William Spence

William Spence (born 31 July 1777 in Greenock, Scotland – died 22 May 1815 in Glasgow, Scotland) was a Scottish mathematician who published works on the fields of logarithmic functions, algebraic equations and their relation to integral and differential calculus respectively.

Early life, family, and personal life

Spence was the second son to Ninian Spence and his wife Sarah Townsend. Ninian Spence ran a coppersmith business, and the Spence family were a prominent family in Greenock at the time.

From an early age, Spence was characterised as having a docile and reasonable nature, with him being mature for his age. At school he formed a life-long friendship with John Galt, who documented much of his life and his works posthumously. After this, Spence visited many places in England, he lived in London for a few months where, in 1809, he published his first work. Throughout his work, he displayed a familiarity with the work of Lagrange and Arbogast, which is notable since at the time very few were familiar with their works.

which he denoted with . In which he took a systematic approach to solving equations up to the fourth degree using symmetrical functions of the roots.

Legacy Spence's work was noted to be remarkable at the time, with John Herschel, his acquaintance and one of Britain's leading mathematicians at the time, had referenced it in one of his later publications Consideration of various points of analysis, which prompted Herschel to edit Spence's manuscripts. Spence was held in such high regard by Galt, and later Herschel that they published a collection of his individual essays in 1819. Posthumously, his work was met with appreciation from his contemporaries, with a review in the ninety-fourth number of the Quarterly Review (reproduced in Galt's The Literary and Miscellanies of John Galt, Volume 1) that described his first work in 1809 as:

" [The] first formal essay in our language on any distinct and considerable branch of the integral calculus, which has appeared since… Hellinsʼs papers on the ‘Rectification of the Conic Sections".