# Creatively Undecided: The Making of Peacock’s Two Algebras

# Creatively Undecided: The Making of Peacock’s Two Algebras

The chapter first details Peacock's mathematical point of departure as evident from his Notes to the Analytical Society’s translation of Silvestre Lacroix’s calculus textbook and early correspondence. It turns to impressive attempts during the 1820s to address the challenge of Babbage’s purely formal system of algebra, first in a book-length study of the history of arithmetic, in which he sought to establish algebra as a richer form of generalized arithmetic than was customary, as in the work of Maseres and Frend. He failed, but, it is argued, his failure was telling. This led, in the second half of the decade to the formulation of his inherently hybrid Treatise on Algebra of 1830, in which algebra is portrayed as a combination of two algebras: “arithmetical algebra” as generalized arithmetic in the accepted sense, that was claimed to “suggest” what he dubbed “symbolical algebra”, conceived as a purely formal system of signs. The two algebras and their forced relationship are analyzed in some detail as the product and expression of profound meta-mathematical ambivalence.

*Keywords:*
George Peacock, Silvestre Lacroix, Francis Maseres, William Frend, Treatise on Algebra (1830), mathematical hybridity, symbolical algebra, ambivalence