Wallace, William

(1768-1843), mathematician

by George Stronach, rev. Maria Panteki

© Oxford University Press 2004 All rights reserved

Wallace, William (1768-1843), mathematician, was born on 23 September 1768 at Dysart, Fife, the eldest son of Alexander Wallace, a leather manufacturer, and his wife, Janet Simson. He received an inadequate school education, but was instructed in arithmetic by his father. In 1784 his family moved to Edinburgh where he was apprenticed to a bookbinder. Here, by his own industry, he mastered geometry, fluxions, and astronomy. In 1788 he attended John Robison's lectures on natural philosophy. Robison introduced him to John Playfair, who assisted him and who remained his patron thereafter. Subsequently he exchanged his occupation for that of a warehouseman in a printing office, and also took on work as a private tutor, learning Latin and French so that he could study continental mathematics.

In 1794, after briefly working as a bookseller's shopman, Wallace was appointed mathematical teacher in Perth Academy on Playfair's recommendation. In the same year he married. In 1796 he submitted his first paper (on geometrical porisms) to the Transactions of the Royal Society of Edinburgh, and wrote the article 'Porism' for the third edition of the Encyclopaedia Britannica (1801). His next paper, submitted to the Royal Society of Edinburgh in 1802, concerned the application of an ingenious method for the rectification of the ellipse to a problem of physical astronomy. This paper established Wallace's reputation as a mathematician, although it later emerged that his method had been anticipated by A. M. Legendre (1752-1833), in a memoir of 1794. This induced Wallace to publish a translation of Legendre's memoir in Leybourn's Mathematical Repository (1809 and 1814).

In 1803, following his patron's advice, Wallace applied for the office of mathematical master in the Royal Military College at Marlow (later at Sandhurst), a post obtained after hard competition. After he moved there his family increased rapidly, and he had three daughters and a son. In 1804 he was elected a fellow of the Royal Society of Edinburgh. A regular contributor of encyclopaedia articles, he submitted papers of a geometrical nature, incorporating applications to geodesy and astronomy; he also contributed several translations of French memoirs and some geometrical problems to the Mathematical Repository. In 1804, writing as 'Scoticus', he proposed for proof a problem, now known as Wallace's theorem, which states 'if four lines intersect each other to form four triangles by omitting one line in turn, the circumcircles of these triangles have a point in common' (Mathematical Repository, n.s. 1, 1804, 22). Wallace was one of those individuals who realized very early the need for a mathematical renaissance in Britain. A decade before the Cambridge reform in 1816, he and his colleague at Marlow, James Ivory, abandoned the fluxional calculus in their contributions to the Repository. However, Wallace considered his most significant step towards fostering mathematics to be his article 'Fluxions' published in the Edinburgh Encyclopaedia in 1815--the first systematic presentation of the continental calculus in Britain.

In 1819 Wallace succeeded John Leslie as professor of mathematics in Edinburgh University. This position was the crowning object of his ambition and he cherished being held in high esteem by his students, such as D. F. Gregory and T. Galloway. Delight in practical applications induced him to invent, and give his name to, the eidograph, with which drawings could be copied to a larger or smaller scale, and the chorograph, a simple calculating device for cartographers to find the position of a station given the angles made to it from three points in the same plane. He superintended the erection of two observatories, one at Sandhurst and another on Calton Hill, Edinburgh, with the nearby monument to Napier, the inventor of logarithms. In 1838 he retired due to ill health, and was accorded a civil pension of £300 a year. He received the degree of LLD from the university on 17 November 1838. He published two books, Conic Sections (1837) and Geometrical Theorems and Analytical Formulae (1839). He died at Edinburgh on 28 April 1843.


Monthly Notices of the Astronomical Society of London, 6 (1843-5), 31-41
M. Panteki, 'William Wallace and the introduction of continental calculus to Britain: a letter to George Peacock', Historia Mathematica, 14 (1987), 119-32
Chambers, Scots. (1872)
d. cert.
A. D. D. Craik, 'Calculus and analysis in early 19th-century Britain: the work of William Wallace', Historia Mathematica, 26 (1999), 239-67
A. D. D. Craik, 'Geometry versus analysis in early 19th-century Scotland: John Leslie, William Wallace, and Thomas Carlyle', Historia Mathematica, 27 (2000), 133-63

Institute of Actuaries, London, MSS
U. Edin. L., notebook |  BL, Macvey Napier corresp.
LUL, letter to G. Peacock, A.L.483 1833
RS, Herschel collection, HS 18: 21-27
U. Edin., New Coll. L., letters to Thomas Chalmers

J. Thomson, oils, c.1825, U. Edin.
A. Geddes, pencil and chalk drawing, Scot. NPG
A. Geddes, portrait, Scot. NPG

Wealth at death  
£1725 12s. 0d.: confirmation, 1843, Scotland

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