Mathematics Is Indefinite: An Ethical Challenge

Mathematics is indefinite with respect to concepts and proofs. Mathematical concepts are constructed and deconstructed, and conceptions of what is considered to be a mathematical proof have changed over time. Mathematics is indefinite with respect to topics and applications. The range of topics that characterise mathematics changes over time, both with respect to advanced mathematics and to school mathematics. Applications of mathematics can take surprising turns; what has been considered pure and harmless might turn out to be crucial for the further development of warfare technology. Mathematics is indefinite with respect to culture, and the Eurocentric interpretation of the history of mathematics draws in part on this indefiniteness to claim ownership of mathematics. Mathematics is indefinite with respect to power, and mathematics can be brought into action in order to serve a variety of interests. The fact that mathematics is indefinite raises a huge ethical challenge to mathematical research practices, to the philosophy of mathematics, and to mathematics education at all levels. Much research and education in mathematics ignores the possible social impacts of bringing mathematics into action, which leads to what is termed the “banality of mathematical expertise.” It is crucial to contest this banality.