BOOLE, George

On a general method in analysis.

Published: London, Taylor and Francis

Date: 1844

4to (270 × 220 mm), pp. 225-282; clean, toned text; small tape repair to outer margin of final leaf; very good in blue paper boards with printed title label to spine, upper joint weak with split at the joint of the opening leaf.

COPAC records UK institutional copies at Edinburgh, Newcastle, Senate House and the Wellcome Library.

Extract from the Philosophical Transactions, 134 Jjanuary 1, 1844): 225-282. George Boole (1815-1864), the son of a shoemaker, received no formal higher education, but having taught himself Latin, Greek and mathematics, and begun to work as a teacher, he started to correspond with other mathematicians. At first he took encouragement from Duncan Gregory (1813-1844) in his endeavours, but from 1842 he also corresponded with Augustus de Morgan (1806-1871). He had already begun to publish his work in the Cambridge Mathematical Journal, when in 1844 he sent De Morgan a copy of a paper entitled ‘On a general method of analysis’, which De Morgan subsequently had published in the Philosophical Transactions. This publication perhaps marks the beginning of his real mathematical acclaim. Having written on invariant theory in an 1841 paper, the present paper deals more generally with the theory of linear differential equations, moving from the case of constant coefficients to variable coefficients, the innovation in Boole’s operational methods consisting in the assertion that operations may not commute. ‘The breakthrough in Boole’s memoir was similar to the key to Sir William Rowan Hamilton’s invention of 16 October, 1843: a loosening of the requirement of commutativity. Instead of applying non-commutativity to quaternions, Boole applied it to operations. Boole emphasized in the paper that “[t]he position which I am most anxious to establish is, that any great advances in the higher analysis must be sought for by an increased attention to the laws of the combination of symbols. The value of this principle can scarcely be overrated.”’ (Sloan Evans Despeaux in Jeremy J. Gray and Karen Hunger Parshall, eds., Episodes in the history of modern algebra (1800-1950), New York and London, 2007, p. 66)

Very good