by Anita McConnell

© Oxford University Press 2004 All rights reserved

**Horner, William George** (1786-1837), mathematician and schoolteacher, was the son of William Horner (1746/7-1826), a native of Ireland who became an itinerant preacher in 1770. Brought to England by Wesley, the elder Horner officiated as a regular minister until 1819. Horner was educated from 1794 until 1800 at Kingswood School, near Bristol, which Wesley had established; he was assistant master there in 1800-04, then, at the age of nineteen, its headmaster, on an annual salary of £50.

In 1809 Horner left Kingswood to found his own school, The Seminary, at 27 Grosvenor Place, Bath; he was headmaster there until his death. A man of high intellectual powers, he suffered from irritability and impatience, and he applied the cane freely to those pupils he considered diligent yet dull. However, many benefited from his teaching and he encouraged bright boys to stay an extra year at school.

An interest in mathematics led Horner to develop a method of finding a rapid means of approximating to a root of a polynomial equation. 'Horner's method', as it became known, was conveyed to Davies Gilbert, read before the Royal Society on 1 July 1819, and published in the *Philosophical Transactions* later that year. Horner was unaware that a similar method had been practised in thirteenth-century China and rediscovered in Italy by Paolo Ruffini in 1807, as were Augustus De Morgan and J. R. Young, who popularized Horner's method among their students. Horner's work represented an early example of thinking in terms of the complexity and efficiency of algorithms, and in it for the first time in modern mathematics a suitable arrangement of data in the plane was explicitly used for economical calculation. The attribution of his name, even if historically debatable, attests to the interest taken in his finding; it joined other such methods, including that known as 'Newton-Raphson'.

In the late 1810s and later, Horner wrote a sextet of other papers on the transformation and solution of equations. He also solved some functional equations, which were popularized in Britain in the mid-1810s by Charles Babbage and John Herschel, as part of their efforts to revive English mathematics. In 1832 he published *Natural magic, a familiar exposition of a forgotten fact in optics, including strictures on A. Gellius and his interpreters.*

Horner and his wife, whose name is unknown, raised several children, one of whom, William Horner, also taught at The Seminary. Horner endured 'a lingering and painful disorder', described as 'a complication of asthma and ossification of the heart' *(Wesleyan Methodist Magazine),* and died at 27 Grosvenor Place 'after a sudden and violent stroke of illness' *(Bath Journal),* on 22 September 1837.

ANITA MCCONNELL

**Sources **

J. L. Coolidge, *The mathematics of great amateurs* (1949), chap. 15

*The history of Kingswood School ... by three old boys* (1898)

*Bath Journal* (2 Oct 1837), 2

*Register of Kingswood School* (1910)

R. Cooke, *The history of mathematics: a brief course* (1997), 235, 385

F. Cajori, 'Horner's method of approximation anticipated by Ruffini', *Bulletin of the American Mathematical Society,* 17 (1910-11), 409-14

*Wesleyan Methodist Magazine,* 60 (1837), 957

*VCH Somerset,* 2.463

M. E. Baron, 'Horner, William George', *DSB*

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