4. Formalism, structuralism, and the doctrine of neutrality

The doctrine of neutrality states that mathematics can be researched and developed without considering any ethical or socio-political issues. This doctrine became elaborated and argued in detail by the school of logical positivism. By the turn of the nineteenth century, a range of paradoxes and inexplicable mathematical phenomena appeared, a situation referred to as the foundational crisis of mathematics. To many, intuition was the scoundrel, and it had to be eliminated from mathematics. Formalism provided a principal approach by identifying mathematics with formal structures. This idea was embraced by logical positivists who claimed that mathematics as the language of science ensures the ethical neutrality of science. They considered mathematics not only as being neutral itself, but also as a guarantee for scientific neutrality in general. In this way, a most profound stipulation of the doctrine of neutrality was reached. Formalism developed into structuralism, which described mathematics as an architecture of pure formal structures. As part of the structuralist conception of mathematics, the doctrine of neutrality was expanded from being a conception of mathematical research to become also a doctrine shaping educational practices in mathematics. I am going to confront this conception. The doctrine of neutrality is a stipulation, which makes us ignore that a profound politicisation of both mathematics and mathematics education might be taking place.