George Peacock and the British origins of symbolical algebra

This paper studies the background to and content of George Peacock's work on symbolical algebra. It argues that, in response to the problem of the negative numbers, Peacock, an inveterate reformer, elaborated a system of algebra which admitted essentially “arbitrary” symbols, signs, and laws. Although he recognized that the symbolical algebraist was free to assign somewhat arbitrarily the laws of symbolical algebra, Peacock himself did not exercise the freedom of algebra which he proclaimed. The paper ends with a discussion of Sir William Rowan Hamilton's criticism of symbolical algebra.