Topics in Philosophy of Mathematical Practice

Course content

This highly interactive summer school offers students from mathematics and philosophy of mathematics the opportunity 1) to gain knowledge about the central topics in the philosophy of mathematical practice and 2) to gain the basic skills needed in order to practice empirically informed philosophy of mathematical practice themselves. 

The course will be organized in two parts, a four-week asynchronous online part (25 hours per week) and a two week synchronous online part (full time). 


The asynchronous online part will include reading of research papers, online discussion of topics raised in the papers, online collaboration and supervision in developing problem formulations for final products. The material will primarily be centered on the following four themes from contemporary philosophy of mathematical practice: 

  • The role of diagrams in mathematical practice 
  • Proofs as vehicles of communication in mathematical practice
  • Experimental aspects of mathematical practice
  • Formal aspects of mathematical practice

Furthermore, the students will familiarize themselves with basic theories of empirical data collection during the online part of the course.


The synchronous online part will consist of the following three elements: 

  • Lectures following up on the four themes in philosophy of mathematical practice covered in the on-line part. 
  • Workshops on empirical data collection.
  • Practical work preparing an empirically informed product in the philosophy of mathematical practice (such as an essay informed by data from e.g. qualitative interviews, a questionnaire or corpus analysis performed by the student).


Students will receive group supervision on their product during the synchronous online part of the course. 

Learning outcome

After following the course students should have the following skills, knowledge and competences:


The students should be able to collect and analyze empirical material


The students should be able to account for central topics in the philosophy of mathematical practice.


The students should be able to:

  • Reflect on the strengths and limitations of empirical methods.
  • Discuss and reflect on central topics in philosophy of mathematical practice.
  • Produce empirically informed written products in the area of philosophy of mathematics.

Online lectures, exercises, group work, group supervision, and practical workshops.

Students will be given a collection of research papers and excerpts from text books. 

It is recommended that at least one of the following three qualifications is fulfilled:
1) BSc in mathematics and knowledge about philosophy.
2) BA in philosophy and knowledge about mathematics.
3) knowledge equivalent to one of the following books:
- Johansen and Sørensen (2014): Invitation til matematikkens videnskabsteori
- Mark Colyvan (2012): An Introduction to the Philosophy of Mathematics

Please note that the course has both online and on-campus activities

Feedback by final exam (In addition to the grade)

The student will be given oral feedback of the short presentations made during the synchronous online part of the course, and a short written feedback of the final exam project. 

7,5 ECTS
Type of assessment
Written assignment
Type of assessment details
Take-home assignment consisting of four small exercises posted during the asynchronous online part of the course and a written project to be produced during the synchronous online part of the course and in the following week. All five parts of the assignment must be handed in no later than friday in the examination week. The assignment will be assessed as a collected whole.
Exam registration requirements

The student must give and pass two short oral presentations during the synchronous online part of the course.

All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
One internal examiner

Resubmission of the written assignment. The revised assignment must be submitted by the end of the re-exsamination week following blok 1, 2024.

If the student has not passed the exam registration requirements the student must 1) give and pass an oral presentation of about ½ hours length for the course responsible and 2) hand in a written report that roughly covers the main activities during the on campus part of the course after closer agreement with the course responsible. The presentation must be held and the report handed in at least three weeks before the start of the reexam week.

Criteria for exam assessment

See Learning Outcome

Single subject courses (day)

  • Category
  • Hours
  • Class Instruction
  • 30
  • E-Learning
  • 100
  • Project work
  • 50
  • Exam
  • 26
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master
On-line part: 1-26 July 2024 (4 weeks at 25 study hours per week)
On-campus: 29 July - 9 August 2024 (full time/40 study hours per week)
Individual project: 12-23 August 2024 (26 hours)
Written project exam assignment, hand in: 23 August 2024
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Science Education
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Mikkel Willum Johansen   (3-7c86794f787d733d7a843d737a)
  • Henrik Kragh Sørensen   (12-716e777b727437747b6a70714972776d37747e376d74)
Saved on the 13-09-2023

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