The translation of 17th-century bubonic plague mortality records into the mathematical foundations of modern actuarial science is one of the most fascinating intellectual leaps in history. It represents a paradigm shift where data collected out of public terror was transformed into a tool for predicting the future, laying the groundwork for demography, epidemiology, and the life insurance industry.
Here is a detailed explanation of how this transformation occurred.
1. The Raw Material: The London Bills of Mortality
In the late 16th and early 17th centuries, London was repeatedly ravaged by outbreaks of the bubonic plague. To monitor the spread of the disease, the City of London began publishing the Bills of Mortality.
These were weekly summaries of births (christenings) and deaths (burials) across the city's parishes. The data was gathered by "searchers"—typically elderly women tasked with viewing corpses to determine the cause of death. Initially, the sole purpose of the Bills was to serve as an early warning system. If the number of plague deaths spiked, the wealthy would flee the city. For decades, these records were viewed merely as a grim tally of the dead.
2. The Catalyst: John Graunt’s Epiphany
The transformation of these records into a mathematical science occurred in 1662, thanks to a London haberdasher named John Graunt. Despite having no formal scientific training, Graunt possessed a profoundly analytical mind. He collected decades' worth of the Bills of Mortality and published a groundbreaking book: Natural and Political Observations Made upon the Bills of Mortality.
Graunt did something no one had done before: he looked past the terrifying spikes of plague deaths and analyzed the data as a whole. In doing so, he discovered statistical regularity. Graunt realized that while individual deaths were unpredictable, death on a societal scale followed strict mathematical patterns.
Among his discoveries, Graunt noted: * More boys were born than girls, but men died at a slightly higher rate, keeping the population balanced. * The number of suicides and accidental deaths remained remarkably constant from year to year. * London's population growth was driven by rural migration, not by the city's birth rates, which were outpaced by its death rates.
3. The Creation of the First "Life Table"
Graunt’s most enduring contribution to actuarial science was his creation of the first rudimentary Life Table (or mortality table).
Using the causes of death listed in the Bills, Graunt estimated the likelihood of a person surviving to a certain age. Out of an initial cohort of 100 newborns, he calculated: * 36 would die before the age of 6. * 24 would die between ages 6 and 16. * Only 1 in 100 would live past the age of 76.
For the first time in human history, Graunt had plotted a survivorship curve. He shifted the understanding of human life expectancy from a matter of divine providence to a measurable, predictable probability.
4. Mathematical Formalization: Edmond Halley
While Graunt introduced the concept, his data was flawed (London was a highly transient city, and the "searchers" were not medical professionals). The next major leap came in 1693 from the brilliant mathematician and astronomer Edmond Halley (famous for Halley’s Comet).
Halley acquired detailed birth and death records from the city of Breslau (modern-day Wrocław, Poland). Unlike London, Breslau had a stable population with little migration, making it perfect for demographic tracking. Halley applied rigorous mathematics to this data to construct a highly accurate life table.
Crucially, Halley took the demographic data and applied it to finance. He calculated the exact mathematical formulas required to price life annuities (a financial product where an individual pays a lump sum in exchange for a guaranteed income until death). Before Halley, governments and private sellers priced annuities based on guesswork and flat rates, regardless of the buyer's age. Halley proved that the price of an annuity must be tied to the mathematical probability of the buyer's survival at a specific age.
5. The Birth of Actuarial Science and Demographic Forecasting
The combination of Graunt's demographic observations and Halley's financial mathematics formed the exact blueprint for modern actuarial science.
By the mid-18th century, mathematicians like James Dodson used these foundations to pioneer the concept of the level-premium life insurance policy. Dodson proved that by using mortality tables, an insurance company could pool the risk of thousands of individuals, calculating the exact premium required to ensure the company could pay out all claims and remain solvent. This led to the founding of the Society for Equitable Assurances on Lives and Survivorships in London in 1762—the world's first modern life insurance company.
Summary
The translation of 17th-century plague records into actuarial science represents the discovery of the Law of Large Numbers applied to human biology.
Data that was initially gathered in sheer panic to track the bubonic plague was meticulously organized by John Graunt to reveal hidden patterns in human mortality. Edmond Halley then attached rigorous probability mathematics to these patterns. Today, every time an insurance company sets a premium, a government projects the future solvency of a pension system, or epidemiologists model the spread of a modern pandemic, they are utilizing the exact mathematical framework born from the ashes of 17th-century plague records.