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Mathematics Extended Essay Guide
A guide to writing an original, well-structured IB Mathematics Extended Essay that explores genuine mathematical ideas beyond the syllabus.
What is a Mathematics Extended Essay?
The Mathematics Extended Essay (EE) is one of the most challenging and rewarding parts of the IB Diploma. Below you will find everything you need to choose a strong topic, design your methodology, and write a high-scoring EE in Mathematics.
Word Count
3,500 – 4,000 words
Excluding bibliography, abstract, and appendices. Budget every section carefully before you start writing.
Assessment
Graded A–E
Combined with the TOK essay for up to 3 bonus IB Diploma points. A strong EE and TOK = maximum bonus.
Timeline
12–18 months
From initial topic to final submission. Most students underestimate this. Start early and plan backwards from your deadline.
Supervision
3 required meetings
Initial, interim, and final (viva voce). Each requires an RPPF reflection. Your supervisor approves your RQ.
Strong Mathematics EE Topic Ideas
| Topic Idea | Why It Works | Difficulty |
|---|---|---|
| How accurately can the Monty Hall problem be modelled using conditional probability, and what does it reveal about human intuition? | Probability, accessible, philosophical dimension | Easy |
| How does the Golden Ratio appear in the geometry of the Fibonacci spiral, and to what extent is it present in nature? | Number theory, geometry, applications | Easy |
| To what extent can the SIR epidemiological model accurately predict the spread of COVID-19 in New Zealand (March–June 2020)? | Differential equations, real data, modelling | Medium |
| How does the Fourier Transform enable signal processing in noise-cancelling headphones? | Applied mathematics, Fourier analysis, technology | Hard |
| To what extent can game theory (Nash equilibrium) explain the tragedy of the commons in fisheries management? | Game theory, applied mathematics, economics | Hard |
| How do prime number distributions relate to the Riemann Hypothesis, and what patterns emerge in prime gaps? | Number theory, analytical mathematics, advanced | Hard |
Subject-Specific Advice
Go Beyond the Syllabus
Explore new mathematics
A strong Maths EE must engage with mathematics beyond the DP course. Choose a topic that requires you to learn new mathematical ideas — not just apply syllabus content.
Mathematical Rigour
Prove, do not just assert
Every mathematical claim must be justified: prove theorems, derive results, or provide rigorous justification. “It is obvious that…” is never acceptable.
Personal Engagement
Show genuine curiosity
The best Maths EEs have a personal voice — explain what drew you to the topic, what surprised you, what questions emerged as you explored it.
LaTeX or Equation Editor
Present mathematics clearly
Use LaTeX, Microsoft Equation Editor, or Google Docs Math to typeset your equations. Handwritten equations photographed and inserted into Word look unprofessional.
Assessment & Common Mistakes
Assessed on: mathematical knowledge, mathematical argument and rigour, clarity of mathematical presentation, and engagement with mathematics beyond the syllabus. A Maths EE that is all calculations without argument or exploration scores in the lower bands.
⚠ Common Pitfall
Students choose topics that are entirely within the syllabus (like “How does calculus work?”) or that are far too broad (like “The history of mathematics”). A Maths EE must explore a specific mathematical question with genuine rigour — proving something, modelling something, or investigating a mathematical pattern beyond what is taught in the course.
Mathematics EE Checklist
- ✓ My topic goes beyond the DP syllabus — I have learned new mathematical ideas for this EE
- ✓ My RQ is a specific mathematical question that can be investigated rigorously
- ✓ All mathematical claims are proved or rigorously justified — no unsupported assertions
- ✓ Equations are typeset correctly (LaTeX or equation editor)
- ✓ My exploration includes original mathematical work — not just summarising known results
- ✓ My conclusion states what my investigation has established mathematically
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