In this paper is presented and discussed the notion of true finite by opposition to the notion of theoretical finite. Examples from mathematics and physics are given. Fermat’s infinite descent principle is challenged.

This paper presents a historical view of the rise of mathematical universalism in modern times. It argues that 20th century mathematical revolution laid the foundations for a new universalism which extended to physics, economics, informatics, and recently biology. It describes the role played by the organization of mathematical work for closer co-operation among scientists on an international scale throughout the century, and stresses the importance of mathematics in the education process.