency product that could meet the needs of the growing, prudent and increasingly wealthy Victorian middle class of the industrial revolution.
In the field of probability, there was an awareness of the need for a theoretical breakthrough to make it fully applicable to scientific endeavour. Mathematical probability had been limited to finding probability distributions of random samples of populations with known properties. The new scientific method would increasingly produce quantitative observational data from which inferences would be made: modern thinking increasingly called for inductive, rather than deductive, reasoning. The inversion of mathematical probability into statistical inference—to make rigorous statements about populations based on sample data observations, rather than to make statements about sample probabilities based on known or assumed population characteristics—was a problem whose solution had so far evaded all the impressive group of thinkers who had tackled probability.