What a Mathematics Extended Essay is
The Extended Essay is an independently planned research project culminating in a paper of up to 4,000 words. In a Mathematics EE, mathematics must drive the investigation, whether the question arises from pure mathematics or a real-world application.
A convincing essay defines its terms, explains the methods used and develops a clear line of reasoning. Results are not only calculated; they are interpreted, checked and evaluated critically.
Develop a focused research question
Broad topics such as “fractals”, “cryptography” or “mathematics in music” are not yet research questions. A manageable mathematical focus emerges only after selecting a specific object, relationship or claim.
- The question enables mathematical reasoning rather than description alone.
- The scope fits the time, word limit and available understanding.
- Relevant sources and necessary data are accessible.
- The investigation allows evaluation rather than simple reproduction.
Depth rather than artificial complexity
Difficult mathematics used only for its own sake adds no value. The chosen concepts should be understood, applied correctly and connected into a coherent argument.
In an applied topic, the mathematical contribution must remain visible. The real context explains why the question matters; it should not replace the analysis.
A possible structure
- introduction with research question, aim and mathematical context
- definitions, assumptions and relevant sources
- development of the mathematical method or argument
- results, checks and discussion
- conclusion answering the research question directly
- bibliography and, where useful, a focused appendix
This is not a fixed template. The structure should follow the mathematical reasoning.
Supervision and reflection
The supervisor supports the research process but does not co-write the essay. Decisions, difficulties and changes of direction should therefore be documented throughout. The required reflection sessions are part of the process and help make development and independent work visible.