Victorian Equations

As familiar as the form of the mathematical equation is to us, the ostensibly simple act of equating unlike things was an achievement many centuries in the making, and one that would ultimately redefine European mathematical enquiry such that its bias toward geometry and the concrete would be displaced by a bias toward algebraic abstraction. The moment of that displacement was the nineteenth century, and its broader significance is on particularly striking display in the British context, where the implications of algebraic abstraction were the object of sustained enquiry among mathematicians, logicians, and economists. This article argues that the ascendance of the algebraic equation, and the transformation in the conception of number on which it was premised, were not simply the product of evolutionary pressures internal to mathematics; the Victorian embrace of algebra was also a response to the practical and cognitive demands of Victorian economic life, which was increasingly reliant on attenuated exchange relations and merely nominal forms of ownership. This was an economy organized around the global extension of trade and characterized by the exponential growth of financial intermediation, of what Walter Bagehot called “number abstracted from reference.” Victorian economic practices thus modeled an abstraction that helped to justify the abstractions of mathematics, and that mathematics in turn was used by economic theorists to argue for the necessity and objectivity of their models. This mutually sustaining dialogue is particularly visible in the writings of William Stanley Jevons, who applied the principles of algebra to philosophy and economic theory so as to reconceive the logic of cognitive and social life in terms of equations. This logic, for which he was merely a spokesman, continues to shape our faith in the special value of abstract, theoretical knowledge.