Mathematics as a Tool

Mathematics as a Tool

October 2012 - September 2016

The ZiF Cooperation Group investigates the role and scope of mathematics as a tool. Its goal is to analyze a particular function of mathematization, namely, establishing the interconnection between theory and experience. The two notions of measurement and intervention will be the main focus. On the one hand, mathematics is relevant when facts are going to be registered, while on the other hand, it is significant when facts are to be changed in a targeted way - or are to be brought about at first. In the first case, mathematics is part of so-called observation theories, while in the second case it is an instrument of technical intervention.

The enormous increase of available computational power has transformed and widenend the ways in which mathematics as a tool is significant. Four aspects receive closer inspection, namely, the use of mathematics

• in automatizing the linkage between theory and experience,
• in imaging procedures,
• in the conception of phenomenological models, and
• in computer simulations.

The first two items deal mainly with registration while the latter items focus on intervention. The investigation of these items requires us to deal with two questions:

• To what extent is lucidity or cognitive transparency fostered or impeded by the use of mathematical methods as tools?
• What are the options for the validation of these methods?