Using maths examples in your TOK essay

The essay in brief

• You answer one of the 6 prescribed titles the IB publishes for your exam session. Your teacher has them; they change every session, and we never reproduce them.
• The maximum length is 1,600 words.
• The essay is external: marked by ib examiners and counts for two thirds of the TOK assessment.

Bringing mathematics into any title

1. Find the knowledge issue in the title. Is it about certainty, evidence, perspective, method, responsibility? Write it in your own words.
2. Ask what mathematics says about that issue. Use the question library to find a matching knowledge question.
3. Choose one or two precise examples, such as the four colour theorem for trust in technology, or the replication crisis for evidence. One well-explained example beats five name-drops.
4. Compare with another area of knowledge where the title asks for it; mathematics is often most interesting as a contrast.
5. Use your own experience: your IA, a proof you found hard, a result that felt wrong.

A paragraph scaffold

Use this to check the shape of a section you have already drafted. It is a frame for your thinking, not text to fill in.

1. Claim: one sentence that answers part of the title.
2. Example: a specific situation from mathematics, with the detail that matters.
3. Analysis: how the example supports the claim, using TOK concepts.
4. Counterclaim: the strongest reason to doubt the claim, with its own example.
5. Evaluation: which is stronger, when and why.
6. Link: what this means for the title.

Evaluating claims about mathematics

• Is the claim about all of mathematics or one part of it (pure, applied, statistics)?
• Does it confuse a method (proof) with how people actually work (intuition, computers, community)?
• Is the 'certainty' claimed conditional on axioms or assumptions?
• Would a mathematician, a statistician and a historian of mathematics agree?
• What would change your mind?

Referencing

Cite every fact, figure, quotation and borrowed idea, in one consistent style your school accepts. Record the source as you read. For historical examples, prefer a reliable book or article to a single website. The referencing guide on our EE pages applies to TOK too.

Free self-check

Tick what is true of your draft. Nothing is saved or sent; this is a checklist, not a mark. We do not offer AI feedback on TOK writing while we check how the IB marks it.