ESHS/HSS Annual Meeting

Mathematics in Manuscripts 1

Session Submission Type: Organized Session

English Abstract

Mathematics and highly mathematized science like Astronomy or Physics often appears rigid, sophisticated, and logically structured in published work. With reference to Hans Reichenbach's distinction between the context of discovery and the context of justification, published work pertains most often to the justification of mathematical ideas. With reference to Reuben Hersh's distinction between the front and back, it refers to that part of mathematics to which the public is admitted and where the public is served. In contrast, private manuscripts may provide insight into the emergence, discovery, and development of ideas. These documents often display a fluidity of reasoning, which is in stark contrast to the finished product of a work that is deemed ready to be put to the criticism of the public. Mathematical manuscripts may give us insights into the heuristics, vague ideas, unexplored methods and notations, false starts, and unexpected surprises in the creative process of elaborating a mathematical theory. On the other hand, a historical analysis of mathematical manuscripts presents specific challenges. Private manuscripts and mathematical notes, exploratory symbolic manipulations and calculations are almost always intrinsically incomplete and fragmentary. They require the speculative reconstruction of individual contexts as well as objective historical conceptual problem settings. In this symposium, we want to explore the specific historiographic challenges posed by mathematical manuscripts of different times and topics.

Sub Unit

• Organized Session

Chair

• Tilman Sauer

Individual Presentations

• What can mathematicians' drafts tell us about the 'back' of mathematics? - Emmylou Haffner, CNRS

• The Problem of Apollonius in the Notes of Thomas Harriott (c.1560-1621) - Stefano Farinello, University of Hamburg

• Leibniz on impossibility and transcendence: What is a result? - Arilès Remaki, University of Mainz

• 'The Limits of Newton's Law': editing the manuscripts of Poincaré's course on 'Lorentz invariants' (1906–1907) - Philippe Katz, Nantes Université

Session Organizers

• Emmylou Haffner, CNRS

• Tilman Sauer