## The project

Although Mathematics is rarely present in public discourses, it counts as one of the leading sciences of our time. It is not only useful in the world of science but also in the world of industry and commerce where it often aids the invention of new products. Thus, credit cards, CD-players, navigation systems, as well as many other technical products and software are based on sophisticated mathematical equations. High technology is always also mathematical technology.

On account of its abstractness, mathematics is one of the most wide-ranging sciences. This leads to an ever-growing amount of mathematical reconstruction of objects and facts in application areas. Language plays an important role in this: Mathematicians have to first get an idea of the relevant characteristics of the objects and facts that are to be modeled. The latter always happens with the help of the respective representatives of the application areas. In addition, mathematicians have to persuade others – such as engineers and managers – of the value of their science for it to be made use of.

The domain of knowledge *Mathematics* will study these modeling and persuasion processes from a linguistic point of view in order to explain the role of language in the development of industrial products by means of representative examples. To do this, the domain will look especially at professional communication within individual organizations. A next step will be the analysis of the use of mathematics in a wider field, such as the development of identification numbers for the control mode of organizations. Thus, the perceived mathematization of the world is to be made empirically subsumable.

The methodological approach is taken from ethnographically oriented works from the area of the sociology of knowledge. Through linguists accompanying selected research and developmental projects as “participating observers”, the inner life of industrial mathematics is to be described. At the heart of this will be the work with texts, which result from such projects, e.g. software documentations and marketing materials.

The partners will be mathematicians, who work in the research and developmental departments of companies, in universities or in extra-facultative institutes for industrial mathematics.

## Aims

The domain will answer the following questions:

- How does knowledge emerge in industrial mathematics? What are the differences to pure mathematics? What interests do the participants have? What role do they understand themselves as playing?
- How is the mathematical knowledge in the application areas made useful? How are theories, concepts and objects defined and redefined, substituted or reinterpreted to be applicable in mathematics? What resistances come up in this process?
- How much of mathematics remains in the application? How much of it is visible and invisible in products, software and texts?
- How are customers persuaded of the usefulness of mathematics? What arguments justify the application of mathematics from the point of view of customers and users?
- Can a mathematical way of thinking be found in the mathematization of the application area? Can a reality constituting force of mathematics be attributed to it?