Bolzano’s early mathematical concepts: Old terms within new practices?

Elías Fuentes Guillén

Pořádá Kabinet pro studium vědy, techniky a společnosti FLÚ AV ČR

anotace pdf

This talk will focus on the early –basic– mathematical concepts of Bernard Bolzano. In particular, I will discuss his notions of quantity and number. There is an established consensus among historians of mathematics concerning the relevance of his “Purely Analytic Proof” for the way it advanced in the direction of the ‘modern’ rigorous analysis. Based on the work done during the short-term stay in Prague thanks to the Josef Dobrovský Fellowship, I will argue that Bolzano was not doing the best with what he had by 1817, i.e. he was not merely using the available terms to work within new practices and develop new concepts, but instead his mathematical notions and practices still featured traits that were heavily deviant from later ones of modern real analysis. And yet, at the same time, he appears as an important pre Weierstrassian author and a pioneering figure because of some innovative features and concerns present in his first writings. 

Questions and discussion following the talk will be led by Dr Steve Russ (University of Warwick, UK).