100 Ideas for Research Projects in Mathematics

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

22. The role of mathematics in cryptography
23. Using linear algebra to understand 3D transformations in computer graphics
24. The mathematics behind machine learning algorithms
25. Analysing the mathematics behind search engines
26. The use of combinatorics in solving complex problems
27. The role of algorithms in solving Rubik’s cube
28. The mathematics behind blockchain technology
29. The role of discrete mathematics in computer science
30. The role of Monte Carlo methods in probability and statistics
31. The use of set theory in computer programming
32. Exploring optimisation algorithms in machine learning
33. Investigating cryptographic methods based on prime factorisation
34. How do algorithms work?
35. The mathematics behind artificial neural networks
36. The role of geometry in computer vision and image recognition
37. The mathematics behind machine learning algorithms
38. The role of Monte Carlo methods in probability and statistics

Research Project Ideas about Mathematics in Physical Sciences and Engineering

39. Exploring the mathematics of elliptical curves and their applications
40. The mathematics of symmetry in crystallography
41. Investigating topology and its application in physics
42. The application of differential equations in engineering
43. The role of eigenvalues and eigenvectors in physics
44. The role of dimensional analysis in physics
45. Exploring the mathematics of fluid dynamics
46. The mathematics of black holes
47. The role of partial differential equations in modelling heat transfer
48. The mathematics of flight dynamics
49. Exploring how Fourier analysis is used in signal processing
50. Investigating the use of calculus in physics
51. The application of calculus in electrical engineering
52. Investigating how calculus is used in pharmacokinetics
53. The use of trigonometry in astronomy
54. The role of probability in quantum mechanics
55. Knot theory and its applications in biology and chemistry
56. Exploring the role of vectors in physics and engineering
57. Exploring the applications of matrix theory in quantum physics

Research Project Ideas about Mathematics in Economics and Finance

58. Game theory and its applications in economics
59. The mathematics behind stock market predictions
60. Mathematical optimisation in logistics and supply chains
61. The role of mathematics in AI
62. Investigating the use of mathematical models in economics
63. Bayesian probability and its applications
64. The role of stochastic processes in economics
65. The applications of linear programming in business optimisation
66. The use of statistics in analysing sports performance

Research Project Ideas about Mathematics in Biology and Medicine

67. Mathematical models of infectious diseases
68. Investigating the role of probability in genetics
69. The role of statistics in health and medical research
70. The use of mathematical models in epidemiology
71. Exploring statistical models in medical research
72. Investigating mathematical modelling in sports performance analysis
73. The use of statistics in analysing sports performance
74. The applications of statistics in psychology and social sciences
75. The importance of mathematical models in ecology
76. Investigating the use of mathematical models in cancer research
77. Investigating the mathematics behind disease spread in populations

Research Project Ideas about Mathematics and the Climate

78. The mathematics of chaos and weather prediction
79. The use of mathematical models in environmental conservation
80. How mathematical models are used in predicting natural disasters
81. Investigating the use of mathematics in climate modelling

Research Project Ideas about Mathematics and the Humanities

82. The applications of statistics in psychology and social sciences
83. The mathematics behind traffic optimisation in urban planning
84. Exploring the relationship between probability and gambling
85. Mathematical models of population growth
86. Exploring mathematical approaches to solving traffic flow problems
87. The mathematics of traffic optimisation in urban planning
88. Exploring the mathematics of social media analysis
89. The mathematics behind solving sudoku
90. Exploring the applications of graph theory in networks and communications

Research Project Ideas about Mathematics and the Arts

91. The mathematics behind architectural design
92. The role of mathematics in music theory
93. Investigating the golden ratio in art
94. The influence of fractals in visual arts
95. Exploring symmetry and patterns in art and design

Research Project Ideas about Mathematics and Politics

96. How statistics can be used to predict election outcomes
97. The mathematics of voting systems
98. The use of game theory in political decision-making
99. Investigating the mathematics of optical illusions
100. Using network theory to understand political alliances

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.