Resource Guide
Research Project Ideas in Mathematics for High School Students
Specific, explorable questions across pure mathematics, applied modelling, probability, and mathematics in society, with guidance on what a maths project actually is.
How to Use This List
A mathematics project worries students more than most, because they imagine it must mean proving something new. It rarely does. The best school-level mathematics research takes a real piece of mathematics, often just beyond the syllabus, understands it deeply, and explains it clearly, sometimes with the student’s own examples, computations, or small extensions.
Use the questions below as starting points. The goal is depth and clarity, not novelty for its own sake. Our guide to writing a research question helps frame a focus, and good mathematical writing rewards the same care as any other scholarly work.
Ideas by Sub-Field
Pure mathematics
- ↳ What makes the distribution of prime numbers so hard to predict, and what patterns are known?
- ↳ How does knot theory distinguish one knot from another, and why is that hard?
- ↳ What can be said about a chosen family of geometric shapes or tilings?
Applied mathematics & modelling
- ↳ How can a simple differential-equation model capture the spread of a disease or a rumour?
- ↳ What does a mathematical model reveal about traffic flow or queueing?
- ↳ How well does a chosen model predict a real pattern in open data?
Probability & statistics
- ↳ Why do counter-intuitive results, such as the Monty Hall problem, arise, and what do they teach?
- ↳ How can common statistical claims in the media be checked, and where do they go wrong?
- ↳ What does the mathematics of risk reveal about a real-world decision?
Mathematics & society
- ↳ How does public-key cryptography use number theory to keep data secure?
- ↳ What does game theory predict about a real strategic situation, and does it hold?
- ↳ How can the mathematics of fairness inform the design of a voting or allocation system?
Understanding Deeply, Explaining Clearly
The mark of a strong mathematics project is not difficulty for its own sake but clarity: the ability to take something genuinely hard and make it understood, with rigour intact. A student who can explain why a result is true, not merely state it, has done real mathematical work.
A mentor helps a student choose a topic at the right level, fill the gaps that textbooks leave, and write mathematics the way mathematicians do, precisely, honestly, and with the reader in mind. That skill is exactly what a mathematics interview seeks to draw out.
Taking a Question Further
Mathematics is the language of physics, computer science, and economics, and projects often bridge into them. For the wider context, see our Technology, AI & Engineering field page, our companion guides to physics and computer science, and our broader research project ideas across all six fields. When you are ready to turn a question into a finished project with a mentor who works in the field, the Research Scholar programme is built for exactly that.
Frequently Asked Questions
What does a mathematics research project look like at high school level?
It is rarely about proving a brand-new theorem. More often it is exploring a known area deeply, working through and explaining a result, investigating a conjecture computationally, or applying mathematics to model a real problem. The aim is genuine understanding and a clear written account of it.
Do I need to discover something original?
No. Original results are wonderful but rare at this level. A project that takes a piece of real mathematics, understands it deeply, and explains it clearly, perhaps with the student’s own examples or small extensions, is genuine and valued.
Can a maths project use computing?
Absolutely. Computational exploration, generating data about a conjecture, visualising a structure, or simulating a process, is a powerful way to investigate mathematics, and it pairs naturally with rigorous reasoning.
How is a maths project useful for university applications?
Mathematics and related courses look for students who enjoy thinking about mathematics beyond the syllabus and can communicate it clearly. A project demonstrates exactly that, and gives an applicant something specific to discuss in an interview.
Summer cohort deadline · Applications due June 25. A few places remain. We assess applications in order of receipt.
ScholarBridge matches students with doctoral-level or equivalent research mentors across six academic fields. Every project is student-led and completed to a standard the student can stand behind in any university interview.
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