Mathematical Selves and the Shaping of Mathematical Modernism: Conflicting Epistemic Ideals in the Emergence of Enumerative Geometry (1864–1893)

Abstract

For more than three decades, fierce debates raged both in private letters and across public spaces over a formula expressed in 1864 by the French geometer Michel Chasles. Proofs and refutations thereof abounded, to no avail: the formula was too useful to be abandoned by its defenders, too elusive to be made rigorous for its detractors. The disputes over Chasles’s formula would not be solved by a definitive proof or rebuttal; rather, the core epistemic issues at stake shifted from generality to rigor and from truth to geometrical significance. This essay tracks the main lines of circulation of Chasles’s formula and shows how the disputes to which it gave rise embody conflicting mathematical selves—that is to say, different normative accounts of what being a mathematician entails. This perspective allows for a renewed understanding of what historians have described as the conflicted rise of modernism in mathematics and a firmer rooting of it within broader late nineteenth-century cultural trends.