Mathematics is often framed as an introvert, abstract and purely objective research area. In this course we contest this definite image by showing that none of these adjectives completely cover mathematics. For instance, as advanced mathematical notions are used in developments in ICT and around big data, mathematics is not just an introvert field. It is a field that also impacts society and everyday life. Furthermore, both the abstractness and objectivity of mathematics are in tension with the fact that mathematics is performed by its practitioners: human beings. 
This course focusses on both these topics and can be summarized by one question: what is the relationship between mathematics, its practitioners and society? Even though such a question is far too broad to uniquely determine the content of this course, this question does motivate the themes of the course.
 
The first theme we discuss is philosophy of mathematics. Roughly speaking, its main question is “What are mathematical objects and how can we know them?” Different schools of thought give sometimes opposing answers to these questions. We discuss several of these views, including formalism, platonism and intuitionism.
 
In the second theme we investigate how we ‘do mathematics’. A more formal term for this line of research is Philosophy of Mathematical Practice. Questions that arise in this field are, for instance, “What is the role of informal proofs in mathematics?”, “What is the role of visualization in mathematics?” and “What is the role of computers in mathematics?”
 
The third theme we encounter is the relation between mathematics and society. We shall see that mathematics has significant impacts on our worldview. To give a quick, but convincing example, consider how the computer has its origin in logic.
One of the tools with which we assess the impacts of mathematics on society is the distinction between soft and hard impacts. 
 
As an appetizer, we list some (but definitely not all) topics that will be discussed in the course:

• The role of big data and mathematical models in daily life.
• The notion of proof: what constitutes a proof and how has this notion evolved over time?
• Game formalism
• Mathematical Research Programmes
• The responsibility of mathematic(ian)s.

 
In addition to the afore mentioned material, we will also devote some time to the question on how to write a proper essay. This will give you clear handles for the final assignment.