Hilbert on Impossibility and Geometric Constructions

GIOVANNINI, EDUARDO N.

Paderborn

Workshop; International Workshop: Geschichte und Philosophie von Logik und Mathematik; 2020

Universität Paderborn

The aim of this talk is to explore the historical and philosophical significance of Hilbert? axiomatic investigations into geometric construction problems. More specifically, we will analyze the meaning of these investigations by considering them from the perspective of the central ?Cartesian? program in early modern geometry, which aimed at the classification of geometrical problems according to the simplest means for their solution. As is well known, throughout La géométrie (1637), Descartes sketched a hierarchy of problems by sorting them out into classes according to the degree of their associated equations. In other words, he showed how the degree of the equation associated with a problem contained information about the constructability of the geometric problem itself, which could be also used to establish an algebra-based classification of problems.