93 maths EPQ ideas and title examples
Every idea has a question-style title, an honest note on scope, the A Level topics it builds on, the maths you would learn, a possible plan, pitfalls and where to start reading. They are starting points: the strongest projects change the title until it is their own.
Accessible ideas build mostly on A Level Maths; Solid ideas need some new maths learned on your own; Ambitious ideas suit students happy to read first-year university material. 33 ideas can be done as an artefact.
Pure maths
- 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?
Applied maths and modelling
- Modelling a school canteen queueCan a mathematical model of the school canteen queue reduce waiting times?
- Timing traffic lightsHow should traffic light timings be chosen to minimise queues at a busy junction?
- Air resistance and the best launch angleHow much does air resistance change the best angle to launch a projectile?
- Modelling the UK populationHow well do exponential and logistic models predict the UK's population?
- How fast does a cup of tea cool?How accurately does Newton's law of cooling predict how fast a cup of tea cools?
- The 37% rule for choosing the bestWhen should you stop looking? How well does the 37% rule work for choosing the best option?
- How reliable is radiocarbon dating?How reliable is radiocarbon dating, and what limits its accuracy?
- Modelling a school evacuationHow long would it take to evacuate your school, and can a model find a faster plan?
- Linear programming and the cheapest dietCan linear programming design the cheapest healthy diet, and should we trust its answer?
Statistics and data
- Benford's law in UK dataDoes Benford's law hold for UK data sets, and could it detect made-up numbers?
- Shared birthdays in real classesHow likely are shared birthdays in real classes, given that births are not spread evenly through the year?
- Why do opinion polls miss?Why do opinion polls sometimes get UK general elections wrong?
- Simpson's paradox in real dataWhen can combining groups of data reverse a conclusion, and how should we decide which answer is right?
- Does sacking a football manager work?Does sacking a football manager improve results, or is it regression to the mean?
- P-values and the replication crisisWhy do so many published results fail to replicate, and how much is the p-value to blame?
- Can people be random?Can people generate random sequences, and how can statistics tell?
- How accurate are weather forecasts?How accurate are UK weather forecasts, and what is the fairest way to measure accuracy?
- Is the lottery a fair game?Is a national lottery a fair game, and what is a ticket really worth?
History and philosophy of maths
- Is maths discovered or invented?Is mathematics discovered or invented? Weighing Platonism against formalism
- Maths and the breaking of EnigmaHow much did mathematics contribute to breaking Enigma, compared with other factors?
- Newton or Leibniz?Newton or Leibniz: who deserves credit for calculus, and did the dispute hold British mathematics back?
- How zero became a numberWhy did it take so long for zero to be accepted as a number?
- What Gödel really provedWhat do Gödel's incompleteness theorems really show about the limits of mathematics?
- Ada Lovelace and Note GWas Ada Lovelace the first computer programmer? Evaluating her Note G
- The parallel postulate and new geometriesHow did doubts about Euclid's parallel postulate lead to new geometries, and are they 'true'?
- Ramanujan and mathematical intuitionHow did Ramanujan reach results without proofs, and what does his work say about intuition in mathematics?
- Why you cannot trisect an angleWhy could the ancient Greeks not trisect an angle with straight edge and compass, and how was it finally proved impossible?
- Florence Nightingale's statisticsHow did Florence Nightingale use statistics and diagrams to change policy, and would her diagrams pass today's standards?
Maths in economics, finance and society
- Game theory and cooperationCan game theory explain why rival firms or countries fail to cooperate?
- What a student loan really costsHow much will a student loan really cost? Modelling repayments over a working life
- How inflation is measuredHow is inflation measured, and does the official figure reflect what students actually spend?
- Pricing an option with probabilityHow can probability put a fair price on a financial option?
- The Kelly criterion: how much to riskHow much should you risk on a favourable bet? The Kelly criterion and the mathematics of growth
- Which auction raises the most?Which auction design raises the most money? Comparing first-price and second-price auctions
- How progressive is UK income tax?How progressive is the UK income tax system once National Insurance is included?
- Measuring inequality with the Gini coefficientHow well does the Gini coefficient measure inequality?
- Which voting system is fairest?Which voting system is fairest? Testing first past the post against the alternatives
Maths and computer science
- How RSA keeps payments secureHow does RSA encryption keep online payments secure, and what would it take to break it?
- Which sorting algorithm is fastest?Which sorting algorithm is fastest in practice, and does Big O notation tell the whole story?
- How search engines rank pagesHow can matrices and probability rank web pages, and how could the ranking be manipulated?
- How QR codes survive damageHow can a damaged QR code still be read? The mathematics of error-correcting codes
- How compression makes files smallerHow can a file be made smaller without losing anything, and what is the limit?
