Completing a mathematics research project allows you to explore real-word applications of mathematical concepts. Choosing the right EPQ or dissertation topic could guide you toward a rewarding career in mathematics. So, check out our list of 100 ideas for research projects in mathematics to find inspiration.

What Makes a Great Research Topic in Mathematics?

Ask yourself what would make a great EPQ topic in mathematics for you. As you make your decision, keep these key points in mind:

  • Scope: while narrowing down a question allows you to limit the scope, ensure that your topic is broad enough to explore.
  • Personal interest: having a personal interest in an EPQ mathematics research project ensures that you remain engaged and motivated throughout. 
  • Application: pick an EPQ topic in mathematics that can solve real-world problems and contribute to the field.
  • Originality: look to approach your chosen research topic from a unique angle to offer a fresh perspective.

100 Research Ideas for Mathematics

Research Project Ideas in Pure Mathematics

  1. The mathematics of chaos theory and its applications
  2. The Fibonacci sequence and its occurrence in nature
  3. Geometry of fractals and their real-world applications
  4. Investigating number theory and prime numbers
  5. What is the Riemann Hypothesis and why is it important?
  6. Exploring the P vs. NP problem
  7. The history and development of calculus
  8. The development and importance of complex numbers in mathematics
  9. Exploring the importance of rigour in mathematics
  10. Understanding non-Euclidean geometry and its applications
  11. Exploring the mathematics of string theory
  12. Exploring the concept of infinity in mathematics
  13. The importance of mathematical logic and set theory
  14. The importance of group theory in abstract algebra
  15. Investigating the role of algebra in solving equations and systems
  16. The role of polynomials in solving algebraic equations
  17. The importance of mathematical proofs in geometry
  18. Exploring the role of algebraic structures in solving equations
  19. The role of symmetry in solving algebraic equations
  20. The use of combinatorics in solving complex problems
  21. How prime numbers are used in cryptography

Research Project Ideas about Applied Mathematics in Technology and Computing

  1. The role of mathematics in cryptography
  2. Using linear algebra to understand 3D transformations in computer graphics
  3. The mathematics behind machine learning algorithms
  4. Analysing the mathematics behind search engines
  5. The use of combinatorics in solving complex problems
  6. The role of algorithms in solving Rubik’s cube
  7. The mathematics behind blockchain technology
  8. The role of discrete mathematics in computer science
  9. The role of Monte Carlo methods in probability and statistics
  10. The use of set theory in computer programming
  11. Exploring optimisation algorithms in machine learning
  12. Investigating cryptographic methods based on prime factorisation
  13. How do algorithms work?
  14. The mathematics behind artificial neural networks
  15. The role of geometry in computer vision and image recognition
  16. The mathematics behind machine learning algorithms
  17. The role of Monte Carlo methods in probability and statistics

Research Project Ideas about Mathematics in Physical Sciences and Engineering

  1. Exploring the mathematics of elliptical curves and their applications
  2. The mathematics of symmetry in crystallography
  3. Investigating topology and its application in physics
  4. The application of differential equations in engineering
  5. The role of eigenvalues and eigenvectors in physics
  6. The role of dimensional analysis in physics
  7. Exploring the mathematics of fluid dynamics
  8. The mathematics of black holes
  9. The role of partial differential equations in modelling heat transfer
  10. The mathematics of flight dynamics
  11. Exploring how Fourier analysis is used in signal processing
  12. Investigating the use of calculus in physics
  13. The application of calculus in electrical engineering
  14. Investigating how calculus is used in pharmacokinetics
  15. The use of trigonometry in astronomy
  16. The role of probability in quantum mechanics
  17. Knot theory and its applications in biology and chemistry
  18. Exploring the role of vectors in physics and engineering
  19. Exploring the applications of matrix theory in quantum physics

Research Project Ideas about Mathematics in Economics and Finance

  1. Game theory and its applications in economics
  2. The mathematics behind stock market predictions
  3. Mathematical optimisation in logistics and supply chains
  4. The role of mathematics in AI
  5. Investigating the use of mathematical models in economics
  6. Bayesian probability and its applications
  7. The role of stochastic processes in economics
  8. The applications of linear programming in business optimisation
  9. The use of statistics in analysing sports performance
A tutor delivering a mathematics class

Research Project Ideas about Mathematics in Biology and Medicine

  1. Mathematical models of infectious diseases
  2. Investigating the role of probability in genetics
  3. The role of statistics in health and medical research
  4. The use of mathematical models in epidemiology
  5. Exploring statistical models in medical research
  6. Investigating mathematical modelling in sports performance analysis
  7. The use of statistics in analysing sports performance
  8. The applications of statistics in psychology and social sciences
  9. The importance of mathematical models in ecology
  10. Investigating the use of mathematical models in cancer research
  11. Investigating the mathematics behind disease spread in populations

Research Project Ideas about Mathematics and the Climate

  1. The mathematics of chaos and weather prediction
  2. The use of mathematical models in environmental conservation
  3. How mathematical models are used in predicting natural disasters
  4. Investigating the use of mathematics in climate modelling

Research Project Ideas about Mathematics and the Humanities

  1. The applications of statistics in psychology and social sciences
  2. The mathematics behind traffic optimisation in urban planning
  3. Exploring the relationship between probability and gambling
  4. Mathematical models of population growth
  5. Exploring mathematical approaches to solving traffic flow problems
  6. The mathematics of traffic optimisation in urban planning
  7. Exploring the mathematics of social media analysis
  8. The mathematics behind solving sudoku
  9. Exploring the applications of graph theory in networks and communications

Research Project Ideas about Mathematics and the Arts

  1. The mathematics behind architectural design
  2. The role of mathematics in music theory
  3. Investigating the golden ratio in art
  4. The influence of fractals in visual arts
  5. Exploring symmetry and patterns in art and design

Research Project Ideas about Mathematics and Politics

  1. How statistics can be used to predict election outcomes
  2. The mathematics of voting systems
  3. The use of game theory in political decision-making
  4. Investigating the mathematics of optical illusions
  5. Using network theory to understand political alliances

Mathematics

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Provides a thorough introduction to diverse academic fields. Ideal for students beginning to contemplate their future academic paths and eager to explore various disciplines.
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Mathematics

In-person

Solve complex equations in Oxford, following in the...

Academic Insights
Provides a thorough introduction to diverse academic fields. Ideal for students beginning to contemplate their future academic paths and eager to explore various disciplines.
A woman writing on a test paper.
Ages: 16-18

Choose a Motivating Mathematics EPQ Topic Today

Feeling inspired by Immerse Education’s list of EPQ topic ideas? Mathematics is a diverse field that offers countless research questions for you to explore. It’s essential that you choose the right one that allows you to investigate the area of mathematics that appeals to you.

Visit the Immerse Education Mathematics Online Research Programme Page to take the first step. Here you’ll find expert academics who can guide your research process and inspire a university-level essay on your chosen EPQ topic. 

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