Maths EPQ ideas: pure maths
Proof, number, infinity and structure. These suit students who enjoy the proof parts of A Level and want to read ahead.
Tip. Pick a result you can prove completely, then a comparison or extension that needs your judgement.
10 ideas
- Proofs that the primes never run outWhich proof that there are infinitely many primes is the most powerful, and why?
- Proving numbers are irrationalHow far can proof by contradiction take us in showing that numbers are irrational?
- Fermat's Last Theorem for n = 4Why can Fermat's Last Theorem be proved for n = 4 with school mathematics when the general case took over 350 years?
- Are some infinities bigger than others?Are some infinities bigger than others, and how convincing is Cantor's argument?
- Why mathematicians accepted imaginary numbersWhy did mathematicians come to accept imaginary numbers, and what can they do that real numbers cannot?
- Is the golden ratio really everywhere?Is the golden ratio really found throughout nature and art, or is it a mathematical myth?
- When does iteration converge?When does the iteration xₙ₊₁ = g(xₙ) converge to a root, and how can the speed of convergence be predicted?
- What makes e the natural base?What makes e the 'natural' base for exponentials and logarithms?
- The four colour theorem and computer proofWhy was the computer-assisted proof of the four colour theorem controversial, and should it be trusted?
- From the pigeonhole principle to Ramsey numbersHow far can the pigeonhole principle take us, from simple puzzles to Ramsey numbers?
Frequently asked questions
Is pure maths a good area for a maths EPQ?
It can be, if you narrow it to one question you can answer with mathematics you understand and evidence you can find. Pick a result you can prove completely, then a comparison or extension that needs your judgement.
Can I use one of these titles as it is?
Use it as a starting point. Change the case, the data or the comparison until the title is your own, and agree it with your supervisor before you start.
Other areas: Modelling · Statistics · History and philosophy · Economics and society · Computer science · Physics and engineering · Biology and medicine · Music, art and sport · Artefacts
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The Extended Project Qualification is offered by several awarding bodies, including AQA, Pearson Edexcel, OCR and WJEC/Eduqas. A Level Math Revision is independent and is not affiliated with or endorsed by any awarding body or university. Summaries of the rules are in our own words: your school and your board's specification have the final say. Every idea here is our own.