William Wallace (mathematician)

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For other people named William Wallace, see William Wallace (disambiguation).

Prof William Wallace FRSE MInstCE FRAS LLD (23 September 1768 – 28 April 1843) was a Scottish mathematician and astronomer who invented the eidograph.


Wallace's grave in Greyfriars Kirkyard, Edinburgh, 2012

Wallace was born at Dysart in Fife, where he received his school education.

In 1784 his family moved to Edinburgh, where he himself was set to learn the trade of a bookbinder; but his taste for mathematics had already developed itself, and he made such use of his leisure hours that before the completion of his apprenticeship he had made considerable acquirements in geometry, algebra and astronomy. He was further assisted in his studies by John Robison (1739–1805) and John Playfair, to whom his abilities had become known. After various changes of situation, dictated mainly by a desire to gain time for study, he became assistant teacher of mathematics in the academy of Perth in 1794. This post he exchanged in 1803 for a mathematical mastership in the Royal Military College at Great Marlow, in which post he continued after it moved to Sandhurst, with a recommendation by Playfair. In 1819 he was chosen to succeed John Leslie (or John Playfair?) in the chair of mathematics at Edinburgh.

Wallace developed a reputation for being an excellent teacher. Among his students was Mary Somerville. In 1838 he retired from the university due to ill health.[1]

He died in Edinburgh and was buried in Greyfriars Kirkyard. The grave lies on the north-facing wall in the centre of the northern section.

Mathematical contributions[edit]

In his earlier years Wallace was an occasional contributor to Leybourne's Mathematical Repository and the Gentleman's Mathematical Companion. Between 1801 and 1810 he contributed articles on "Algebra", "Conic Sections", "Trigonometry", and several others in mathematical and physical science to the fourth edition of the Encyclopædia Britannica, and some of these were retained in subsequent editions from the fifth to the eighth inclusive. He was also the author of the principal mathematical articles in the Edinburgh Encyclopædia, edited by David Brewster. He also contributed many important papers to the Transactions of the Royal Society of Edinburgh.[1]

He mainly worked in the field of geometry and in 1799 became the first to publish the concept of the Simson line, which erroneously was attributed to Robert Simson.[2] In 1807 he proved a result about polygons with an equal area, that later became known as the Bolyai–Gerwien theorem.[3] His most important contribution to British mathematics however was, that he was one of the first mathematicians introducing and promoting the advancement of the continental European version of calculus in Britain.[2]

Other works[edit]

Wallace also worked in astronomy and invented the eidograph, a mechanical device for scaling drawings.[2][4]


  • A Geometrical Treatise on the Conic Sections with an Appendix Containing Formulae for their Quadrature. (1838)
  • Geometrical Theorems and Analytical Formulae with their application to the Solution of Certain Geodetical Problems and an Appendix. (1839)


Wallace was married to Janet Kerr (1775-1824).

His daughter, Margaret Wallace, married the mathematician Thomas Galloway. His sons included the Rev Alexander Wallace (1803-1842) and Archibald C. Wallace (1806-1830).


  1. ^ a b Chisholm 1911.
  2. ^ a b c O'Connor, John J.; Robertson, Edmund F., "William Wallace (mathematician)", MacTutor History of Mathematics archive, University of St Andrews .
  3. ^ Ian Stewart: From Here to Infinity. Oxford University Press 1996 (3. edition), ISBN 978-0-19-283202-3, p. 169 (restricted online copy, p. 169, at Google Books)
  4. ^ Gerard L'Estrange Turner: Nineteenth-Century Scientific Instruments. University of California Press 1983, ISBN 0-520-05160-2, p. 280 (online copy, p. 280, at Google Books)

 This article incorporates text from a publication now in the public domainChisholm, Hugh, ed. (1911). "Wallace, William (Scottish mathematician)". Encyclopædia Britannica (11th ed.). Cambridge University Press. 

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