Abstract

The canonical view of Hobbes the mathematician is of a doddering old man tilting at quadrature. That picture arises from his twenty-five year debate with John Wallis, an English algebraist, Savile Professor of Geometry at Oxford, and a founding fellow of the Royal Society of London. In 1655, Hobbes attempted to square the circle, Wallis promptly proved him wrong, and their vitriolic exchange was born ;Hobbes is always portrayed as the clear loser. Recently, however, scholars have noticed both flashes of insight in Hobbes's mathematical writings and his excellent reputation among mathematicians on the Continent during the 1640s. Yet the overall picture remains confusing. Hobbes's apparent errors ranged from very subtle to downright bizarre, even when he discussed works by his former colleagues. ;Drawing on the history of mathematics, education, and popular culture, I argue that Hobbes's reputation rests on two systematic errors: misrepresentation of the events of his life, based in his reputation as a purely political philosopher, and a misunderstanding of the nature of mathematics that conceals the deep diversity among early-modern mathematicians. Once those errors are addressed, Hobbes looks considerably more knowledgeable---although still incorrect. ;I begin by reviewing the lives of both Hobbes and Wallis, contending that when the debate started 1655, Hobbes had extensive training in formal mathematics while Wallis had virtually none. Then, by examining four mathematical traditions that flourished in the mid-1600s, I show that terms such as of "mathematical," and "demonstration" have settled meanings only in reference to a single practice. Finally, I explore issues from the Hobbes-Wallis debate, arguing that they center on terms whose meaning had not been generally established, and that Wallis touted an algebraic form of applied mathematics while Hobbes defended the standards of classical geometry. ;Neither Hobbes nor Wallis can be accurately described as right. Hobbes had genuine technical limitations but a firm grasp of methodological issues, while Wallis's technical brilliance was offset by his frequent inability to appreciate the requirements of rigor and universality. Reexamining the debate in light of those differences reveals a wealth of issues in early-modern mathematics, Hobbes studies, and historiography