ESHS/HSS Annual Meeting

Leibniz on impossibility and transcendence: What is a result?

• In Event: Mathematics in Manuscripts 1

English Abstract

The exploration of new unpublished manuscripts by Leibniz dating from 1979 highlights an original working method. These works focus on transcendental curves and the possibility or impossibility of quadrature. The German mathematician's approach is not to look for problems and then seek solutions. On the contrary, he seems to have focused his efforts on two problems in geometry, the solutions to which are already known and even published (a method for squaring the circle by Gregory and a method for rectification by Sovero). Leibniz writes and rewrites the reasoning that leads to the result, changing the approaches and, above all, the way in which the problem is formalized. This exploration actually shows a meta-mathematical work that does not consider the content of the problem to be solved, but rather the very modalities according to which this solution can be accomplished and expressed. The choice of these two problems is also not unrelated to Leibniz's objectives.
In this presentation, we will therefore show how this corpus provides an interesting example of mathematical drafts in which what may appear to be reasoning leading to a result is in fact the very substance of the author's thinking. The genetic approach is an indispensable tool for discerning these different levels of discourse.

Author

• Arilès Remaki, University of Mainz