Benjamin Gompertz

Benjamin Gompertz (5 March 1779 – 14 July 1865) was an English self-educated mathematician and actuary, who became a Fellow of the Royal Society. Gompertz is now best known for his Gompertz law of mortality, a demographic model published in 1825. He was the brother of the early animal rights activist and inventor Lewis Gompertz and the poet Isaac Gompertz.

Life Of the German Jewish family of Gompertz of Emmerich, Gompertz was born in London, where his father and grandfather had been successful diamond merchants. Debarred, as a Jew, from a university education, he studied on his own from an early age, in the writings of Isaac Newton, Colin Maclaurin, and William Emerson. From 1798 he was a prominent contributor to the Gentleman's Mathematical Companion, and for a period won the annual prizes in the magazine for the solutions of problems. Gompertz married Abigail Montefiore (1790–1871) in 1810; they had three children. which was afterwards adopted by the Jewish board of guardians.

where N(t) represents the number of individuals at time t, and c and a are constants.

This model is a refinement of a demographic model of Robert Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.