Philosophy of Mathematics at the start of the 20

^{th} century focused on questions like ‘What is a mathematical object?’ and ‘How can we know mathematical truth?’. Even though they are interesting in their own right, these questions were not directly relevant for those conducting actual mathematical research. Algebraic topology flourishes regardless of whether numbers are mental constructs or formal entities devoid of meaning or objects in a realm independent of space and time.

As a response to this foundational tradition, several Mathematicians and Philosophers of Mathematics started zooming in to what working mathematicians (and mathematics students) were actually doing. This resulted in the field Philosophy of Mathematical Practice.

In this course we will discuss several topics from the Philosophy of Mathematical Practice (PMP) and we will relate this to the students’ experience with mathematics. Basically, the goal is that students focus in this course on the

*why* of mathematics and reflect on their activities as mathematicians and on the accepted methods in mathematics in general. This also involves discussing the material with peers.

The course starts with an introductory lecture in which we also give a rough overview of main schools of thought from the foundational Philosophy of Mathematics. Then we will treat a different topic from the Philosophy of Mathematical Practice each week.

The list of topics includes, but is not limited to:

- The role of visualization in mathematics
- The role of informal proofs in mathematics
- Mathematical beauty
- Mathematical explanation
- Mathematical definitions

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.

**Instructional Modes**