Gompertz, Benjamin

(1779-1865), mathematician and actuary

by David Philip Miller

© Oxford University Press 2004 All rights reserved

Gompertz, Benjamin (1779-1865), mathematician and actuary, was born on 5 March 1779 at 3 Bury Street in the City of London, the fourth of five sons of Solomon Barent Gompertz (1729-1807/8), a successful diamond merchant, and his second wife, Leah Cohen (1747×9-1809). His mother was Dutch by birth, the daughter of Benjamin Cohen, and his father's family was from Emmerich in the Netherlands. Excluded from the universities on the grounds of his Jewish religion, Gompertz was privately educated and self-taught, showing early interest in mathematics in the works of Maclaurin, Emerson, and Newton.

In 1797 Gompertz joined the Spitalfields Mathematical Society. He later became president and served in that office when the society merged with the Royal Astronomical Society of London in 1846. From 1798 he contributed regularly to the Gentleman's Mathematical Companion, winning the prize competition of that journal every year between 1812 and 1822. His paper on imaginary quantities was published in the Philosophical Transactions of the Royal Society of London in 1806, but subsequent work on this topic was privately printed in two volumes in 1817 and 1818 having, it is said, been rejected by the Royal Society as so profound that no one would understand it. However, these works established his mathematical reputation. Gompertz was elected FRS in 1819 and served on the Royal Society's council in 1825 and 1831.

Gompertz was an early member of the Astronomical Society of London and served on its council from 1821 to 1829. Over the same period he published a number of papers in its Memoirs, dealing variously with the theory of astronomical instruments, the aberration of light, a differential sextant of his own design, and the convertible pendulum. He began in 1822, with Francis Baily, the calculation of tables of the mean places of the fixed stars. The publication of Bessel's Fundamenta astronomiae anticipated them, but their work was of great importance to the construction of the Royal Astronomical Society's complete catalogue of stars. Gompertz's work in astronomy was of a kind that took best advantage of his mathematical and computational skills.

Gompertz married, on 10 October 1810 at the Hambro Synagogue, London, Abigail Montefiore (1790-1871), the sister of Sir Moses Montefiore. They had a son, Joseph (1814-1824), and two daughters, Justina Lydia (1811-1883) and Juliana (1815-1873). In 1809 or 1810 Gompertz entered the stock exchange, leaving in 1824, the same year as the death of his only son. When the Guardian Insurance Office was established in 1821 Gompertz was an unsuccessful candidate for the position of actuary, being denied it reputedly on the grounds of religion. Perhaps partly in response, but also to take advantage of Gompertz's mathematical prowess, his brother-in-law, Sir Moses Montefiore, and Nathan Rothschild in 1824 set up the Alliance British and Foreign Life Assurance Company, to which Gompertz was appointed actuary. He was also chief manager of the related Alliance Marine Insurance.

Gompertz and the companies under his charge were very successful, but his lasting fame derived from his philosophical interest in life tables. While others treated these only as working tools, Gompertz tried to understand the laws which produced consistent age patterns of death. The law of human mortality associated with his name was propounded in papers published in the Philosophical Transactions in 1820 and 1825, with a supplementary paper published there in 1862. What is now called the Gompertz equation describes the exponential rise of death rates in a population between sexual maturity and old age. He attributed this phenomenon to a law of mortality, stating that 'the average exhaustions of a man's power to avoid death' are such that 'at the end of equal infinitely small intervals of time' he loses 'equal portions of his remaining power to avoid destruction' (PTRS, 115, 1825, 518). His expertise in this area led to his being consulted by government, including giving evidence to the select parliamentary committees on friendly societies in 1825 and 1827, and he did important computational work for the army medical board. His insights have remained central to the study of human mortality.

Gompertz's mathematical, astronomical, and actuarial work was closely connected. Like his collaborator Francis Baily, who was also simultaneously involved in astronomy and assurance, Gompertz's capacity for sustained, complex computation underlay all his work in whatever field. Tables of lives and tables of stars were generated by the same qualities and both represented a rationalizing spirit which informed the social philosophy of Gompertz and his friends among what W. J. Ashworth called the 'business astronomers'. However, unlike many of his colleagues in the Astronomical Society who promoted the differential calculus as a mathematical and physical tool (such as Herschel, Babbage, and Ivory), Gompertz clung fiercely to Newton's method of fluxions throughout his life. He defended fluxions against what he called the 'furtive' notation of Leibniz, furtive in the sense that it seemed to him to give Leibniz greater claim to originality at Newton's expense than was warranted.

After retiring from active work in 1848 Gompertz devoted much time to mathematics and science. His Hints on Porisms was privately published in 1850 as a sequel to earlier papers on imaginary quantities. He investigated comets and meteors, but this work was not published. He was a founding member of the Statistical Society of London in 1834, and contributed a work on human mortality to the International Statistical Congress in 1860. He was also, in 1865, one of the original members of the London Mathematical Society, for which he was preparing a paper at the time of his death. Gompertz was prominently involved also with the Society for the Diffusion of Useful Knowledge, the Royal Literary Fund, and various Jewish charities. He died on 14 July 1865 of a paralytic seizure at his home, 1 Kennington Terrace, Vauxhall, and was buried in the Jewish cemetery near Victoria Park, Hackney.

DAVID PHILIP MILLER

Sources  
P. F. Hooker, 'Benjamin Gompertz', Journal of the Institute of Actuaries, 91 (1965), 202-12
R. M. Gompertz, A branch of the Gompertz (privately printed, 1979)
M. N. Adler, 'Memoirs of the late Benjamin Gompertz', Assurance Magazine and Journal of the Institute of Actuaries, 13 (1866), 1-20
Monthly Notices of the Royal Astronomical Society, 26 (1865-6), 104-9
The Athenaeum (22 July 1865), 117
W. J. Ashworth, 'The calculating eye: Baily, Herschel, Babbage and the business of astronomy', British Journal for the History of Science, 27 (1994), 409-41
DNB
S. J. Olshansky and B. A. Carnes, 'Ever since Gompertz', Demography, 34 (1997), 1-15
C. Roth, ed., Encyclopaedia Judaica, 16 vols. (Jerusalem, 1971-2)

Archives  
Institute of Actuaries, London, MSS |  BL, Babbage corresp.
RAS, letters and MSS
RS, Herschel corresp.

Likenesses  
portrait, repro. in Hooker, 'Benjamin Gompertz', 202

Wealth at death  
under £25,000: probate, 25 Aug 1865, CGPLA Eng. & Wales


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