Areas of knowledge - Maths
Maths
Scope, perspective, methods and ethics
The problem TOK students have with mathematics is that they are certain it is certain. A proven theorem stays proven; a valid argument cannot become invalid. That certainty is real - but it does not tell you what mathematics is, where it comes from, or what it does when it reaches the world. Is mathematics discovered or constructed? Does it belong to all cultures equally, or has the history of who gets credited been written by some and not others? Does the authority of a number make the tools built with it neutral?
The four pages of this theme follow those questions across the TOK framework: what kind of knowledge mathematical certainty is and where its limits lie, whose traditions have shaped what counts as mathematics and who has been credited for it, how mathematical tools produce knowledge and what they cannot reach, and what follows when models that claim objectivity make decisions about people's lives.
Mathematics claims a kind of certainty no other discipline can match. A theorem proven in ancient Greece is as secure today as the day it was established. This page examines what kind of knowledge that is - whether mathematics is discovered or constructed, and what follows from beauty being part of the mathematician's test for a good proof.
Mathematical results are typically presented as culture-free: proven or not, anywhere. But the history of mathematics has been written by particular people in particular places, and traditions from India, China, and the Islamic world were excluded when European historians wrote the standard account. This page examines how perspective has shaped what counts as mathematics and who gets credited for it.
Mathematics produces knowledge through proof - a form of justification that eliminates uncertainty rather than reducing it. But what does a proof actually establish, and what changes when machines verify proofs faster than humans can read them? This page examines how mathematical knowledge is generated, and where formal proof ends and tacit knowledge begins.
A number carries authority that an opinion does not. A model, a risk score, an algorithm - these feel objective in ways that make them hard to challenge. This page examines cases where that authority was misused: where tools were built to confirm prior conclusions, and where models made high-stakes decisions about individual lives.