ArgumentThis article offers a social history of the “Galois Affair,” which arose in 1831 when the French Academy of Sciences decided to reject a paper presented by an aspiring mathematician, Évariste Galois. In order to historicize the meaning of Galois's work at the time he tried to earn recognition for his research on the algebraic solution of equations, this paper explores two interrelated questions. First, it analyzes scholarly algebraic practices and the way mathematicians were trained in the nineteenth century to (...) reconstruct the scientific meaning of Galois's research. By emphasizing the historically contingent nature of scientific debates, the paper argues that to historicize the work of a mathematician, we must historicize the scientific world as well. The second part of this article goes further to seek a fresh perspective on Galois's short career by analyzing the cultural, social, and institutional dynamics that governed how the mathematical community came to recognize an aspiring mathematician as one of its own. (shrink)

Until the first quarter of the seventeenth century there was a great deal of agreement about the nature of mathematical practice. Mathematicians, as well as their patrons and clients, viewed all possible aspects of their work, both theoretical and practical, as being included within their discipline. Although the mathematical sciences were a fairly recent foreign import to England, which can barely be traced back beyond the mid-sixteenth century, by the beginning of the seventeenth century there was a large and growing (...) body of practitioners with a unified view of their subject's identity. Divisions began to appear, however, and they were often framed in terms of the proper mixture of theory and practice in mathematical education.One early sign of the emergence of this tension is the kind of accusation made in the priority dispute between William Oughtred and Richard Delamain taking place around 1632. Their bitter conflict began over who first invented the Horizontal Quadrant, a form of sundial, and the Circles of Proportion, a logarithmic calculating device that can be considered a precursor of the slide rule, and ended in a dispute over what constituted proper mathematical practice. Oughtred accused Delamain of making his students ‘only doers of tricks, and as it were Juglers’ by teaching them the use of instruments without any theoretical foundation. Instruments, Oughtred claimed, could only be used with understanding by students who had a proper theoretical foundation. He advocated postponing their use until after the theoretical foundations of a subject had been thoroughly mastered. Delamain, on the other hand, was perfectly willing to teach practical instrumental operations without insisting upon a theoretical grounding. This paper will use the dispute between Oughtred and Delamain to investigate the breakdown of consensus over internal mathematical boundaries, the rhetoric and strategies involved in attempts to gain authority by mathematical practitioners, and the extent to which their roles were negotiated, both with other practitioners, and with their patrons and students. (shrink)