Summer School 2021

Freedom and mathematics


Dr Gregory Fried, senior lecturer, Department of Philosophy, University of Cape Town

Some think of pure mathematics as a rigid discipline that denies free choice by insisting on necessary inferences. This course proposes otherwise, arguing that mathematics provides a rich and tolerant field for the exercise of intellectual freedom, untrammelled by the constraints of physical reality and even the limits of human imagination.

To show how mathematics offers a distinctive source of freedom, it compares two innovations of the nineteenth century. One was the advocacy of individual liberty, pushing freedom of expression beyond traditional pieties. The other was the introduction of non-Euclidean geometries, which extended the science of spaces past Euclid’s ancient framework, and rebutted Kant’s idea that geometry aims simply to describe our intrinsic way of seeing the world. Finally, the course turns to recent reflections on the varieties of liberty that mathematics can bring.


  1. Champions of individual liberty: Mill and others
  2. Far beyond Euclid: Bolyai, Riemann and others
  3. The freedom of doing mathematics: Lakatos, Villani and others

This course will be offered on the Microsoft Teams platform. Participants will be sent a link.


Date: Wednesday 20–Friday 22 January
Time: 11.15 am