Mathematics — Certainty, Perspectives, and Applications

Mathematics presents TOK with its sharpest questions about certainty and the nature of knowledge. This lesson examines whether mathematics is discovered or invented, the limits of its certainty, and its relationship to the other areas of knowledge.

Discovered or invented?

The central perspectival debate in mathematics is whether mathematical truths are discovered or invented. Platonists hold that mathematical objects and truths exist independently of human minds, and that mathematicians discover them much as explorers find new lands; the fact that different cultures arrive at the same theorems, and that math describes the universe so well, supports this view. Formalists and constructivists counter that mathematics is a human creation, a system of rules and symbols we build, and that its ob