ABSTRACT

From Chapter 15, by sorting through the ideas appearing in and concepts studied in the history of mathematics, we discover that some ideas and concepts, such as those of infinitesimals, infinities, limits, etc., underlie each crisis in the foundations of mathematics. After introducing the concepts of actual and potential infinities, in this chapter, we are able to uncover some hidden contradictions in the system of modern mathematics and see the return of the Berkeley paradox in the foundations of mathematics. By formally mapping the history of mathematics onto our yoyo model, it can be shown using available statistics that the periodic transitions between uniform and symmetric flows and chaotic currents existing in rotating fluids, the dishpan experiment, imply that the fourth crisis in the foundations of mathematics has occurred.