Benjamin Gompertz
Encyclopedia
Benjamin Gompertz was a British 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 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.
In line with his father's wishes, he entered the London Stock Exchange
. He became a member of the Mathematical Society of Spitalfields, and served as its president when it was merged with the Astronomical Society of London. In 1819 he was elected a F.R.S., and in 1832 became a member of the council. The Astronomical Society was founded in 1820, and he was elected a member of the council in 1821.
On the death of his only son he retired from the Stock Exchange, and absorbed himself in mathematics. When the Guardian Insurance Office was established in 1821, he was a candidate for the actuaryship, but the directors objected to him on the grounds that he was a Jew. His brother-in-law, His brother-in-law Sir Moses Montefiore with his relative Nathan Mayer Rothschild
then founded the Alliance Assurance Company (1824), and Gompertz was appointed actuary under the deed of settlement. His management of the Alliance Company was successful, he was consulted by government, and made computations for the Army medical board.
In 1848 he retired from active work and returned to his scientific labours. He was a member of many learned societies, and was also one of the promoters of the Society for the Diffusion of Useful Knowledge
. Of the leading Jewish charities he was a prominent member, and he worked out a plan of poor relief (Jewish Chronicle, 6 October 1845), which was afterwards adopted by the Jewish board of guardians.
Gompertz died from a paralytic seizure on 14 July 1865.
From 1806 he was a frequent contributor to the Philosophical Transactions of the Royal Society; but his early tracts on complex number
s and porism
s (1817–18) were self-published. Gompertz was an old-fashioned Newtonian who retained and defended the notation of fluxions.
Astronomy
For ten years he actively participated in the work of the Astronomical Society, contributing papers on the theory of astronomical instruments, the aberration of light
, the differential sextant, and the convertible pendulum. With Francis Baily
he began in 1822 the construction of tables for the mean places of the fixed stars; the work was left uncompleted, because of the publication of the Fundamenta Astronomiæ of Friedrich Bessel
. Their efforts, however, led to the complete catalogue of stars of the Royal Astronomical Society
.
The Gompertz model
He worked out a new series of tables of mortality for the Royal Society, and these suggested to him in 1825 his law of human mortality, which he first expounded in a letter to Francis Baily. The law rests on an a priori assumption that a person's resistance to death decreases as his years increase. The model can be written in this way:
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.
Gompertz's descendant Simon Gompertz is an economics
presenter for the BBC
.
Attribution
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
, who became a Fellow of the Royal Society. Gompertz is now best known for his Gompertz law of mortality, a demographic
Demography
Demography is the statistical study of human population. It can be a very general science that can be applied to any kind of dynamic human population, that is, one that changes over time or space...
model published in 1825.
Life
Of the German Jewish family of Gompertz of EmmerichEmmerich
Emmerich am Rhein; , meaning Emmerich at the Rhine is a city on the lower part of the River Rhine in the northwest of the German federal state of North Rhine-Westphalia...
, he 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
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
, Colin Maclaurin
Colin Maclaurin
Colin Maclaurin was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him....
, and William Emerson
William Emerson (mathematician)
William Emerson , English mathematician, was born at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school...
. 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.
In line with his father's wishes, he entered the London Stock Exchange
London Stock Exchange
The London Stock Exchange is a stock exchange located in the City of London within the United Kingdom. , the Exchange had a market capitalisation of US$3.7495 trillion, making it the fourth-largest stock exchange in the world by this measurement...
. He became a member of the Mathematical Society of Spitalfields, and served as its president when it was merged with the Astronomical Society of London. In 1819 he was elected a F.R.S., and in 1832 became a member of the council. The Astronomical Society was founded in 1820, and he was elected a member of the council in 1821.
On the death of his only son he retired from the Stock Exchange, and absorbed himself in mathematics. When the Guardian Insurance Office was established in 1821, he was a candidate for the actuaryship, but the directors objected to him on the grounds that he was a Jew. His brother-in-law, His brother-in-law Sir Moses Montefiore with his relative Nathan Mayer Rothschild
Nathan Mayer Rothschild
Nathan Mayer, Freiherr von Rothschild , known as Nathan Mayer Rothschild, was a London financier and one of the founders of the international Rothschild family banking dynasty...
then founded the Alliance Assurance Company (1824), and Gompertz was appointed actuary under the deed of settlement. His management of the Alliance Company was successful, he was consulted by government, and made computations for the Army medical board.
In 1848 he retired from active work and returned to his scientific labours. He was a member of many learned societies, and was also one of the promoters of the Society for the Diffusion of Useful Knowledge
Society for the Diffusion of Useful Knowledge
The Society for the Diffusion of Useful Knowledge , founded in 1826, and wound up in 1848, was a Whiggish London organisation that published inexpensive texts intended to adapt scientific and similarly high-minded material for the rapidly expanding reading public...
. Of the leading Jewish charities he was a prominent member, and he worked out a plan of poor relief (Jewish Chronicle, 6 October 1845), which was afterwards adopted by the Jewish board of guardians.
Gompertz died from a paralytic seizure on 14 July 1865.
Works
MathematicsFrom 1806 he was a frequent contributor to the Philosophical Transactions of the Royal Society; but his early tracts on complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s and porism
Porism
A porism is a mathematical proposition or corollary. In particular, the term porism has been used to refer to a direct result of a proof, analogous to how a corollary refers to a direct result of a theorem.-Beginnings:...
s (1817–18) were self-published. Gompertz was an old-fashioned Newtonian who retained and defended the notation of fluxions.
Astronomy
For ten years he actively participated in the work of the Astronomical Society, contributing papers on the theory of astronomical instruments, the aberration of light
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
, the differential sextant, and the convertible pendulum. With Francis Baily
Francis Baily
Francis Baily was an English astronomer, most famous for his observations of 'Baily's beads' during an eclipse of the Sun.-Life:Baily was born at Newbury in Berkshire in 1774...
he began in 1822 the construction of tables for the mean places of the fixed stars; the work was left uncompleted, because of the publication of the Fundamenta Astronomiæ of Friedrich Bessel
Friedrich Bessel
-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...
. Their efforts, however, led to the complete catalogue of stars of the Royal Astronomical Society
Royal Astronomical Society
The Royal Astronomical Society is a learned society that began as the Astronomical Society of London in 1820 to support astronomical research . It became the Royal Astronomical Society in 1831 on receiving its Royal Charter from William IV...
.
The Gompertz model
He worked out a new series of tables of mortality for the Royal Society, and these suggested to him in 1825 his law of human mortality, which he first expounded in a letter to Francis Baily. The law rests on an a priori assumption that a person's resistance to death decreases as his years increase. The model can be written in this way:
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
Life insurance
Life insurance is a contract between an insurance policy holder and an insurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death of the insured person. Depending on the contract, other events such as terminal illness or critical illness may also trigger...
. The equation, known as a Gompertz curve
Gompertz curve
A Gompertz curve or Gompertz function, named after Benjamin Gompertz, is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period...
, is now used in many areas to model a time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.
Family
He married Abigail Montefiore in 1810.Gompertz's descendant Simon Gompertz is an economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
presenter for the BBC
BBC
The British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...
.
External links
Attribution