- How a neural network learnsHow does a neural network learn, and how much of it is calculus you already know?
- Quick routes for the travelling salesmanHow close can quick methods get to the best route in the travelling salesman problem?
- How computers fake randomnessHow can a computer, which follows rules, produce random numbers, and how random are they?
- Hash collisions and the birthday problemHow likely are two different files to share a hash, and what does the birthday problem say about security?
Maths in physics and engineering
- Hanging chains and bridgesWhy is a hanging chain not a parabola, and does the difference matter in bridge and arch design?
- Kepler's third law from NewtonHow can Kepler's third law be derived from Newton's laws, and how well does it fit the planets and moons?
- When the small-angle approximation failsHow large can a pendulum's swing be before the small-angle approximation fails?
- Why rockets have stagesWhy do rockets need several stages? What the rocket equation shows
- Moments in a shelf or simple bridgeHow does the position of a load change the forces on the supports of a shelf or simple bridge, and can a model predict failure?
- Modelling a skydiverHow does a skydiver reach terminal velocity, and how well does a quadratic drag model fit real jumps?
- How satellites locate your phoneHow does a phone use satellite signals to work out where it is, and what limits the accuracy?
- Exponential charging in circuitsHow closely does a charging capacitor follow the exponential model, and why does it matter in circuit design?
- The limit on wind turbine powerHow much power can a wind turbine extract from the wind, and why is there an upper limit?
Maths in biology and medicine
- Modelling an epidemicHow well does a simple SIR model capture the spread of an epidemic, and what does it imply for vaccination?
- When a positive test is probably wrongWhy can a positive result from an accurate medical test still be more likely wrong than right?
- Planning repeated drug dosesHow do exponential decay and geometric series explain the dosing of repeated medicines?
- Predator and prey cyclesCan the Lotka–Volterra equations explain the cycles in predator and prey populations?
- How big should a clinical trial be?How many patients does a clinical trial need for enough statistical power, and what goes wrong when it is too small?
- Is BMI a good measure?Is body mass index a sound measure, mathematically speaking?
- DNA evidence and the prosecutor's fallacyHow should a court interpret the chance of a DNA match, and how has probability been misused in trials?
- Models of tumour growthWhich growth model best describes tumour growth: exponential, logistic or Gompertz?
- Why giants cannot existWhy can't giants exist? Scaling laws in biology from ants to elephants
Maths in music, art and sport
- Why a piano cannot be perfectly in tuneWhy can't a piano be perfectly in tune? Equal temperament versus just intonation
- Why instruments sound differentWhy do a violin and a flute playing the same note sound different? Fourier analysis and timbre
- Perspective in Renaissance artHow did Renaissance artists use geometry to create perspective, and how accurate were they?
- Tilings and EscherWhich shapes can tile the plane, and how can symmetry be used to design an original Escher-style tiling?
- Predicting race timesCan you predict a marathon time from a 5 km race? Testing a power-law formula
- Game theory and penalty kicksWhere should a penalty taker aim? Game theory and mixed strategies in football
- Fair targets in rain-hit cricketHow does the DLS method set fair targets in rain-affected cricket, and is it fair?
- How Elo ratings workHow does the Elo rating system work, and is it a fair way to rank teams or players?
- Why tennis scoring rewards the better playerWhy does tennis scoring turn a small edge on each point into a big edge in matches?
Artefact projects
- An interactive epidemic simulatorCan an interactive simulation help Year 12 students understand how epidemics spread?
- A puzzle resource for teaching inductionCan a set of puzzles teach proof by induction better than a textbook explanation?
- Designing a fair board gameCan a board game be designed so that every player has an equal chance of winning?
- A spaced-practice formula appCan a spaced-practice app improve how well students remember A Level formulae?
- Building an arch from a hanging chainCan a model arch shaped by a hanging chain carry more load than a semicircular arch?
- An honest climate data visualisationHow can an interactive visualisation make UK climate data clearer without misleading?
- A working cipher machineCan a working model cipher machine show why rotor ciphers were strong, and where they were weak?
- A fractal art generatorHow can iteration with complex numbers generate fractal art, and why is the Mandelbrot set's edge so intricate?
- Building a tuned instrumentCan the mathematics of vibrating air columns be used to build an in-tune set of pipes?
- A Sudoku solverCan a program solve any Sudoku, and how does computer backtracking compare with human logic?
No ideas match those filters. Try fewer.
How to choose
- Shortlist three ideas in an area you enjoy and read a little about each.
- Check you can follow the core maths: try one worked example from a source.
- Check the evidence exists: data you can get, sources you can read.
- Narrow it to one case, one comparison or one data set.
- Take your shortlist to your supervisor before you commit.
Then test your title with the title checker and plan it with the timeline planner.
Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.
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.