ABSTRACT
The chapter aims to give a critical presentation of Jacob Klein’s study on the origin of the modern process of formalization. It is divided into three strictly related parts. In the first one, I set forth Klein’s general motivation and philosophical principles that guide his investigations in the history of mathematics. I argue that entire perspective can be consistently interpreted as “critical” in the sense I introduce. In the second part, I take into account Klein’s specific thesis concerning the “exemplary case” that he considers, namely the difference between the Greek and the modern formalized concept of number. In the last part, I draw some conclusions from the two first moments of my chapter in order to offer a plausible interpretation of Klein’s account of the transformation of the concept number and to propose some brief explanatory philosophical consequences.
